ABSTRACT NATURAL DRYING OF CASSAVA b y Gonzalo Roa Annual world-wide transactions of dried cassava, Manihot esculenta Crantz, to the European Economic Community (EEC) from developing countries are estimated at one hundred million dollars. The product is used for animal feed mixes and both foreign and local markes are expected to increase rapidly. Cassava production surpases 100 million tons per year . Is is presently dried in the developing countries by slow, and risky operational systems. Experimental and analytical studies were conducted with several cassava varieties and different ages to evaluate conventional and newly designed systems of drying cassava under variable weather conditions. Differences in the systems were attributed to the relative positions of the layers of the product ( in mesh trays) and the floor, or to different geometrical forms of the cassava particles. The influence of varieties and ages were not significant in drying. A mathematical model predicated about 1700 hourly experimental moisture content values with an average arror of 2 pe rcent,wet basis. The final moisture content value at the end of a drying day could also be predicated within three percent (w.b.) by using average atmospheric conditions. Sensitivity analysis based on the model indicated that the p” p. .bs . a u. nap . o .r. .~ ‘ .r.. c.— . .C. i o . . L... . y» 1 . . I. I t... , . ..— . . . . p?» . . . .l. 9 . ~Pu . i. . u .b» .‘D . .v“ ~ . .7." ~‘- “I « _... ... ... a .. . . . . . z. .1. H ..\ , .. y ...l. .b. .ov . i . ... .2. \. .... . . .t .1 O“ m Gonzalo Roa (,4 maximum weight of a layer that could be dried deterioration, depended mainly on the size of the particles, the saturation water vapor pressure deficit, and the wind velocity. A vertical type of drier consisting of two parallel wire panels was found to be the most efficient form of drying cassava. The cassava layer takes nearly all the required energy for evaporation from the air enthalpy. The vertical position of the layer and an adequate product geometry permits the air to move through the product and creates turbulence. The air gives off part of its sensible heat and removes the evaporated moisture. When the vertical cassava layer is covered by a roof, the drying rates are not reduced; thus drying may continue over- night or while raining. Drying of the product in horizontal, elevated mesh trays is a less efficient method than the vertical drier, but more efficient than the conventional system of drying cassava on concrete floors. Two low-cost cutting mechanisms were designed to produce rectangular cassava bars, the optimum geometric figure found among several studied, including those traditionally used. The mechanisms are :.(a) a manual press, and (b) a disc cutter which produces a geometry resembling the rectangular bars‘at a rate of 240 kg/hr when operated by a bicycle pedal mechanism,o about-500 kg/hr when operated by a motor. A deterioration criterion was established to recommend maximum I. u . . .v. . . . . ~, ‘ . at. . .. Gonzalo Roa densities allowed to dry safely as a function of average environmental conditions and the the type of drying system. A cost analysis of a commercial operation was made based on the experimental work and the simulated results. Limitations of natural drying of cassava are summarized and suggestions for future work in this field are made. The original data and the computer programs of analysis are included in the appendices . r/ / “/j , , /,/ " fl’ . / / ' / ‘ ’ ,. x"; ///~ /JLJ/;Ifl$/V /{%hfl ,, /'/7‘ /3a2.:2 we» _ , I, ,5 U 7- 21 7% A W 0‘0” aw. f2 NATURAL DRYING OF GASSAVA BY Gonzalo Roa A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering 1974 r, Zoila To my mothe l'il’ll'lil'lllf ACKNOWLEDGEMENTS The author is indebted to many persons and institutions who contributed to make this a complete project. Dr. Fred W. Bakker- Arkema's instruction and examples of research work associated with meaninful forms of living oriented and challanged the author to submit this work. Mr. Loyd Johnson's guidance was a key factor in orienting the work to the practical objectives of the CIAT's Agricultural Engineering Program . Dr. James Cock, coordinator of CIAT's Cassava Program, was always interested in the research progress and participated actively in it. The author extends his gratitude to the Rockefeller Foundation for their total financial support during the. author's stay at Michigan State University (MSU) and especially to Dr. Patrick N. Owens, representative of the Foundation in Cali. The Agricultural Engineer- ing Program of MSU contributed to make, this work an overseas thesis. The Centro’lnternacional de Agricultura Tropical (CIAT) supported the author and provided all material and research facilities needed. The Agricultural Engineering Program of the Universidad del Valle collaborated in the project by allowing the author time, encourage- ment and financial support to the author during part of the work. To Dr. J.V. Beck, Dr. D.D.Harpstead and Dr. D. Heldman for iii serving on the author's guidance committee. To Mr. G. Falk, Dr. D. Franklin, Dr. A. Leon, Mr. L.E.Quintero, Dr. J.C. Toro, Dr. L.G. Villa and Dr. N. Wilde for their suggestions for improving this disser- tation. The author wishes to thank Dr. P. Andersen and Mr. M. Infante, from CIAT'S Economics Program for their assistance in the cost evaluation section . The author also thanks to Mr. Roberto Aguirre for helping in writting and running the computer programs, to Miss Lohelia Valois and Ana Luci’a Quifiones for the typing of the thesis. To Mr. J. Roa for his help. iv III . IV. TABLE OF CONTENTS LIST OF TABLES ................ . ...... LIST OF FIGURES ......... . ............. LIST OF SYMBOLS ........ . .............. INTRODUCTION . . . ............... . ...... REVIEW OF LITERATURE . . . ...... . ....... 2.1 Introduction ..... '2.2 Utilization of Cassava . . . . . . . . . . ...... . 2.2.1 Composition ..... . 2.2.2 Cassava as Human Food . . . . . ...... 2. 2. 3 Cassava in the Non-Food and Feed Industries.............. ....... 2.3 Cassava in the Feed Industry . . . . ......... 2.4 StorageofCassava.................... 2.5 DryingofCassava............. ....... 2.6 Tray Drying . .............. . ........ 2.7 Drying Theory . ......... . . . . . ........ 2. 7.1 Thin Layer Drying ............... 2.7.2 DeepBedDrying.......... ..... . 2.7.3 NaturalDrying................. 2.7.4 Evaporation ...... OBJECTIVES O O O O ...... O O O O O O O O O 000000 O 0 EXPERIMENTAL PROCEDURES AND PRELIMINARY ANALYSIS 0 O O O O O O I O I O C O O O O O O O O O O O O O O O O O 4.1 Importance of Differences of the Cassava _, Porous Structure in Drying . . . . . . . . . ."2' . . 4.2 Cutting Mechanisms . . . . . ....... . . . . . . 4 3 Field Experiments. First Experimental Period 4.3.1 HorizontalTrays................ 4.3.2 SolarDriers.................. 4. 3.3 Measurements and Instrumentation . . . a, ix DJ mAAw 11 12 14 16 16 22 26 37 41 42 42 47 54 55 57 57 Vi VI. VII. #345- O‘U1 U1U'1U'l o~o~o~o~ O owns-w 4. 3.4 Preliminary Results and Analysis . Field Experiments. Second Experimental Period Black Floor . . . . . . . 4.4.2 Vertical Trays . . 4.4.3 Vertical Driers . . . . Summary of Total Number of Observations . . . . Laboratory Experiments . ............... Porosity . . ....... . . . . . 4.6.2 Bulk Density . . . . . . . 4.6.3 Layer Thickness . . . . . . 4. 6.4 -Equilibrium Moisture Content ...... . Product Quality 4.4.1 4.6.1 Empirical Drying Equation . . . . . Equilibrium Moisture Content Estimation of Parameters in Drying Equation . . . Environmental Variables . . . ........ 5. 3. 2 Layer Densities 5.3.3 Geometric Properties . . . . 5.3.1 Comparison of Experimental and Calculated Moisture Contents. Comparison of Different Natural Drying Systems Simulation . . . . Solar Cabinets Product on the Floor . . . . . . Cassava Chips . . . . . --Disc Cutter Bars . . . . Rectangular Bars . . . . . Vertical Drier . . . Layer Drying Equation . . . . . . . . . Maximum Density Allowable . . . . . Limitations of Natural Drying . . . . . . . . . Sensitivity Analysis Based on Maximum Density 6.2.1 TABLE OF CONTENTS ( Continued ) DEVELOPMENT or A MATHEMATICAL MODEL or NATURAL DRYING or CASSAVA THICK LAYERS . . . ANALYSIS ..... . ............. . .......... COST ANALYSIS . . .......... . ............ 000000 000000 83 83 85 90 9O 97 98 102 102 107 107 112 114 114 116 116 120 123 128 134 134 142 VIII. IX. XI. TABLE OF CONTENTS { Continued ) Page 7.1 Cutting Data . .......................... . ..... 145 7.2 Drying Data .... ................... . ......... 145 7.2.1Concrete Floors ........ . ...... . ........ 145 7. 2. 2 Horizontal Trays ....... . ............... 145 7.2.3 Vertical Drier ......................... 146 7. 3 Cutting Costs . . . ............................. 146 7.4 Drying Costs .. ...... . ....... . ..... . ......... 147 7.5 Total Processing Costs ........ ........ 147 SUMMARY AND CONCLUSIONS ........ 151 RECOMENDATIONS FOR FUTURE RESEARCH ...... 153 APPENDICES ................................... 155 APPENDIX A .................................... 155 APPENDIX B ..... . .............................. 180 BIBLIOGRAPHY .................................. 228 vii Table 10 11 12 13 14 15 16 17 LIST OF TABLES Page Predicted Demand for Cassava in the EEC f0r1980............... oooooo oooooooooooo.ooooo 9 Predicted Supply of Cassava for 1980. ............ 10 Average‘Ambient Conditions During Experimental Hours.......... ............ ......... ........ .. 43 Total Number of Hourly Observations . . . ......... . 74 Distribution of Observations for the Rectangular BarSIOOOOOOOOO ..... OOOOOOOOOOOOOO 0000000000000 74 Relative Humidities Produced by Saturated Salt Solutions............................ ....... 80 Hygroscopic Coefficients for Different Crops ...... 88 Characteristics of the Nine Drying Systems . . . . . . . 93 Ambient Coefficients and Associated Statistics . . . . 94 Density Characteristics for each Drying System . . . 99 Density Coefficients and Associated Statistics . . . . . 99 Density Coefficients of a Parabolic Density Function 100 Geometric Coefficients, Characteristics,and Sta- tistics 0.00.... ...... 0.....00000000000000000O... 101 cutting COStS . 0 O O O O O O O I O O O O O O O O O O O O O O O O O O 00000 O O 146 Drying Costs for Low Densities . . . . . ....... . ...... 147 Drying Costs for High Densities . . .. . .. . . . . .. . . . . . 148 Total Processing Costs .149 viii LIST OF FIGURES Figure Page 1 Experimental Thin Layer Drying Curves . ..... . ...... 21 2 Stationary Deep Bed Drier . ........ . . . .............. Z3 3 Boundary Layer in Natural Convection . .............. 27 4 Natural Drying by Horizontal Trays . . . . . ............ 45 5 Internal and Exte rnal Resistances in Drying . . . . . 46 6 Manual PFess to Cut Cassava Rectangular Bars . . . . . . 48 7 Cutting Section of the Manual Press . . . . ............. 49 8 DiscCutter................ ....... ............ . 50 9 Schematic View of the Disc Cutter Assembly . ..... . . 51 10 Cutting Discs and Particles Produced . . . . . . . . . . . . . . . 52 11 Drying Performance in two Consecutive days ........ 56 12 Solar Driers .. ........ . ....... ....... ........... .. 58 13 Solar Cabinet Performances ........... ......... .. 61 14 Performances of Different Cassava Geometries . . . . . .. 62 15 Desorption Curves at Fixed Air Conditions . . . . . . . . . . 65. 16 Influence of the Ambient Conditions on Drying . . . . . . . . 66 17 . Characteristicsofthel? values..................... 67 18 Natural Drying by horizontal and Vertical Trays . . . . . . 70 19 VerticalDrier.......... ..... 71 ix Figure 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 LIST OF FIGURES ( Continued) Vertical Drier Modified with Wings . . . . . ..... . . . . . . . Porosity and Bulk Density of Rectangular Bars ....... Equilibrium Moisture Content of Cassava . . ....... . . . Quality Deterioration in Natural Drying . . . . . . . . . . . . . . Equilibrium Moisture Content for Some Crops . . . . . . . . Comparison of Experimental and Calculated Values . . . Comparison of Experimental and Calculated Values . . . Comparison of Experimental and Calculated Values . . . Comparison of Experimental and Calculated Values . . . Comparison of Drying by Simulation . . . . . . . . . . . . . . . . . Comparison of Bars Produced by Disc and Press . . . . . Comparison of Rectangular Cross Sections . .......... Vertical Drier Performances .. Comparison of Performances of Drying Systems . . . . . . CassavaDeepBedDrier.............. ............ . Maximum Density Allowed. Drying Hours . . . . . ...... Maximum Density Allowed. Weather Conditions . . . . . Maximum Density Allowed. Drying Systems . . ....... Sensitivity Analysis . Typical Weather . . . . . . . ..... . . Sensitivity Analysis. Independent Variables . . . . . . . . . . Sentivity Analysis. Drying Systems . . . ............. . . Page 72 76 79 82 89 108 109 110 111 115 119 121 122 127 130 131 133 137 138 139 LIST OF SYMBOLS Symbol A surface area, m2 ai i=1, 2, 3, . . . constants without physical meaning bi i=0,1, 2, . . .functional relationship used to shorten equation (6. 2) i i=0,1,2,...index C water vapor concentration in air, kg/m3 Ca water vapor concentration in undisturbed air, kg/m3 Cs water vapor concentration in air at the surface, kg/m3 Ca specific heat of dry air, J/kg °C Ci i=0,1, 2, . . . functional relationship used to shorten equation (6. 2) Cm air specific heat, J/kg °C cp product specific heat, J/kg °C cv water vapor specific heat, J/kg °C cW water specific heat, J/kg °C D density or initial load per unit area, kg/m2 De diffusion coefficient of water in aporous body, mZ/sec Dmax maximum density allowable to dry without deterioration, kg/mz db bulk density, g/cm3 d. i=1, 2, 3, . . . constants without physical meaning K11 LIST OF SYMBOLS (Continued ) i=1, 2 constants without physical meaning e=2. 7183, . .base of natural logarithms water vapor pressure, mm of Hg saturation water vapor pressure, mm of Hg geometric property defined by equation (6. 3) i:0,1, 2, . . . functional relationship used to shorten equations (6. 6) and (6. 7) air flow rate, kg/mzs Grashof number in natural convection mass transfer analysis, dimensionless. Grashof number in natural convection heat transfer analysis, dimensionless. gravitational aceleration = 9. 80665 m/S'2 i=0,1, 2, . . . . functional relationships used to shorten equations (6. 6) and (6. 7) absolute humidity, dimensionless, decimal convective heat transfer coefficient, W/m2°C convective mass transfer coefficient, m/s modified convective mass transfer coefficient, 8'1 latent heat of evaporation, J/kg drying proportionally “constant", hr"1 drying proportionality "constant" calculated by leaving the density and geometric properties fixed, hr"1 drying proportionality "constant" calculated by leaving the geometric properties fixed, hr'1 xii Symbol Km Meq LIST OF SYMBOLS ( Continued ) drying proportionality "constant" calculated without restriction in the variables, hr"1 length of the rectangular bar, cm layer thickness, cm average moisture content of a particle, decimal, dry basis molecular weight of air, mass units/mole equilibrium moisture content, decimal, dry basis (except in equations 5.3 and 5. 5 where it is given in percentage, dry basis) initial moisture content, decimal, dry basis local moisture content at position x, decimal, dry basis mass flux, kg/s mass flux in units equivalent to energy flux units, W dimensionless number defined by equation (2. 23) Nusselt Number, dimensionless index n=0, 1, 2, . . . porosity, decimal Prandtl Number, dimensionless atmospheric pressure, N/m2 i=0,1, 2, . . . coefficients without physical meaning heat flux, W i=0, 1, 2, . . . coefficients without physical meaning Reynolds numbe r , dimensionles s xiii Sc Sh SS LIST OF SYMBOLS ( Continued ) incident solar radiation, cal/cmzhr net radiation, W universal gas constant = 0. 8479 kg m/mole °K Relative humidity, decimal coefficient of determination, dimensionless Sphere particle coordinate, m sphere radius, m geometric property of rectangular bars given by equation (5. 2), cm'2 Schmidt Number, dimensionless Sherwood Number, dimensionless sum of squares, variable units air dry bulb temperature, ° C undisturbed air temperature, °C absolute temperature, ° K surface temperature. ° C time, 3 wind velocity, m/s velocity component in the x direction, m/s velocity component in the direction, m/s thickness of a slab or width of a rectangular bar square section, cm Symbol W1,W L?‘ - ,.t<> :Fl 2 LIST OF SYMBOLS ( Continued ) dimensions of the rectangular bar section, cm sensitivity coefficients, kg/m2 space coordinate, m i=0, 1, 2, . . . independent variables, variable units experimental value, variable units average value of experimental values, variable units estimated value, variable units space coordinate, m thermal diffusivity, W/m °C volumetric coefficient of thermal expansion, "C"1 volumetric coefficient of concentration expansion,m3/kg kinematic viscosity, mZ/s increment in time,hr thickness of the concentration boundary layer, m thickness of the thermal boundary layer, m thickness of the. velocity boundary layer, m errors, hr"1 lack of fit errors, hr'1 pure errors, hr'1 product temperature , °C functional relationship, variable units XV Symbol 87m 5’. LIST OF SYMBOLS ( Continued ) fluid density, kg/m3 product density, kg/m3 . -2 variance , hr (upper bar) = hourly average value sign. xvi .33 I INTRODUCTION Dried cassava is exported from developing countries to the European Economic Community (EEC) for animal feed mixes. Cassava diets are usually considered of equal quality but of lower cost than those based on cereals as the source of carbohydrates. The present annual value of the world-wide cassava transactions is estimated close to one hundred million dollars (Phillips, 1973a) . The demand in the EEC for drier cassava is expected to increase significantly at least until 1980 (phillips,1973a). Local demand for dry cassava will become more important as knowledge of its value as a feed component becomes known to the local feed manufacturing industries. The crop's characteristics and its hight perishability in the fresh form make it desirable for feeding uses provided that low cost and efficient methods of drying of the product in the field are available. Exporting countries dry cassava by inefficient,high-risk methods ‘which yields a product that is not always acceptable to the buyers due to the degree of deterioration and poor handling properties by the feed industry's modern equipment. The common drying procedure is to spread irregular pieces of the product on concrete floors or on wooden trays and to stir the product in order to obtain high surface exposure to the solar radiation. This practice results in low capital cost, and ease of the operation. The procedure is an inefficient form of utilizing 2 the available natural energy to dry cassava. Literature relevant to this multimillon-dollar industry is scarce, vague, and qualitative, the common denominator being the limited knowledge of the physics involved. The general objectives of this study are to understand the effect of the important variables affecting the drying process, to use this knowledge in improving the drying efficiency without increasing the costs, to develop and test a mathematical model which describes the process, and to utilize the model for generating useful information. Specific objectives are given in Chapter III. II REVIEW OF LITERATURE 2.1 Introduction Cassava is a root which is scarcely known in temperate regions. However, it is a major source of calories for 200 to 300 million people of the tropics (Nestel, 1973a). The plant is known as cassava in English-speaking countries of North America, Europe and Africa; as manioc in French-speaking countries; as tapioca in English-speaking countries of Southeast Asia; as mandioca in Brazil and as yuca in Spanish- speaking countries of South America. Cassava had remainded an obscure icrop until this decade when two major research centers, the International Center for Tropical Agriculture (CIAT) in Colombia and the International Institute forTropical Agriculture (IITA) in Nigeria started research programs to study basic aspects associated with the production and utilization for this commodity. The first efforts are directed towards determining the actual and future impor- tance of the crop and defining the short and long run research priorities. A major contribution is the preliminary report of a study of the utilization and potential markets of cassava (Phillips, 1973a). Cassava is a subsistence type of crop for several reasons: 3 4 (a) yields are high, (b) it is easy to propagate and grow in poor soils, (c) it has a high drought tolerance, (d) it is an excellent source of carbohydrates, (e) it has a high value per unit area of cultivation,and (f) it is a low risk and non-season bound crop. Cassava production has been restricted in the past because it was considered an infe- rior,toxic, soil depleting, low value, and high production cost crop. Cassava is produced in more than 80 developing countries. Brazil, Indonesia, Zaire.Nigeria and India produce two thirds of the world production (92.2 million tons were produced in 1970, FAO ,1971). Average yearly world yield is 9.4 tons/ha. Yields of 70 tons/ha have been obtained under controlled conditions (Nestel, 1973a). Yields of 30 tons/ha can be easily obtained. Yields in terms of calories per unit area and unit time give cassava the first position among all staple food crops (de Vries et al. , 1967). Coursey and Haynes (1970) calculated the following figures in thousands of calories p.e,r.hectarea per day: 250 for cassava, 200 for maize, 176 per rice, 114 for sorghum and 110 for wheat. It is expected that these figures will change in favor of cassava because of the recent technical attention that cassava is receiving and the shortage of carbohydrates in the developing countries (Cock, 1973). 2. 2 Utilization of Cassava 2. 2.1 Composition Cassava roots contain approximately 30 to 40 percent dry matter. About 90 percent of this weight consists of carbohydrates in the form of starch and sugars. Starch makes up about 97 percent of the carbohydrates but when the root reaches and age of 16 to 18 months, the starch content begins to transform rapidly into sugars (Grace, 1971). Cassava starch is classified as a starch of low-,amylose and high-amylope‘ctin content. The protein content of cassava roots is low, usually 0. 5 to 1.5 percent.Fats, vitamins and minerals account for even smaller percentages. Amino acid distribution is similar to that of the corn with low levels of methionine. Cassava leaves, however, have protein content values between 21 and 36 percent on a dry weight basis (CIAT, 1973b). Cassava roots contain linamarin, a cyanogenic glucoside, which can be transformed into hydrocyanic acid by hydrolysis . The amount of the released acid varies from 10 to 150 parts per million, depending on the variety. Sweet and bitter varieties are traditionally classified omthese values (CIAT, 1973b). " 2.2.2 Cassava as Human Food The most important use of cassava is human consumption. ‘Q 9 About 78 to 90 percent of the world production is used for this pur- pose. Cassava provides approximately 8 to 10 percent of the calories man requires. It. is expected that the number of people depending on cassava's energy will double by the end of this century (Nestel,1973a). The cassava root is processed by man in a number of differ- ent processes; (a) The root is peeled, then cooked, boiled, baked, or fried similarly to potatoes and finally served as the basic ingredient of certain dishes. (b) The root is peeled, grated, packed in leaves and pressed to extract the juice leaving the pulp. This pulp is the basic constituent of the "farinha de mandioca" or the cassava bread Helmuth,K. B and Scholz,W.(1971) . In the preparation of farinha,the pulp is mixed with fermented pulp and sieved to give a slightly damp meal, which in turn, is evenly heated by turning it continuosly during 3 to 4 hour produCing a granular roasted product. Cassava bread is obtained from the pulp in a similar way. The heating is more inten- sive, without stirring, thus producing a solid brown cake,which is further dried in the sun. The bread is eaten after being dipped in gravy, and can also be stored indefinetely under favorable ambient conditions (Grace, 1971). (c) The grated cassava tubers are fer- mented,the mass is semi-dextrinized by heat, and finally dried to give a final product known as gari (Grace, 1971). Gari is a very popular food in West Africa and Nigeria. Present mechanized pro- duction is accepted by the tradional consumer.s(Nestel,1973c ).(d) Shredded tubers are pressed in a cloth until most of the juice is squeezed out. The mass is whirled in winnowing baskets until pellets are formed. The pellets are steamed and dried in the sun for several days to produce cassava rice, a substitute for rice and maize in the Philippines. (e) Cassava roots are boiled and pounded into a very smooth mass which is consumed as a vegetable loaf, like the popular ”fufu" in Ghana (Grace, 1971). Instant fufu powder is being commercially produced (Nestel,1973c) ,(f) The root is peeled, sliced,dried and pulverized to pro— duce the cassava flour. Cassava flour is used as a substitute for wheat flours in Brasil as well as in some other cassava producing countries, Good progress has been made in the use of cassava flour in bread making (Netel,1973b). (g) Cassava roots are being used, in experimental trials, as a substrate to produce fungal protein. Progress has been made in this form of utilization (Nestel,1973b). (h) Cassava is used widely in the food industry in the form of a thickener using the paste properties of starch in soups, baby foods, sauces, puddings and gravies. It is also amployed as a stabilizer for its high water holding capacity. 2. 2.3 Cassava in the Non-Food and Feed Industries Cassava is used in the non-food and feed industries as starch. The l-‘ow-amylose, high-amylopectin content gives it desirable visco- sity (Whilt 1er and Paschall, 1965) for high quality adhesives, and for use in the paper and textile industries. Grace (1971) gives a detailed list..of other industrial uses of cassava starch. The present industial market of cassava, located primarily in the United States, Canada and Japan, accounts only for less than one percent of the total demand for cassava (Phillips, 1973b). 2. 3 Cassava in the Feed Industry The present importance of cassava in the feed industry is due to the demand by the European Economic Community (EEC). The low digestable protein of cassava is not a constraint in modern feed mixing formulae if cassava is supplemented with high pro- tein sources like the soybean cake meal. Compound feed based on cassava is considered of gOOd quality and less expensive,for favorable tariff reasons, than cereal—based feed formulations (Phillips, 1973a). Studies at CIAT (CIAT,1973a) confirmed that when cassava rations are supplemented with methionine, two beneficial results are achieved: (a) the diet is partially balanced, and (b) part of the methio- nine sulfur converts cyanide to thiocyanate which is excreted in the urine, resulting in the detoxification of the meal. One of the Europe's largest feed compounders seccesfully processed feeds with 60 percent cassava level, showing,that technical constraints do not exist for this industry (Phillips, 1973a), The demand for dry cassava has increased approximately 300 percent from 1962 to 1971. The 1972 demand for cassava is esti- mated at 1, 700, 000 dried tons. The EEC demand for 1980 is expected to increase from 246 to 634 percent with respect to the 1970 demand (Phillips, 1973a). Low and high estimates of the 1980 demand for dried cassava are given in Table l. Table 1. Predicated Demand for cassava in the EEC for 1980 (1000 dried metric tons) Country Low High Estimated Estimate Netherlands 1020 2380 France 157 1950 Denmark 558 1227 W. Germany 677 1161 United Kingdom 472 947 Belgium 472 725 Italy 117 577 TOTAL 3473 8967 Source: factors: Phillips, 1973a The rise in demand for dry cassava depend upon the following (a) SUPPly. (b) quality, and (c) competitive price. Ouality requirements in particular will increase and result in the following standards, some of them already existing: (a) moisture content less than 14 percent, wet basis (w.b. ), (b) starch content greater than 70 or 75 percent, (c) fiber content less than 5 percent, ((1) foreign material less than 3 percent, and (e) product efficiency to be handled in pneumatic conveying mechanisms and modern type of handling and storing equipment. “0...;- -..-¥ iv"- ~oa. i ._. A no ~ u\\ .u.- nae ‘ .1 AL . , .t. .. f1 ( ,i b « A. U E... W... 10 The last requirement is that the product must present a firm mechanical structure to prevent production of fines and powder during the handling process. Traditional cassava chips cause difficulties in pneumatic and small bore auger equipment. Between 80 and 90 percent of the present world market for cassava is supplied by Thailand and Indonesia. Supply predictions for fresh cassava are given in Table 2. Supply of cassava in Latin America and the Far East substantially exceeds human demand. Table 2. Predicted Supply of cassava for 1980 (1000 fresh metric tons) Low High Region Estimate Estimate Latin America 48, 052 60,491 Africa 37,107 37, 207 Far East 26,357 29,592 TOTAL 111,516 127,290 Source : Phillips, 1973a It‘is surprising that no cassaV/a feed market exists in the exporting countries where feeders buy cereals at prices higher than the cost of cassava (Nestel,1973a) . Instead they prefer to use known technologies instead of investing in the development of new ones appropriate to the country (Johnson, 1970). Price relationships ,. II a nu . i .1. ' A . 1.. . ,., . . L. ~.. .F. . . n‘u L . tit . .- I .?. . . . .l. . . . Ml. ?. n ~ #1.. .91.. ,. . s. . u , .t u u. 0 '.§ 1 11 between presently available feeds and the swine produced are unfavorable to the Colombian cassava producer. Unless feed is produced on the farm, a reasonable return on investment is doubtful (CIAT,1973a). The cassava price paid in the EEC had changed from US $65. 00 to $78. 00 per dry metric ton in the last few years. End-user prices of about $90. 00 to $95. 00 per dry metric ton are expected for 1980. Production and processing costs should be in the range of $16. 00 to $22.00 per ton of fresh root (Phillips, 1973a). 2.4 Storage of Cassava Ingram and Humphries (1972) made an extensive review of cassava storage in its fresh and dried forms. They concluded that the present knowledge on the subject is vague and that few reliable data exist. The only tested methods for safe storing cassava for periods exceeding two months are : (a) freezing the root, (b) drying the roots to a moisture content of 13 percent and keep up it to this level at ambient temperatures, (c) leaving the roots in the ground until 16 or 18 months for age. Cassava tuber severely rot at ambient temperatures within a few days after being harvested. The rotting starts as vascular streaking at the surfaces at a rate proportionally to the mechanical damage of the root when harvested (CIAT,1973a). Two promising methods of extending the shelf-life of the fresh product have been investigated: (a) experiments with paraffin 12 wax dips (Young et al. ,1971) and (b) storing the roots piled in the ground in a structure resembling the European potato "clamp". Roots have been stored by this method for five weeks without deterioration. The success of “clamping" in preventing deterioration suggests that either the conditions within the clamp (temperatures above 38°C and relative humidities above 90 percent) prevent the invasion of wounds or that the wounds heal preventing deterioration (CIAT,1973a). Dried chips with moisture contents equal to or less than 13 percent, wet basis (w.b.) ,can be stored for more than one year without molding. At higher moisture content values, the product is susceptible to molding at rates proportional to the moisture content. No quantification of molding versus moisture content, time, air temperature and air relative humidity has been published. At least fifteen different insects attack dried chips (Ingram and Humphries, 1972). The use of chemicals, like methyl bromide, ethylene dibromide and the mixture of ethylene dichloride has given complete control of infestations (Pingale et al. ,1956; Anon. ,1962). 2.5 Drying of Cassava Cassava pellets and chips are the common forms of using cassava in the feed industry. Chips are produced in Thailand and Indonesia by mechanical slicing of cassava followed by natural dry- ing of the product in layers on concrete floors or wooden trays. In Brazil (Helmuth,K. B.and Scholz,W. , 1971) cassava slices are . . . . . . tut .y i. . ‘5 ML AI\ «5. .f. .n.- c.» ' a I . A‘d A. p \\ cl- I‘i "I A“ . R" U . I i t ‘ A .‘ld .r» . . v . . « ~ . y . y 0‘ 4 L. ~\u 1r 1 ¢ . . . ,7 .a v - a . .I. p .6. p . I - . u i 6‘. n . a. . s .I» . . . \ - ~75. ,Ei . .i . y . , , p . i i . . L . . .. .u. .. 2. a! A. C.. .1. .. . .. .. .i. .. .. i .. I . v . o u u. . , p?» s . . u y . u .. 1 o s c . u g c . x . 6 _ r . . . .4. .1 . . a 13 pressed to reduce significantly their moisture content prior to drying them in continuos type of driers. The product is pulverized in hammer mills resulting in cassava flour. Washing and trimming before these processes are done by hand or by inexpensive machinery. Pellets are produced from the cassava flour in special machinery (Helmuth, and Scholz (1971). Several types of cassava cutters have been designed (Hachero, 1951; Gill, 1972; Grace, 1971; Lavigne, 1966), but the desirable drying and handling properties are not specified. The most widely accepted machine consists of a rotating, notched cutting disc which produces non-uniform, thin slides of high surface to I volume ratio. The slices present a weak structure because bending forces during cutting and releasing of the particles produce internal shearing strains. This product is fragile when wet and dusty when dry. Generally recommended drying procedures are: (a) the _ product should be spread in the sun on concrete floors of wooden trays as soon as it is cut, (b) the layer density should not exceed 5 to 15 kg/mz, (c) the chips should be turned periodically during dry- ing, (d) if rain threaten8, the chips should be piled up under' a r00f or covered with sheets. In good sunshine the drying period is usually 2 to 5 days (Grace, 1971; Kuppuswamy, 1962; Lavigne, 1966). No Critical desorption rates related to quality deterioration have been I! " .0 n-I'fi .>-' 'k . - 4 :"c Q ,. ,nu‘ ~ - |Fq .. , _—- J .. I .. n . I i .‘y . w- -6: 'I- “-u u. I 'I, \. :i‘er . ‘9». I‘. "in. ‘I . 14 reported. Lavigne (1966) concluded in his study of natural drying of cassava, that if drying trays were loaded with 10 to 15 kg/m2 and stirred every day, it would take 70 sun-hours to dry the product. Onn (1972) conducted a number of experimental drying studies with cassava chips using air heated by collected solar radiation and blow- ing the air through the layer with the aid of a fan. He encoutered aerodynamic problems with the non-uniform air circulation through the layers of chips and concluded that drying of thick layers with solar heated air was not feasible. Gill (1972) dried cassava chips on a tray by heating ambient air artificially and forcing it through the layer by a fan. The data obtained was discussed with respect to average drying of different bed depths. No recomendation were made regarding optimum air flow-temperature relationships for the different tray loads. Gill also encountered poor air flow distributions. Chirife and Cachero (1970) and Chirife (1971) analyzed the forced, high temperature air drying of cassava layers of different dephts. The data was analyzed by using moisture diffu- sion equations valid only for thin layers of cassava fully exposed to the air. 2.6 Tray Dryiri High moisture content products like vegetables, roots, fruits, as well as many chemical products of rather difficult drying 15 charactheristics, are dried commercially in layers. Modern tray driers consist of insulated cabinets with integral centrifugal fans and heating coils. Perforated trays with a surface area between 0. 3 2 are commonly loaded in uniform layers from 5 to 15 kg/m2 to 1. 0 m to a depth of 0.1 to l. 0 m (Keey,1972). Air velocities between 1 and 10 m/sec are maintained over the surfaces. The driers are designed to assure uniform air circulation. In more sophisticated designs,the air is forced through the layers. Higher tray loads can be processed with this type of drier (Keey, 1972). Van Arsdel (1963) presented the status of research on tray- drying of vegetables and roots. The study consists ofa discussion of the drying characteristics of isolated laboratory experiments, and a study of a commercial operation. In Van Arsdel's report all variables of importance were fixed, except the one being tested. The specific variables studied were: (a) kind of the product, (b) cross section of the product cut in rectan- gular bars, (c) initial load per unit area (density), ((1) air temperature at constant wet bulb depression, i. e. , variation in dry and wet bulb temperature leaving the temperature difference constant, and (e ) air velocity. Results of the analysis with carrots and potatoes indicated that (a) carrot drying rates per unit dry matter content were higher than those of potatoes because of the carrot's higher initial moisture 16 content, (b) the smallest particle tested, a rectangular bar of O. 3x0.4 cm in section, was the most efficient to dry. Air at 70°C and at 4m/sec was forced over the particles. The tray density (initial load of the fresh product per unit area) was 7.4 kg/mz, (c) drying rates reduced material- ly when the tray densities were increased, the differences being higher at the early drying stages, (d) drying at the begining of the process -- drying in the constant-rate drying period -- were correlated to the wet-bulb temperature depression and to the air velocity, (e) drying rates of potato half-dice were shown to be not effected by increasing the air velocities beyond 3m/sec. Air temperatures was kept at 70° C . The tray density was 7.4 kg/mz. 2. 7 Drying Theory Mathematical modeling of drying of biological products is a subject of increasing interest in many research institutions. The first successful attempt was reported by Sherwood (1929), who theorized that molecular diffusion of water in the liquid or vapor states was the drying force that makes the mass of water flow through the porous structure of the particle. Mathemetical models which describe the physics of the phenomena are highly desirable because many applications can be obtain- ed quantitatively from a reliable model. Z.7.1 Thin Layer Drying In developing models for any drying configuration it has been 17 generally accepted that it is first necessary to describe the drying behevior of the single particle of which the system is made. The unsteady state theory for a one dimensional slab is expressed by the second partial differential equation 9M 9M x- 0 (De ______}5_) (2.1) ’bt 9x ”(D x where Mx is the local moisture content inside the particle. The position (x) and the process time (t) are the inciegendent variables. The diffusion coefficient (De) is, in general, a function of the mois- ture content and the product temperature. The internal gradient is caused by a lower moisture content at the product surfacethan at the interior of the drying particle. The moisture driven force at the surface is given by the difference between the vapor pressure at the particle surface and the vapor concentration of the surrounding air . The functional relationship is approximated by the boundary condition for aquation (2.1) 623}. -M ,0 x eq) (2.2) = - hd(sz W x=W Meq is the equilibrium moisture content of the product at the air condictions, hd the convective mass transfer coefficient, and W the thickness of the slab. When the initial moisture content is given, the model is complete in its differential form. Integration in varying 18 conditions and non-constant product properties is only possible by transforming the formulation to a finite-difference form and using a numerical method with the aid of a computer. If the initial mois- ture content is assumed uniform, the diffusion coefficient a constant, fixed boundary conditions (szw =Meq) and no shrinkage, the analytical integration gives (Crank, 1956) M-Meq 8 00 1 (2n+1)ZfiZDet E _____z.exp - (2.3) M ‘_ M “Z (2n4-l) 4W2 0 eq [1:0 where M is the average moisture content of the slab. The left-hand term is the moisture ratio, a normalized moisture variable with unique advantages in representing drying processes. The moisture ratio represents physically that portion of water which remains in the particle, at a given time (t), but that could be evaporated totally by just giveng sufficient time to complete the diffusion process at the same air conditions. The right-hand term depends on the physical properties of the product and process time. If the term (flzDet/4W2) is greather than 1. 2 the second and following terms of the sum can be neglected without appreciable error (Pabis and Henderson, 1961). The solution takes the form M—M 8 2 eq- exp(- " Det ) — Meq 1r 4W2 (2.4) Mo 19 With“ generalization under the same approximate conditions the diffusional process in a rectangular bar can be expressed by the equation (Pabis and Henderson, 1961) 2 M - M 512 D t l 1 l - 4 Mo Meq ‘W L W1 W2 where L,W1,W2, the dimensions of the bar, are assumed to be constant. In real conditions they change their lengths due to plastic deformation that take place to some extent during drying (shrinkage phenomenon). The shrinkage of the linear dimension of the piece.is approximately a linear function of the moisture content (Van Arsdel, 1963). If the boundary conditions are of the more general form of equation (2. 2) the analytical solution of equation (2. 1) consists of infinite sum of trigonometric terms which are usually expressed in graphical forms (Heisler Charts) and is presented in standard texts of heat transfer (Kreith, 1973). The disadvantages of this solution are (a) its complexity and time—consuming to use (Beck, 1972), and (b) the non-availability of the diffusion coefficient function for most crops. Investigators have been forced to accept semi-empirical or empirical types of thin layer formulations which have provided approximate results for selected ranges of the variables of interest. 20 The most widely used equation is dM_ ‘3‘“KlM’Meq) (2.6) with solution M - Meq —_ = exp( - Kt) , (2.7) Mo ' Meq K is known as the drying proportionality constant. Several functional relationships had been given for K, but no agreement exists between them (Henderson and Pabis, 1961; Morey and Peart, 1971; Kemp et al. , 1972; Midden at al. ,1973). The most commonly form accepted for K is d2 K = d ex (--——— 1 p Tabs ) (2.8) Equation (2.8) is known as the Arrhenius function for the diffusion coefficient. The constants C11 and d are estimated to fit the experi- 2 mental data for each particular product. Equation (2. 8) does not contain a moisture flow potential function. Experimental data of thin layer drying reveal, sometimes, two differences with respect to the theoretical analysis presented above, see Figure 1. They are : (a) there may exist a period in which the drying rate remains constant. Constant drying rates are caused by the presence of free water on the particle surfaces at the 21 M is . dt \ critical .4 points g b / C U) o 3 O m C 0 a: \ H =3 2° 31 ”S -H 1H g o Drying Time Drying Time Figure 1. Experimental Thin Layer Drying Curves beginning of the process. The length of the constant drying depends on the kind of product, its initial moisture content and the drying capacity of the air. The estimation of the moisture losses in this period is treated by convection theory (Villa, 1973), (b) the drying rates during the diffusional process that follows the constant drying period -- also called the falling drying period -- might not be a smooth falling function but present some discontinuities -- critical points -- . The critical points divide the curve in two, three or more falling drying periods, Hall (1957). No general explanations have been given of this phenomena. The modeling of drying systems becomes more complicated when the moisture removed from one particle affects the state of the air surrounding other adjacent particles by reducing the saturation v“ '1 n . "I" \ u ‘p i. .1! ‘K‘. 5 ‘I Oil. iv!" ,‘.I i. . I l u. «N “vie Ib . "x, ‘.K V i ‘ . I‘ Hi: .. , 22 vapor pressure deficit. This is, however, the practical situation in drying biological products in layers or in the deep beds of commercial driers. This problem is a complex interaction of momentum, heat and mass transfer. 2. 7. 2 Deep Bed Drying Only very recently rigorous heat and mass balances have been written and solved to model commercial driers (Bakker - Arkema and Brooker, 1970). The alternative of empirical models has also been used (Thompson, 1970). The Michigan State Drying Model for a stationary bed of grain is described below (Bakker-Arkema et al. , 1974). The following assumptions are made: (a) the bed does not reduce its original volume due to shrinkage, (b) the single particle does not present temperature gradients, (c) heat is not transfered by conduction from one particle to another, (d) the air flow is uniform through all sections of the bed, (e) the drier walls act like a perfect thermal insulator, (f) gradients of temperature and humidity with respect to time are small compared with the gradients of the same variables with respect to position. A sketch of the drier is given in Figure 2. A differential volume (A.dx) is chosen in an arbitrary position of the bed. Heat and mass transfer balances are written for the air and product in the general form: 23 _1_ dx .m \QYJ.‘ . T __ ______ IL heated air “H ——i Figure 2. Stationary Deep Bed Drier. energy ' ' energy entering at x minus leaving at x+dx equal to mass mass energy nerg of evaporation plus change in the product interna mass ass The system of the simultaneous equations after simplifying terms is presented below with the diffusion equation of the single particle, which completes the needed number of equations to solve fo r the unknowns . 9T: hA(T-GL (2.9) ”a x Gaca+Gach 24 99 ___ hA (T -6) _hfg+cV(T-G-) 9M1 3t Ppcp+PprMr Cp 2“?ri at (2.10) 9H =__ P9 aMr (2.11) @x Ga ’3 t 9 9 ’3 at: = r12 22‘ (,2De 9Mr1:__) (2.12) rO M = '3 M 1'2 dr r3 r (2.13) 0 Equations (12) and (13) represent the diffusion of water in a single particle which is assumed to be a sphere. In practical simulation studies they can be replaced by an equivalent empirical thin layer equation. The boundary and initial conditions needed to solve the system are: T(O,t) = T T(x' 0) = Tinitial inlet H“, 0) = Hinitial mm” = Hinlet 6"" 0’ :Ginitial WK» 1" 0): Minitial ’2 M _ De ‘ -hd(Mr=ro “ Meq) (2.14) 21‘ rro Mt. O . h).- in ‘ d a I 0 n k . p . :- -. .cp :I'E.’ u" ,. .."' 25 where T is the air temperature, h is the convective heat transfer coefficient, A the product surface area, 9 the product temperature, Ga the air flow rate, Ca the dry air specific heat, C‘v the water vapor specific air, H the air absoluts humidity, Pp the dry product density, cp the dry product specific heat, cW the water specific heat, M the average moisture content of the particle, hfg the latent heat of vapor- ization, Mr the local moisture content inside the particle, r the space dimension inside the perticle, re the radius of the sphere. The hygroscopic data represented by Me is given for each q product as a function of the air temperature and relative humidity by a functional relationship. The system is solved with the aid of high a speed computer. after replacing the differential forms into algebraic equations by using standard finite-difference methods. The solution is the values of the five unknowns T,-6, H, Mr,and M .for each point of the bed and for any time during the drier operation. Comparison of calculated and experimental data has given good results when the settling of the bed was negligible and the air flow uniform (Bakker- Arkema et al. , 1974). The model developed and tested, has many practical applications including: (a) construction of simple nomograms to specify drying procedures for certified Red Kidney Bean seed (Bakker- Arkema et al. , 1971), (b) use of the model in conjuction ,-- -r 6;- :1“ .0 l' "32 L V" n.1-"‘ _.-..ov n..¢. . 112.. O 2":- ”I". ,.. I i .‘i‘ - u". N n '5' 6 V”: 26 with sensitivity analysis to recommend optimum design parameters as function of ambient and economic considerations for a given geographital area (Farmer and Bakker-Arkema, 1971), (c) the stationary model in modified form to describe the three most common types of continuous-driers: concurrent, contercurrent and croos flow. By using the cross flow model it was possible to explain the high efficiency of the popular Hart- Carter commercial drier and suggest forms of improving it (Lerew et al., 1972). 2.7.3 Natural Drying Evaporation rates from surfaces of the cassava paticles drying in thick layers under variable atmospheric conditions -- with solar radiation effects neglected -- depend (a) on the diffusion process of the water inside particles as was discussed at the begining of this section, and (b) 6n the flow characteristics and properties of the air surrounding the particle surfaces. Any of these two physical processes, or both, can be the controlling mechanisms in natural drying. The latter phenomenon Constitutes a simultaneous process of momentum and convective heat and mass transfer. The rates of heat and mass exhange between a given surface and the surrounding .moistai'r are given by the general convective heat and mass transfer equations , respectively: q=hA(T8-Ta) (2.15) 27 m=hdA(Cs- Ca) 7 9 (2.16) where q is the heat flux, h the convective heat transfer coefficient, m the mass flux, T8 the surface temperature, T the undisturbed air temperature, C8 the concentration of the water vapor at the surface, Ca the water vapor concentration of the undisturbed air. The temperature, concentration and velocity profiles (T, C,u-) within the thin film of air adjacent to a surface (boundary layer) are schematically shown in Figure 3, where moist air moves upwards in fully developed laminar flow over a vertical, porous flat plate. The boundary layer dimensions (r , (flu, [T are the‘thicknesses of the thin layers, i.e. ,e‘ the maximum distances from the wall in which gradients of concentration, velocity and temperature are present. Y * «v _41 a. water "‘ a. vapor .) injection -. at the " , Q surface (3), T8. c, .. -. v3=0 : o undisturbed air : (Ta' Csa’ ua) c. x Figure 3. Boundary Layer in Natural Convection .. ,::_ ,, Hunk. "I ‘5’... " k...) ‘~' CDZC " ‘ w. 1;. ... 28 The air moves upwards due to bouyancy forces caused by the heating and the water vapor injected from the porous surface. Fluid jets and plumes also create buoyancy forces in the atmosphere. These processes are treated similarly by natural convection theory (Gebhart, 1973). The main objective of the analytical of convection problems over surfaces is to find mathematical expressions for the convective coefficients h and hd. When they are obtained, the heat and mass transfer problem is essentially solved. Analytical expressions for the convective coefficients are obtained by equating the expressions (2. 16) and (2.17) to other heat and mass transfer expressions which require the knowledge of the exact distribution of temperature and concentration within the boundary layer (Rohsenow and Choi, 1961). The temperature and concentration distributions are obtained by. . solving the simultaneous momentum, heat, and mass transfer " differential equations with apprcpiiate boundary conditions. The boundary layer solution might be very difficult, if not impossible, to Obtain for practical problems. One alternative is to utilize the known governing differential equations of the boundary layer problem to derive empirical formulations consisting of dimensionless numbers and unknown Parameters. The parameters are estimated from the experimental data. Natural convection of fluids moving over surfaces or in free spaces are of great importance in many areas of science. Today,natural 29 diffusion of gases and liquids in the atmosphere and water reservoirs, respectively, is a topic of concern. Protection of hot surfaces by evaporative cooling, condensation of water vapor, humidification and dehumidificat ion of air, heating of buildings, evaporation from lakes, rivers, and irrigation channels, evapotranspiration, and many indus- trial processes, like drying, are additional examples fo the applica— tions of natural convection. Gebhart and Pera (1971) reviewed relevant work on natural convection flows resulting from combined buoyancy effects of thermal and mass diffusion. Gebhart (1973) also reviewed the general topic of natural convection. The problem of combined buoyancy effects has received little attention in spite of the fact that flows in nature, at all scales, result to a significant extent from simultaneous thermal and concentration gradients. Gill et al. (1965) solved, after some simplifications, the boundary value problem ilustrated in figure 3, i.e. , the steady and laminar flow over a vertical porous wall. Bouyancy forces were originated by heating and injection of water vapor from the surface. This study revealed that at very low water injection rates the heat transfer increases, but at high concentration values the rates decreased markedly because of the thickening of the boundary layer and because of the lower thermal diffusivity of the moist air compared to that of dry air. Sparrow et al. (1966) corro- borated this finding by an experimental and analytical investigation of 30 natural convection around a horizontal cylinder. The boundary layer was created by injection of steam through a porous cylinder located in still air. The analysis was in good agreement with the experimental results for low mass injection. At higher concentrations, the mass rates predicted by the model fell about 25 percent below the experi- mental data. The difference was attributed to the turbulent flow created by the water vapor injections. Gebhart and Pera (1971) solved the simultaneous, steady, momentum,heat and mass transfer equations (written below) for a two dimensional steady flow of an incompresible fluid with constant properties. Concentration differences were assumed very small, as it is the case in many flows in the atmosphere. Additional momentum and energy fluxes due to mass transfer and viscous dissipation were considered negligible. The simplified equations are: continuity: 79’ux Tathr + ’5)! ’5? = o (2.17) momentum balance: 2 Eu u 9“}; ,(. ux ax + 3.57:? a yz+gfl(T-Ta)+g/§(C-Ca) (2.18) heat t ransfer balance: 31 9T 9T 92T u +u = _T ‘ 2.19 X a x Y2 y 9 Y ( ) mass transfer balance: 1 u 99in}. 9C=De—-29C (220 where ux is the velocity component in the x direction, uy the velocity in the y direction, X the kinematic viscosity of the fluid, T the air temperature in the boundary layer, Ta the air temperature in the undisturbed air, g the gravitional aceleration,/§ the volumetric coefficient of thermal expansion given the by the expression _ 1 91).. fl -- Pm ( a T )P'C 1 (2°21) . 4' where fm is the fluid density, p the fluid pressure,fl the volumetric coefficient of expansion with concentration given by the expression *=’-——1 (gym) 222 fl y... ’50 m ‘-° ’ and d is the thermal diffusivity of the fluid. The system of equations was integrated for different boundary conditions. The importance of the two buoyancy forces g¢3(T-Ta) and gfiflC-Ca) of equation (2. 19) was studied by varying the N number defined as 32 _ fl‘ic - ca) - [b (T ~— T.) The solution of the system, i.e. , the velocity,temperature, N (2.23) and concentration distributions within the boundary layer, were shown to be functions of the Grashof numbers: : g/5x3iTh -Ta)‘G _ gfl‘x3(C8fCa) Orx31" 82 rx,c X z (2.24) note also N — er,C 7 2.23 er,T ( ) The buuoyancy forces due to concentration gradients were shown to be of importance for atmospheric conditions. For example, N can take the value of 3 for air at 20° C. N 'is zero for no thermal diffusion, positive for both effects aiding to drive the flow, and negative for opposed effects. The Prandtl (Pr) and Schmidt (Sc) numbers: 0‘ ‘ Sc: (2.25) were varied in this study for air at atmospheric conditions (Pr=0. 7 and Sc=0.l to 10). The study also considered the interactions between the air velocity and the rates of heat and mass transfer. 33 If the diffusion equation is neglected, the solution of the system of equations (2. 17) to (2. 20) is given, approximately,by the empirical equation (Rohsenow and Choi, 1961) Nux _ 0.676 PrO'5 0.25 0.25 (2.26) (O'ZSer,T) (0.861+Pr) where Nu is the Nusselt number h x Nux = k (2.27) Equation (2. 26) is also the solution of the boundary layer system for neglegible thermal effects. For this case the Grashof numbers are interchanged, the Schmidt number replaces the Prandtl number and the Nusselt number is replaced by the Sherwood (Sh) number, where th = (2. 28) Forced convection results when the buoyancy forces are small compared with external forces applied to the fluid in the bound- ary layer. The system of equations (2. 17) to (2. 21) becomes simpler to solve (Rohsenow and Choi, 1961). The solution for the dependent variables are given as function of the Prandtl,Schmidt, and Reynolds (Re) number, where 34 Re =.l__ (2.29) Lamimar flows are usually followed by turbulent flow. Turbulence is created by the roughness of the surfaces, high Reynolds numbers, instability of the fluid, duration of the process, etc. The analytical treatment of turbulent flows is not as well developed as it is for laminar flows. The knowledge gained from the laminar flow solutions is utilized to design empirical formulations consisting of dimensionless numbers with unknown parameters. The parameters are estimated from the experimental data. Good correlation was obtained , for example, between experimental data on evaporation of liquids in a wetted wall column (Rohsenow and Choi, 1961) with the following empirical equation 0.83 0.4 Sh = 0.023 (Re) (Sc) 4 (2.30) The Reynolds and Colburn analogies (Rohsenow and Choi, 1961) can be utilized to estimate mass transfer coefficients as a function of the corresponding heat transfer coefficients. The use of the transfer analogies is voided for low rates mass transfer, i.e. when the velocity profile is not affected by the mass transfer (Welty et al. 1969). Most natural convective processes found in nature occur on a large scale and are of such long dutration that the transport mechanism 35 is largely turbulent (Gebhart, 1973). The flow characteristics vary from laminar flow, stable stratified fluid, unstable laminar flow,transi- tion flow, to newly developed turbulent flow (Gebhert,1973). Nonsteady state behavior of the flows complicates the analysis even more. Transient boundary layer problems have been solved by numerical integration for conditions of particular interest. The results have not been found to be of general application (Gebhart, 1973). The nature of the fluid flow over cassava particles drying in horizontal or vertical layers under atmospheric conditions can be generally described as boundary layer flow with the following characteristics :- (a) three dimensional, unsteady state, with water vapor injection from the surfaces; (b) natural or forced flow influen- ced by unpredictable air flow characteristics; (c) laminar, in transition, or turbulent flow . The magnitude and direction of the air will determine the nature of the flow over the surfaces. Exter- nal and internal particles of the layer are subjected, simultaneously, to different flows as result of the resistance presented by the layer y (static pressure) to the air flow. At high wind speed and appropiate wind direction the air can be forced through the thick layer. In this limiting case, the system of equations (2.9) to (2. 14) applies to the natural drying problem. In conclusion, the complex natural drying phenomenon can not be analyzed theoretically with the present state 36 of knowledge. Consideration of the solar radiation effects for products with not neglegible solar absorptivity, result in a substantial complica- tion. Most of the reported efforts on natural drying have been directed to improve the efficiency of collecting the solar radiation and to utilize the solar heated air to dry the moist product. The methods proposed are in some form similar to the solar stills. Good know- ledge exists of the heat transfer process that occurs in collectors made of selectedisurfaces, covered by glass or plastic sheets trans- parent to the high frequency solar radiation but opaque to the low frequency radiant energy emitted by the heated surfaces (Buelow, 1956', Whillier, 1964; Malik and Van-Vi Tran, 1970; Satcunathan and Deonarine,.197l). Solar cabinets have been designed in several forms. The collectors have been selected surfaces, the product itself or a combination of both. The product position has been varied inside the cabinet. The released moisture escapes the cabinet by diffusion, natural convection, condensed water, or with the aid of a fan naturally powered by the wind (Ismailova, 1957; Khan, 1964; Lawand, 1966; Nahlawi, 1966: Headley and Springer, 1973). Although the cabinets have been more efficient than drying the product naturally on horizon- tal surfaces, the maximum drying rates reported for yarns are 2.8 kg/m‘2 of water removed in 20 hrs (Headley and Springer, 1973) and 1.2 kg/m2 in 24 hrs (Nahlawi, 1966). 37 Wilson (1961) found that in drying grapes in Australia, the combined effect of solar radiation and natural air circulations was more effective and less expensive that the use of solar collectors or supplementary heat. In summary, the applied natural drying literature is scarce, qualitative and imprecise. Mathematical modeling of the process has been considered a difficult subject because of the uncontrolled variability of the environment and the slow response of the product to the environmental changes. On the other hand, some models have been developed under controlled conditions but not tested in the field. Kemp et al. , (1972) attempted to incorporate a single evaporation variable into an empirical drying equation for hay : (1 Mo ' Meq where d3 and d4 are constants estimated from the experimental data, hfg is the latent heat of evaporation. 2. 7. 4 Evaporation Mathematical modeling of evaporation from free water surfaces, soils and vegetated fields (evapotranspiration) has been a challenging research subject in engineering. Scientific interest in 38 the physics of evaporation dates back to Aristotle (384-322B. C.) who stated that "wind is more essential in evaporation that the sun". Evaporation was considered in section (2. 7. 2) as a coupled phenomena of momentum, heat, and mass transfer which occur si- multaneously in the boundary layer. Natural or forced convection drive the moisture to the atmosphere. The system of equations (2.17) to (2. 20) applies to the tWo dimensional, natural evaporation case. The solar radiation absorved by the water surface should be considered in applying the boundary conditions in the analytical solution of the system. Solution to the boundary layer problem is not used in practical estimations because its complexity and the need to estimate evaporation rates from large, non-homogeneous surfaces. Empirical formulations are extensively used instead. Equation (2. 16) can be transformed into an empirical equa- tion by assuming that the moist air surrounding the surface is an ideal gas with a temperature equal to the temperature of the water surface. The resulting equation is '—r—X— = ha (es ' ea) (2.32) where hd = hdMa/RoT M is the molecular weight of the moist abs’ a air, R0 the universal gas constant. Equation (2. 32) was first suggested by Dalton (17th century, A. D.) A linear function of the wind velocity has been proposed to 39 account for the air velocity effect on the modified convective mass transfer coefficient ( hd ) % 2 (d4 +d5u) (es -8 (2'33) 2,) where d4 and d5 are constants estimated from the experimental data. No consistency has been found for these constants (Slatyer, 1967). Penman (1948) derived the most commonly used evaporation equation. It is based on a simplified energy balance aided with an empirical function a. s .2; R" 5T +(d6+d7u) (83' 6“) (2.34) A 983 —®—rf— +0.27 Rn is the net solar radiation;ges is the slope of the saturation curve 9T evaluated at the dry bulb temperature of the air, d6 and d7 are con- stants : m' is the mass flux in energy flux units. Equation (2. 34) is commonly modified in estimating rates of evapotranspiration from different canOpies (Slatyer, 1967). The effect of the total incident solar radiation on evaporation can be very small compared with the energy supplied by the air, even in good sunny days. Lemon et al. (1957) ilustrated this phenomena by us a... ~u« ~.-. nu. ... 4O measuremets made inan irrigated cotton crop. The ratio of the air enthalpy given off 'to the net radiation was 1. 5. The microclimatology budget of a region can be altered substantially by changing the solar absorptance characteristics of the floor surfaces. Aderinkhing (1951) made observations, during three years, of the air temperature at 50 cm above three different types of surfaces : (a) natural soil, (b) artificially darkened, and (c) artificially lightened. On windless days he observed temperature differences of 3 to 5°C over the dark and light surfaces and 2 to 3 degrees over the dark and natural surfaces. It was expected that the natural drying of cassava could be explained by the present theories on drying, evaporation and solar absorption. III OBJETIVES The objetives of this study were: A. To develop a mathematical model capable of accurately simulating different systems of natural drying of cassava layers in arbitrarily chosen environmental conditions. To utilize the model to (a) compare the physical efficiencies of several natural drying systems, including the traditional methods of drying cassava on concrete floors of wooden trays (the drying systems differ one from the other in the relative position of the layer with respect to the floor, or in the form of the cassava particles), (b) recomend maximum loading of the cassava layers to be dried without significant quality deterioration as a function of the first-day ambient conditions, and the drying system, (c) study the influence of changing the important independent variables on the changes of the maximum layer loads, and (d) estimate the relative economic efficiency of commercial operations of three natural drying systems. To design (a) low- cost cutting machinery to produce cassava particles suitable for drying efficientely, and (b) inexpensive dry- ing systems with higher drying efficiencies than conventional systems. 41 IV EXPERIMENTAL PROCEDURES AND PRELIMINARY ANALYSIS Extensive experimental work was performed during the study because (a) the available information did not provide effective gides to concentrate the efforts in one specific field on natural drying, (b) a large number of non—controlled independent variables were important in the process, and (c) the analysis of the prelimi- nary results suggested new and more efficient forms of natural drying. The independent information on drying, evaporation and solar collectors provided guidelines to design the first scaled experiments. The sequence of analyzing preliminary results and improving the drying system was repeated until a prototype of a commercial drier system with obvious advantages over the other drying forms was built and tested. The description of the experiments follow their chronological sequence. 4.1 Importance of Differences of the Cassava Porous Structure in Drying The first drying experiments were performed on August 31, September 1, and September 2,1972 (See Table 3 for average weather conditions and Appendix B for the detailed experimental data) 42 43 Table 3. Average Ambient Conditions During Experimental Hours. Hours Temp. Rel.Hum. Wind Vel. Radiation Day hr °C ”70 m/sec cal/chZ-hr Aug 31,72 5 31.3 49.6 1.09 61.0 Sep. 1 9 29.4 55.3 0.62 40.7 Sep. 2 4 28.2 66.8 0.62 53.3 Sep.14 7 33.0 47.3 1.87 45.2 Sep.21 8 30.9 54.3 0.81 53.2 Sep.29 6 34.2 44.3 1.60 51.4 Oct 5 6 32.9 46.8 1.90 56.0 Oct 17 6 34.0 38.9 0.90 49.5 Oct.27 6 34.1 41.4 1.47 45.4 Mar 7,73 5 28.6 57.9 0.92 - Mar 8 9 29.9 54.9 1.45 - Marlo 4 29.1 53.4 3.67 27.2 Mar 11 3 26.8 67.0 0.78 30.1 Mar 14 5 33.1 46.9 2.40 47.8 Mar 15 9 30.4 52.5 1.75 43.2 Mar 21 6 32.8 41.4 2.34 39.8 Mar 22 9 31.5 47.5 1.93 41.2 Mar 24 7 30.4 - 58.7 2.71 37.9 Mar 25 5 28.5 56.2 0.91 41.5 Mar 28 6 31,8 47.5 2.99 36.0 Mar 29 9 29.7 54.6 0.91 29.5 Mar 31 6 31.9 49.8 2.28 29.3 Apr 1 5 27.5 65.2 0.97 53.8 Apr 4 5 32.8 40.9 2.20 31.3 Apr 5 9 27.1 59.7 1.80 31.2 Apr 7 5 27.1 63.1 1.96 31.2 Apr 8 4 28,3 58.8 0.59 46.2 Apr 11 7 28.4 50.5 1.61 35.9 Apr 12 8 28.6 49.1 1.39 47.5 Apr 14 6 31.8 41.1 2.16 36.6 Apr 15 5 26.7 54.0 0.63 42.1 Apr'17 12 21.2 88.3 0.63 - Apr 17nightlz 22.2 87.9 0.39 0.0 May4 10 25.9 78.5 1.17 30.7 May 5 9 27.9 61.0 1.54 48.7 May 9 10 28.1 50.5 2.04 37.2 May 14 6 28.2 61.8 1.01 14.2 May 15 9 30.4 51.3 1.36 42.9 May 21 9 28.8 71.3 1.34 24.4 May 22 9 29.8 62.8 1.24 40.3 May 25 10 29.5 58.6 1.06 39.0 May 26 9 30.4 55.9 1.39 40.3 May 29 10 28.1 70.3 1.03 23.5 May 30 5 27.3 71.6 1.02 31.8 Jun 1 9 30.3 62.5 1.38 36.0 Jun 2 9 29.4 61.7 1.59 4.1.7 44 to establish if differences in the internal structure of the product -- possible different diffusion coefficients -- could affect significant- ly the drying rates of cassava. ‘Llanera variety roots having ages -- time elapsed after planting and before harvesting -- of nine months and two years were chosen for the purpose because of the obvious differences in their internal structure. The old roots were yellowish, soft and spongy while the young ones presented a white, firm structure. In the three day experiment, five identical perfo- rated wire trays -- 50x50x10 cm -- loaded with five kilograms of rectangular bars of cassava were wighed every hour during working .hours, Figure 4. Three of the trays were loaded with the two year old roots. Two of these were elevated 30 cm from the floor, and the other was placed on the floor directely. The two trays with the young roots were also elevated 30 cm from the floor. The bottoms of the elevated trays were left free to the air. Desorption curves of experiments are presented in Figure 5. The moisture ratio (expressed in equations 2. 3, 2. 4, and 2. 5) was used as the dependent variable to eliminate the influence of different initial moisture contents. Meq values were estimated to be proportional to those of other starch products because no reported values were available at this stage of the study. The product on the floor changed its original color to brown (Figure 23) and produced fermenting odors indicating that deterioration occurred in the second drying‘day'due to slow 45 . nadufi “3:05.”on >0. mnKuQ Hangmz .w 0.3th 46 I \. \. Aug. 31, 1972 - # Bars on the floor 0.4 0 Two year old roots. Tray A " A Two year old roots. Tray B . X Nine month old roots. Tray A 0° 3 r: ' Nine month old roots. Tray B Drying Hours 1.0 0.9 0.8 0.7 0 6 _ 0.6 0.5 ). Sept. 1, 1972 0.5 - 0.4 __ (Same legend as above) 0.4 __(Same legend as above) 0 3 _ 0.3 __ 0.2 ,_ 0.2 _ 0.1 1 . 1 1 I 1 0-1 1 1 1 l 1 2 3 4 5 0 l 2 3 4 Drying Hours Drying Hours Figure 5. Internal and External Resistances in Drying 47 deydration rates. The curves show that although differences in drying can be attributed to different diffusion coefficients, they were small when compared with those originated by modifying the air circulation through the particles. The external resistences to the moisture flow were more important than the internal resistance differences. g No special attention was given in selecting uniform cassava samples for the experiments, although, different cassava structures in age, variety, and position along the roots were recognized. A single experiment showed differences of moisture content higher than 5 percent, wet basis (w. b.), for the same fresh root at different positions along the tuber. A study of dry matter distribution along the roots, reported by Umanah (1971), supports this finding. Unpeeled Llanera variety between 8 to 18 months of age furnished most of the cassava samples used in the experimentation. No signi- ficant differences in average drying rates could be attributed to differences in cassava ages and varieties. i 4. 2 Cutting Mechanisms The production of the cassava particles received special attention in the study. Two different mechanisms were used to produce sixteen types of cassava geometry, different in their forms of dimensions. The general appearance and schema tic views of the mechanisms are shown in Figures 6, 7,8,9, and 10. Figure 6. Manual Press to Cut Cassava Rectangular Bars 49 0.8,l.0,1.2 cm I \ Wood Grooved \ ) ) Matrix Cassava Cylinder L 3.2,4.0,4.8 cm _\_ 4 Level Blade Set Rectangular Bar of Dimensions : ‘ 0. 8x0. 8x L cm 1.0x1.0x L cm l.2x1.2x L cm Figure 7. Cutting Section of the Manual Press .g .3 3 "4. Figure 8. Disc Cutter 50 51 g Bicycle 25 cmfl Pedal PK Mechanism 115 cm Disc I “J Cutter Figure 9. Schematic view of the Disc Cutter Assembly Figure 10. , e “é“ Uniform slices 1:9 :L 1:) 4 1): 1.2 cm Cutting Discs and Particles Produced. Large Chips i. i” iabw 0.5 cm Uniform slices A «avg v v 0 Law 9 , 1.2 cm Figure 10. Cutting Discs and Particles Produced. 53 The first device is a manual press (Figure 6 and 7) consisting of (a) a matrix of rectangular bars made of metal or wood which push a previously cut cassava clyilinder downward, and (b) a station- ary set of blades. The cutting set was partitioned in a blade arrange- ment made in four horizontal planes. Each plane consisting of crossed, vertical, one millimeter steal blades distributed as shown in Figure 7. The four planes were properly aligned to produce thin krectangular bars with dimensions depending on the distances between the blades . Each plane produced a cut to the cylinder. Three sets of knives were made to produce bars with sections of 0. 8x0. 8, 1.0x1. 0, and 1.2x1. 2 cm . The bar's length was the height of the cassava cylinder. The product of the press presented a neat solid figure, free of product fines (very small product particles undesira- ble for drying purposes). One man could cut about 40 kg of cassava per hour. The second device is a' model of a chipper used in the south- east Asian cassava exporting countries. It consists essentially of a circular disc.with built-in knives which cut the root when fed in the hopper (Figure 8). The disc can be powered by a person using a bicycle pedal mechanism, by the power take-off of a tractor or by a motor. The conventional disc and three modifications were used to obtain different geometries. A schematic view of the discs and the approximate form of the chips are shown in Figure 10. 54 A more detailed illustration of the disc which produces a geometry resembling the rectangular bars (1. 0x1. 0x3. 0-9.0 cm) is given in the bottom of Figure 9. In this particular disc a small series of knives about one and half millimeters thick were soldered along concentric radii to the disc. The root is cut first by these knives producing grooves one centimeter apart. A second set of large blades make the final cut to produce the rectangular bars of varia- ble length. The end products of the disc cutter presented a weak internal structure due to shearing stresses produced in the cutting of the particles and the release of them by the disc. Product fines were also produced but they could be reduced when the roots were posi- tioned firmly. In this case a second man was required to feed the roots. Yields of this mechanism were about 240 kg/hr when opera- ted by a man or about 500 kg/hr when operated by an engine. 4. 3 Field Experiments. First Experimental Period The field experimentation was divided in two periods: (a) from August 31 to October 27,1972 and (b) from March 7 to June 2, 1973. During the first part, experiments were designed to compare the reported drying methods with possibly more efficient ones and to obtain data that could be analyzed to identify the relative importance 55 of each environmental variable on the drying process. In the second period, similar experiments were performed but quantitative know- ledge of the process permitted experiment with improved models to the point that a close prototype of the recommended drier for a commercial operation was built and tested. The experimentation of the first part consisted basically of the following general procedures: (a) a given amount of a cassava geometry was placed on horizontal perforated trays, separated one from the other by a distance at least equal to the tray length, or in two types of solar dryer (Figures 4 and 12), (b) the loaded tray or cabinet was weighed at one hour intervals during the working hours of one, two,or three consecutive days. Figure 11 shows the desorption curve for a two-day natural drying experiment, (c) measurements of the variables were" taken during the experiments at one hour intervals, ((1) at the end of the experiments the product was placed in convection type ovens at 75°C for 48 hrs to estimate the dry matter content. A detailed description of the tests follows. 4. 3.1 Horizontal Trays All trays used were made of galvanized iron mesh (0. 5 mm spacing between wires). Tray dimensions were 50x50x10 cm. Heavier galvanized iron wire reinforced the tray structure. The trays rested on supports made of conduit tubes, designed to not interferwitn the air circulation underneath the trays (Figure 4). veg-t...- x} c I.... cad... decimal. Moisture Content Dry basis, 1.0 1.9 .- 1'8 " Vertical Drier 1.7 .. \ 4' _ 2 1.6 h \\ D—25.3kg/m «iv 1.5 _ \\ 1.4 - a 1 3 \ Average Conditions " 3 . May 25,1973 May 26,1973 1.2 _ \ . T=29.5 °C T=30.4 °C 1.1 2 . RH=58.6% RH: 55.9% \\ u :1.06m/sec u =1.39m/sec 1.0 .. a Ri=39.0cal/cmz-hr Ri=40.3cal/cmZ-hr 09 h- \.§ .8 ' P .7 F .6 _ .5 _ 4. experimental .4 .3 ' calculated .2 01 - 01111111111111411 81012246 81012246 am pm am pm Drying Hours Drying Hours Figure 11. Drying Performance in two Consecutive Days. 56 57 4. 3. 2 Solar Driers Two types of solar dryer were tested. The first consisted of a collector, made of a series of wire screens painted with a lamp-black base enamel and covered by two sheets of window glass (Figure 12a). A vertical wood frame made of plywood prevented lateral heat losses and gave support to the collector and glass sheets. The product was positioned inside the frame using three Configurations: (a). cn a‘ wire tray at about 10 cm from the collector, (b) on a perforated plexiglass sheet touching the collector and the screen resting on the top of a baffle system of corolite crossed rectangular plates 2 cm apart and '8 cm high. This type of solar dryer is denominated as a solar cabi- net. The second solar drier tested consisted of the same glass sheet arrangement with a collector made of a black metal sheet with a fin system soldered on its back (Figure 12b). The chips were placed in a perforated tray and the collector fins rested on the particles. 4. 3. 3 Measurements and Instrumentation Wind velocity was measured hourly by reading the counter of a totalizing Belfort 3 cup anemometer, Cat. No. 5-349-A. The cup centers were positioned 30 cm above the floor. Dry bulb temperature and air relative humidity were averaged for each hour from the recording chart of a Belfort hygrothermograh, 58 collector Glass sheets 1cm Wood frame \\\\\\\\'\ ' r —:' Cassava particles I * rformated base Solar Cabinet Glass sheets Black collector 1 cm 50 cm // X 1 lateral view '“777 Cassava particles Triangular fins l bottom view Solar Collector (b) Figure 12. Solar Driers 59 Cat. No 5-594, placed at 30 cm above the floor. A weekly gear and chart set was used during the first experimental period and a daily set for the second. Temperature average was meassured approximately within I 1 ° C error with respect to a potentiometer. The air relative humidity was measured within ‘1’ 2 percent error with respect to a aspirator pshychrometer. Total incoming shortwave radiation was measured by a Grczynsky solarimeter (Solorgor) during the first period and part of the second part. The signal was integrated hourly and printed by an EKO solar printer (Solarin), model RR-ll. The trays were weighed each hour in a Ohaus beam balance, 20kg of capacity and l g of sensitivity. Errors in weighing measurements were less than 1 percent of the total weight. A portable Honeywell potentiometer with copper-constantan 24 gauge thermocouples and an Athkings portable aspirator pshychrometer were used to make auxiliary measurements of the drying product and to calibrate other instruments. Indicationsxof the percentage of short wave reflected radiation from the horizontal cassava trays were determined with a portable EKO Line pyrheliometer connected to a millivoltmeter.. The experimental datajof the first experimental period was utilized to graph, in preliminary analysis, the natural desorption curves. 60 4.3.4 Preliminary Results and Analysis Observations of desorption curves during the first experimental period helped to identify some obviously inferior forms of natural drying of cassava and to gain knowledge on the physics of the process. Figure 5 shows that by elevating the perforated trays from the floor, the drying efficiency improves significantly ( the quality of the end-products can be appreciated in Figure 23). Figure 13 shows the solar cabinet perfomances compared with natural drying of the same product on perforated, elevated trays. The solar cabinet and the solar collector tested did not result in appreciable advantages over natural drying although high radiation levels were recorded during the tests. (See Table 3 and Appendix B). Figure 13c shows the dehydration curves of untreated cassava ~bars and the same product dusted with black activated charcoal powder. The differences can be attributed to the higher solar absorption of the black surfaces. Two sizes of the conventional cassava chips (Figure 14) are com- pared with rectangular bars,1x1x5 cm,for three initial layer loads or densities 1 : 8,12 and 16 kg/mz. Curves (a) and (b) show that no Densities are defined in this study as the initial fresh weight per unit area (kg/m2 ) . The density values (D) are proportional to the product dry weight used in the analysis. Moisture Content Ratio Moisture Content Ratio . Figure 13. 61 1.0 (a) 1.0 0.9 1x1x5 bars at 10 cm 0.9 below the collector 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 Sept.21, 1972 .4 0.3 0. "O Solar Cabinet 0 2 1- Horizontal elevated t ray 0 2 D = 8 kg/mz 0-1 I 1 1 I 1 1 9'1 0 l 2 3 4 5 6 1.0 Drying Hours 1.0 0.9 (c) 0.9 + 1x1x5 bars on perforated 0. 8 plexiglass touching the 0. 8 "' collector - large holes 0. 7 0. 7 0.6 0.6 )- 0.5 0.5 0.4+_Oct.5,1972 0.4 0. 3 0 Solar cabinet 0.3 bfi- Horiz.ElevTray \+ 0' 2 __A Bars dusted black 0' 2 0 1 D =8 kg/m2 \ 0 1 ° I 1 1 1 I 1 ’ 0 1 Z 3 4 5 ' 6 Drying Hours Solar Cabinet Perfo rmances r (b) _, \ 1x1x5 bars on perforated \ plexiglas s touching the collector- srnall holes. .4. h- Sept. 22,1972 L- f \+ \+ - 0 Solar Cabinet + Horizontal, elevated tray D: 8 kg/mz I l I I 1 I 0 l 2 3 4 5 6 Drying Hours (d) 1x1x5 bars on tray touching the collector with straightener baffle system f __ Oct.17,1972 \ 4’ OSolar Cabinet \, '— §Horiz. Elev. Tray D = 8 kg/mz 1 I I I 1 I O 1 2 3 4 5 6 Drying Hours Moisture Content Ratio Moisture Content Ratio 1.0 (a) 0.9 - Oct.17,1972 0.8 __ '\ A 0.7 _ _ \\. '§\ 0.4 \\'A — . Large chips, D=12 \? 0'3 " : 1x1x5 cmbars, D=12\ 1x1x5 cm bars, I): 8 0.2 0 Large chips, D = 8 0.1 I I 1 I I L 0 1 2 3 4 5 6 Drying Hours 1.0 1972 0.9 Oct 27, Small chips, D=12 q D=12 D=12 0 Large chips, 1 1x1x5 cm bars, Drying Hours 62 1.0 (b) 0.9 r A\ Oct.17, 1972 0.8 '\, 0.7 \\\ " A\ 0.6 .\ \\ b o\ 0.5 0.4 _ , Large chips, D=16 0.3 Alxle cm bars, D=16\ _ +1x1x5 cm bars, D= 8\d o - 0.2 _ Large chips, D— 8 0-1 I 1 I 1 I 1 0 1 2 3 4 ’ 5 Drying Hours 1.0' 0.9 Oct. 27,1972 .1. TASmall chips, D=16 0 Large chips, D=16 - I" 1x1x5 cm bars D=16 0.1 I 1 l I I Drying Hours Figure 14. Performances of Different Cassava Geometries. + 63 differences could be observed for the thin layer but large differences, due to a better air circulation promoted by the rectangular bar geome- try, were found for the thicker layers. The drying characteristics of the big chips were superior to those of the small ones for 16 kg/m2 because of higher void space (porosity) between the particles (Curves c and d). The hourly stirring effect on densities of 16 kg/m2 was only of 0.03 (moisture ratio) after six hours of sunshine. This experiment (not shown in the graphs) also indicates the low solar absorption of the white cassava surface. Although the study of the dehydration curves gave an insight into the problem, it was not possible to establish the particular effects of the ambient variables. The unlimited combinations that could be drawn in the design of the experiments together with the limited number of experiments per day ( to minimize errors due to different weighing times, the number of trays was limited to nine) indicated that an understanding of the phenomenon was mandatory in order to suggest better drying forms. Thefirst attempt made was to calculate a drying parameter which is nearly independent of the current moisture content at any instant of the drying process. The proportionality drying constant K of the empirical layer equation (2. 6) was estimated by the finite- difference expresion valid for any time: 64 '13:" :1- M1+1 -M1 1 (4.1) At M. + M. _ Meq where Mi+l and Mi represent two consecutive values of the average moisture content with At equal to one hour. The assumed values for Meq (see section 4.1) were taken for cassava as function of the ave- rage wheather conditions. The choice of equation (2. 6) for the preliminary analysis was supported by the results of drying a thin layer of cassava slices under controlled conditions in the agricultural Engineering Processing Labo- ratory at Michigan State University, and (b) by the drying data of Chirife's studies (1970 and 1971). Booth sets of results are reproduced in Figure 15. I The experimental K' and the ambient conditions were drawn for each day. Figure 16 and 17 show some examples. An ordinary linear least squares standard IBM (1130 System) routine was used to investigate the relative importance of the environ- mental variables in the natural drying phenomenon. The model proposed W381: I=a0+alTi + a2 Ri+a3T +a4I~T (4.2) 1 This method is an approximate approach to the general procedures of esti- mation of parameters (Beck,‘1972) in a differential aquation. See discussion in Chapter V. ' 1.0 0.9 0.8 0.7 _ 0.6 24 °C, 70 % RH 7 ‘ \ ~ Thin Layer 0.5 _ 1» A\ \ ., 0.4 _ \ O\ K t K 0.3 \ \ \ .. .\ * . 0 \° \\ .2 '- \ O 84°C, 370 RH + °D = 62.2 kg/mZ \ Chirife 8: Cachero,1970 o O 0.1 \* \ 0.09" 0.08 _ \g 0 0.07_ \ . 0.06 _- ’ .2 0.05 _ 0 iii m 0.04 _ , ii . *5 0.03 84 °C 3 % RH o ‘- 0 + D=11.3 kg/mz \’ a.) E 0.02 .. ‘/ Chirife 8: Cachero,'1970 .3 o 2 0.01 __ 0.00? 0.00 _ 0.007,. 0.006_ 0.005_ . I ' 1 I 1 1 1 " 1 1 I I 1_ ,0 10 20 30 4O 50 6O 7O 80 90 100 110 Drying time, min (Cl'n'rife & Cachero, 1970) 1 I 1 1 1 1 1 1 1 1 1 0 2 4 6 8 10 12 14 16 18 20 22 Drying time. hrs. Figure 15. Desorption Curves at Fixed air Conditions E 0.4 M. *5 (d 23 0.3 C O o f: g 0.2 .2 1'3 0 0.. O 3.. o. 0.1 DD 5 '>. L: o 0.0 H .121 I ~- 8 R S «I U 34 60 32 50 30 40 28 30 26 20 24 10 22 0 Figure 16. 66 Oct. 5, 1972 A D: 8 kg/m2 .5 D =12 kg/mz 0 1 2 3 4 5 Drying Hours - o D=16 kg/m2 1» no 7' \ " no I" \\ q 0.017 253—— A .. 0.015 I: Radiation ' '- 7 Air temperature '- .. 0-014 _ A Air absolute humidity ~ 0 - 0.013 0 Wind velocity " -‘ 0.012 " _ 0.011 v' 1 5 I 1 0.010 0 l 2 3 4 5 Drying Hours Influence of Ambient Conditions on Drying. O. 0 67 masom magnfl a m a m N a o .. _ _ . _ I. w Na. 4 1. _ a . . +114 ‘ ‘ I 0H 0 C \+ .. ON. C + I am. 4 mm mm am am 1 mm. om em ANEEV: O m@ on 725 e .1 NM. 32 .2 5.82 mega? M of mo mofimaaouomnmgo .NH madman mnsom thCQ m w m N u _ . _ Eu mxHNH Hm So 1303 cm cabogoou 02 “mph. m2: .2 €32 mm. mm. wm. VN. 9353 mGTCQ m a. m N a a _ a _ .2 x. . A W U 9 I S \ a: u. 0 O n I _ I. T. \ om. E. 8 m... 1 . a... an . mm 8 4m ANE\wv$ 0 mm a 25 e 1 mm. 22 .3 .332 68 ‘where L: fiLT, and 1:1. are the average wind velocity, incident radiation, air dry bulb temperature, and air absolute humidity for each elapsed hour. The K' values correspond to experimental tests of the same product geometry and density. Statistical tests associated with the linear regression indicated that dry bulb air temperature and wind velocity variations explained about 75 percent of the changes in the K' values. The regression coefficients a2 and a were not significantly different from zero. (The 4 results of the regression analysis are not shown for this preliminary test). The regression results suggested possibilities of improving the already satisfactory performances of the elevated horizontal wire trays. ' 4.4 Field. EXperiments. Second'Experim'ental Period 4.4. 1 Black Floor A 10x10 m2 area covered by a layer medium gravel was painted with a lamp-black base enamel. Temperature differences of 1, Z, and 3 °C coTild‘ be measured at 10 cm above the floor with respect to the natural adjacent soil. The temperature differences depended on the evironmental variables, the higher differences corresponded to the case of high radiation and low wind velocity. No attempts were made to study this complex micro-meterological phenomenon that supports the finding of Aderinkhin (1951). 69 4.4.2 Vertical Trays The 50x50x10 cm trays were adapted with a mesh frame to permit sandwiching of the cassava layer and to place them in a vertical position with the aid of a screw mechanism and an iron structure (Figure 18). The vertical layers were positioned against the predominant direction of the winds. This position was the most unfavorable with respect to the recepted solar radiation. Weighing and weather variable measurements were made in the same form outlined in the first experimentation period. Ovens set at 100 °C were used for dry matter determination. 4.4. 3 Vertical Driers An experimental drier was built and tested during the last part of the. study (Figure 19). The unit consisted essentially of two 1. 5x2. 0 m vertical and parallel frames covered with galvanized wire screens (8 mm spacing between the 1 mm wires). The frames were pinned on two vertical wooden boards set in the ground. The boards also served as the lateral walls of the drier. A roof was supported by the boards. Provisions were made (a) to vary the distance between the screens, (b) to load the drier by a hopper built on the top, (c) to unload the drier by a door hinged at the botton of one of the frames and (d) to unpin the drier and let it rest on a platform scale for continuos weighing. When the drierrested on the scale it also touched one of the horizontal iron angles that joined the boards on mxmufi amofluokr and fimunonmuom 3 Mafia 3.332 .3 ouumwh u . u. .I.Hlll41.ilu.|nluiq . H91- 71 Figure 19. Vertical Drier 72 $33 £5 wofivoz .520 :83»; .8 charm 73 the top. Friction forces due to this interation and those between the product and the lateral drier walls were tested to be about 0. 5 kg while the average load of drier was above 50 kg. Sensitivity of the scale was about 0.5 kg. Better drying effects were designed for by adding four wings to the drier as shown in Figure 20. The experiments with the modified drier constituted the end of the field experimentation. 4. 5 Summary of Total Number of Observations The complete distribution of the hourly measurements during the study is summarized in Table 4. More that 70 percent of the observa- tions came from tests with bars of section 1 x l and 1.2 x 1.2 cm2, on vertical and horizontal trays. Discrimination of these with respect to layer densities and lengths of the bars are presented in Table 5. Fifty-four percent of the possible evaporable water (average value) was dried during the daily experiments. In some experiments,however, only 13 percent of the potential evaporable water was lost, while in others 75 percent was removed. The mean hourly moisture content for all measurements was 48..6 percent, w.b., but the entire practical moisture content range for cassava (67 to 12 percent, w.b.) was recorded in the experiments. The tests lasted one, two or three consecutive days. Daily measurements were taken during a period of 3 to 12 hours with an average value of 7 hours. The detailed data is presented in the Appendix B, a summary of the average weather variables for each experimental day 74 Tablel4. ' Total Number of Hourly Observations Geometries Drying Rectangular Bar Small Large Disc 81' T 1 System. Sections Chips Chips Bars ices ota .8x.8 1.xl. l.2xl.2 Vert. Trays 7 490 172 - - 261 — 930 Hor. Trays 14 429 102 12 24 89 8 678 On Floor - 31 - - - - - 31 Solar D. - 23 - - - - - Z3 Vert. D. - - - - - 54 - 54 11& Wings _ _ - - - 7O - 70 TOTAL 21 973 274 12 24 474 8 1786 Table 5. Distribution of Observations for the Rectangular Bars. VERTICAL TRAYS Density Section: 1x1 cm2 Section: 1 . 2x1. 2 (kg/mg Length (cm) Length 1 2 3 5 7 8 9 Total 5 7 Total 16 - - - 44 14 - - 58 38 14 52 20 47 11 29 101 15 - 7 210 74 - 74 24 23 11 12 67 - 3O - 143 35 - 35 28 12 - 12 4o - 15‘ - 79 11 - 11 TOTAL 82 22 53 252 29 45 7 490 158 14 172 HORIZONTAL TRAYS 54 - - - 54 _ _ _ 12 - - - 24 - - - 24 - - - 16 25 ll - 4O - l4 - 9O 14 14 28 20 7 - - 219 - - 7 233 74 - 74 24 - - - 27 - - - 27 - - - TOTAL 32 ll - 364 - l4 7 428 88 14 102 75 are presented in Table 3. The temperature varied from 20 to 35°C, relative humidity from 40 to 95 percent, wind velocity from 0 to 4.6 m/sec, and solar radiation from O to 75.9 cal/cm2 - hr. 4.6 LaboratorLgxperiments Selective properties of cassava were evaluated in the laboratory to explain their importance in natural drying of cassava. The signi- ficant properties are : porosity, bulk density, and equilibrium moisture" content. 4. 6.1 Porosity Porosity P, or void space fraction of the total volume of the cassava particles was measured by a wet procedure. A cylindrical tank, 31. 5 cm in diameter and 38. 3 cm in height was filled by releasing gentely and randomly the fresh product particles. Water was added to complete the tank volume. The volume fraction of water represented the void space fraction of the complete volume of the" tank. This simple procedure was readily applicable to cassava because its saturated initial state and because of its higher density than water. POrosity,values for different rectangular bar dimensions are presented in Figure 21. Porosity values of the bars produced by the disc were Porosity Figure 21. 0.6 76 Bar Section A 1. 2x1. 2 cm 0 l.0xl.0 cm Po rosity / Bulk Density I 1 1 1 n g I l 2 3 4 5 6 7 Length of the bars, cm Porosity and Bulk Density of Rectangular Bars. Bulk Density, g/cm3 77 about 0. 5. Conventional cassava chips presented values between 0.42 to 0.46. Porosities of the particles made by the disc had the tendency to reduce the-compression forces due the weight of the particles. The weak structure of the disc products caused this phenomenon. Cassava bars produced by the manual press maintained their original firm structure. Porosity of the rectangular bars were fitted to equation (5.16). 4. 6. 2' {Bulk Density Bulk density of fresh cassava bars (1x1x5 cm) was measured by weighing the tank, used in the porosity determination, filled with the particles. The value was 0. 51 g/cm3. This figure and the O. 52 porosity value corresponding to this geometrical figure (Figure 21), gives a true cassava density value of 1.06 gm/cm3. Bulk density of “We“: , 3 cassava db can be expressed in g/cm by , s db=1.Q6(l-P) (4.3) Bulk density figures are also presented in Figure 21. 4. 6. 3 Layer Thickness The initial layer thickness (Lt) can be given by D b 78 where D is the density in kg/mZ, db the bulk density in g/cm3 and Lt the layer thickness in cm. An approximate estimate of the initial la- yer thickness in cm can be obtained by dividing the initial layer density in kg/mz by 5. 4.6.4 Ecmilibrium Moisture Content Saturated salt solutions were used for conditioning dried cassava bars. Fresh cassava was not used in the experimentation, i.e. , no hysteresis effects were studied. One hundred and twenty ml, wide mouthed jars were equipped with stainless steel wire screens supported by tripods with the same material inside the jars. Two of three cassava bars were placed on the screen above the solution level. The jars were kept at fixed temperatures in a growth chamber or in a forced convection oven. Temperature accuracy was within IL 2 ° C. The samples were left until they reached constant weight. Conditioning times varied from seven to ten days. The solutions, temperatures and relative humidities of the conditioning air are presented in Table 6. Equilibrium moisture content was determined by drying the conditioned bars in forced convection ovens at 100°C for 48 hours. A precision Mettler balance, sensitive to the milligram, was used for the measurements. The data points and adjusted equilibrium isotherms are presented in Figure 22. Description of the adjustment procedures is given in the next chapter. The observed errors can be attributed to the possibility of non-homogeneous cassava samples, mold growing in the 79 “Cooked 33::ng o>$§om m>mmmm0 mo 33:00 ougmwoz Eswuflfidvm 1. amum magmas ooH oo ow on 00 cm ow om om OH o . w u. . . m o m w Ca ma om 0 mu 1 mm co 0. 3. h .. CM CM + L m“ 0 mm Do 0 x 4 Ca. L 350m 3:05:09an may .. Am .3 cofimsvm mamas woumfldufimo II III L . Am .3 :33on means mcfiflsofimU om siseq Alp ‘1U9313d ‘quaiuog exnistow ~42- . t 80 Table 6. Relative Humidities Produced by Saturated Salt Solutions Temperature °C Salt 0 15 30 45 60 75 LiCl H20 (Lithium Chloride) ‘ 13.5 13.0 12.0 11.5 10.5 9.5 MgClZ 61120 (Magnesium Chloride) 35.5 34.0 32.7 31.5 30.0 29.0 NazcrzC)? (Sodium Dichromate) 61.5 57.0 52.5 48.0 43.5 39.0 NaCl (Sodium Chloride) 76.5 76.0 75.5 75.0 74.5 74.0 K2C1‘O4 (Potassum Chromate) 87.6 86.7 86.0 85.0 84.0 83.5 (Potassium Sulfate) 99.0 98.0 96.5 95.0 94.0 92.5 Source: Hall, 1957 jars with potassium salt solutions, and errors in the relative humidities values. 4. 7 Product Quality Deterioration of cassava roots after harvesting largely depends on the degree of mechanical damage incurred during the harvesting. Slicing or chipping of the roots constitute a multiple process and deterio— ration becomes visible in less than twelve hours in the non-treated 81 products. Current research on storage of the fresh product (CLAT,1973a) indicates that retardation of deterioration is obtained by dipping the sliced roots in alcohol solutions. Dehydration to a critical moisture content within a day is one way to avoid the deterioration during the subsequent natural drying days. The critical moisture value is higher when the product surfaces are sterilized. During the natural drying experiments subjective observations were made for signs of product deterioration such as loss of white color and smell of fermenting odor. The change of color criteria (Figure 23), was chosen because this is also a Thai quality criterion (Standards,l966) for exporting cassava chips. More precise objective methods of product deterioration are recognized in the literature. It was established(using the subjective criterion) that cassava particles do not deteriorate during the first three days after cutting if their moisture content reduces to 50 percent w.b. during the first drying day. This criterion is valid within the temperature range under which the experiments were performed, i.e. between 20 to 35 °C. It is also assumed that drying started inmediately after slicing or chipping, and that the roots were in a normal state of naturity , i.e. between 9 to 18 months. Dipping of the particles in a 50 percent alcohol solution for two minutes raised the critical ' moisture content to 54 percent. The development of the relatibnships between all measured variables is the objective of the next chapter. 82 MOOdh NEH. ZO m>ZOO AéDfide .wm QHHMQ mmom< .mp9 .N Row .2920. .8 mg. 20 on 825:. mass 20 m a 2 33m. zofiom>zoo q. Fitted Fitted L1 X ”U s 20 _ 20 _ " /6 J 0°C 21°C a: 5 ° 26° A "E 15 _ A 15 _ 38° 0 O o d) y 10 10 I; . 5 i— 1— ;; ‘/?°/Z/ ¢ 2 ,f/x/ — / 0 I J 1 l I O L J 1 I 1 0 20 40 60 80 100 0 20 4o 60 80 100 rig/L11. e 24. Equilibrium Moisture Content for some Crops. k 90 Higher variances were given to the high moisture values. Sensitivity analysis was used to eliminate unnecesary parameters (Beck, 1972). The resulting equation was Meq = [665.707RH-1261.97RH2+622.394111-13 exp[-.OO85RH+.01055RH3)TabS] (5. 6) The weighted, non-linear parameter estimation method presents, at least, three advantages with respect to the linear-polynominal method previously described: (a) three coefficients were eliminated, (b) Meq is forced to zero when RH is equal to zero (as is required for physical reasons), (c) the data can be weighted in a more scientific manner. Comparisons of the models (5. 3) and (5.6) for temperatures of 0 and 75C are presentented in Figure 22. 5. 3 Estimation Omarameters in Drying Equation 5. 3.1 Environmental Variables The coefficients a0,al, . . ,a8 of equation (5. 1) can be a2, . estimated simultaneously using a non-linear least-squares routine, as was discussed in section 5.2. The problem is more involved, however, because the parameters appear in a non-linear differential equation, in which several independent variables are discrete functions of time. Numerical integration should be used to solve for the moisture values, whic h are utilized to form the objective function. The estimation problem .1 , fit A C. .11. w“ I . Y, . . . odd .Pv .n.. . v pvt. 1 . .r- "I l 1‘ I :0 .m n.1a. o‘- -'v D ‘fil 9&1 3 1 -.f. ' E It‘i‘i HIJ p c 1 . uh. 91 is handled by coupled integration and minimization routines (Dye and Nicely, 1971). A different, but precise, solution was utilized in this study due to the limited computing facilities ar the site of the analysis. The estimation procedure was made in three stages. Data was selected in such a form that the density and the geometrical properties of the products were fixed. The third and fourth factors of the right hand side of equation (5. 1) were made equal to 1 in the first stage of the esti- mation. The drying rates were approximated by the finite expresions : dM : M1+1- M1 (5.7) dt At M. +N. — 1 and M = 1 +1 (5.8) 2 the resulting linear equation (in the parameters) is ‘ " (5.9) d V ll :11 o + :11 p—I c + SD NA “I I ml N + m ”L m | o Experimental R'values were calculated using equation (4.1) each two consecutive hourly moisture content measurements. Equation (5. 3) was used to calculate the equilibrium moisture content corre- sponding to the average temperature and relative humidity values for the elapsed hour. Two FORTRAN subroutines, EQEO and KEXP (listed in Appendixes A1,A2), were written to calculate the equilibrium d3 ta and the dependent variable E'. a. . y. . . .n ... .1: .. . . . .1. 1 .. . . .\.- In pt I.» 2: Pp; ru la 1)1 .n 4 L111. .1. 1... r . ,u. h. . . V. .#a C» a . 91.4 92 The values of the independent variables fi,('e' - 5a)M,(ES—'é S a) were the average hourly values which corresponded to the same hour for which E'was calculated. The water vapor pressure deficit (erg—ea) values were calculated using the average temperature and relative humidities and the psychrometric model of Brooker (1970), using a set of FORTRAN functions and subroutines by Lerew (Bakker- Arkema et al. , 1974) and adapted to the IBM 1130 computing system. The subroutine for calculating the saturation water vapor pressure deficits (VPDIF) is included in Appendix A3. The moisture content value in the term a2(‘US—'6a)1\—/I was aproximated by equation (5. 8). An ordinary (unweighted) linear least square estimation technique, written as a FORTRAN package for the IBM 1130 compu- ting machine, was used for estimating the coefficients. The proce- dure was applied to data of nine drying systems. Differences in systems were attributed to various forms of drying (relative position of the layer and the floor) or to different geometric forms (Table 8). Results of the estimated coefficients and associated statistical figures are presented in Table 9. The estimated parameters are divided by the standard errors (Draper and Smith, 1966) to obtain the calculated t values (Table 9). Calculated t values marked with a double asterisk (**) and a single 3! ate risk (*) indicate that the parameters were significantly higher or lower than zero at a level of 0. land 0.05 respectively. This is 93 Table 8. Characteristics of the Nine Drying Systems Drying Number Description Geometric Density System Observ. Drier Syst. Form (kg/m2) 1 66 vert.tray 1x1x5 cm 24 2 27 hor. tray 1x1x5 cm 24 3 67 vert.tray disc bars 24 4 54 horiz.tray disc bars 20 5 44 vert.drier disc bars 26 6 61 vert.drier disc bars 26 8: wings 7 13 hor.tray large chips 12 8 6 hor.tray small chips 16 9 18 on the floor 1x1x5 cm 20 a result of comparing the calculated t values with one-sided t statistics at the corresponding degrees of freedom. (Steel and Torrie, 1960). The multiple correlation coefficient and the F values (Draper and Smith, 1966) were compared with corresponding values of standard statistical tables with the appropiate degrees of freedom.Single and double asterisks indicate the adequacy of the model (Steel and Torrie, 1960). The test statistics were particularly useful in developing the empirical model. No t values were calculated for the ao coefficients because the routine utilized did not provide this option. Some of the regression 94 Table 9. Ambient Coefficients and Associated Statistics Drying Number Estimated Stand. Calc.t Mult. F System Observ. Parameters Error Value C.C. value 8.0 = 0.0476 - - 1 66 a1: 0.0181 0.0044 4.112** . a2 =-0.0023 0.00049 -4.688** 0.708** 20.85"* a3 = 0.0075 0.00122 6.132 a0 =-0.0026 - — #0:: a1: 0.0119 0.00326 3.631 2 27 a2 =-0.0018 0.00046 -3.914** 0.881** 26.71** a3 = 0.0069 0.00087 7.889** a0 =-0.0138 - - 3 67 a1: 0.0248 0.00515 4.812** a2 =-0.0051 0.00051 -9.978** 0.939** 155.7** a3 = 0.0131 0.00083 15.812** a0 =-0.0046 - - a1=-0.0011 0.00272 —0.366 4 54 a2 =-0.0022 0.00039 5464’” 0.947** 144.74** a3 = 0.0086 0.00057 14.895** a0 =-0.0023 - - a1 = 0.0535 0.00767 6.975** 5 44 a2 =-0.0044 0.00101 -4.347** 0.905** 60.23** a3: 0.0101 0.00133 7.527** a0 = 0.0178 - - a1= 0.0144 0.00978 1.473: W 6 66 a2 =-0.060 0.0112 -5.369"‘"‘ 0.774** 28.40““ a3 = 0.0128 0.0175 7.277M 30 - 0.0702 - - a1: 0.0330 0.01705 1.935 7 6 a2 =-0.0007 0.00269 —0.268 0.957** 6.74 a3 = 0.0010 0.00214 0.449 8.0 = 0.1279 - '- a1 = 0.0475 0.00929 5.114"* ‘ . 8 13 a2 =—0.0022 0.00077 -Z.804 0.96*"‘ 35.41” a3 = 0.0017 0.00082 2.02* a0 = 0.0077 - - 9 18 a1 = 0.0417 0.02272 1.836* a2 =-0.0009 0.00089 -1.022 0.641 3.26 a3 = 0.0026 0.00162 1.580 ‘ 95 coefficients of systems 4, 7, 8 and 9 were not significantly different from 0 at level of 0. 01 because, most likely, of the small number of degrees of freedom. The confidence intervals for these coefficients were relatively imprecise. The average coefficient of determination R2 was 0. 72. A R :1- (5.10) *5 (Yr .1? )2 where Yi represent experimental E' values calculated by equation (4.1), 91 the 13' values calculated using equation (5.9), and g the average Yi values. This analysis indicates that 72 percent of the changes in 12' were explained by the linear model. The remaining 28 percent should be attributes to (a) improper model, and (b) to stochastic errors which occurred in the field measurements. A discussion of the results of the regression analysis is aided by writing the model in the form 12': 3.0+a1+a2‘(eS - ea)M+a3(es - ea)+€' +‘ e" (5.11) where Q ' represents the errors due to the lack of fit of the model and 6 " refers to pure errors which might be listed in a suggested order of importante as follows : (a) measured errors in the dependent variable I?’ (Figures 16 and 17) due to slow drying responses with respect to the a verage ambient changes, (b) weighing errors due to losses of the Prod net in the form of "fines" during the experiments and during the dry .7. I. . I V. .F. .1. .6» u a. 0‘6 ,. .u 96 . matter content determination, (c) errors of the different drying effects due to wind direction, not accounted for in the measurements, (e) errors caused by measurements made at intervals different from the fixed one hour interval, (f) errors due to non-homogeneous cassava product, (g) errors due to the inaccuracy of the Meq model, (b) human errors in taking the measurements, and (i) errors of calibration and accurary of the instruments. These errors violate some of the standard assumptions made in the ordinary least squares estimation with respect to the value of the estimated parameters and the statistical tests (Kmenta,1971). The least squares assumptions and a brief analysis of the violations are: l. Homoskedasticity,which states that the variance of the errors is constant expected (6 12 2 0'2)] , did not strictly apply because the experimental errors were known to be higher at low moisture content values, when the difference (M - Meq) approximated zero and when more "fines" were lost. 2. Nonstochasticity of the independent variables [expected (xi) 2 xi] was slightly violated by the time measurement errors. 3. Non-autoregression [expected (6i 6 k ) = 0] for different measurements 1 and k. This assumption, also known as errors C O I‘related , errors not-independent, etc., (Beck, 1972) ,did not apply. N “’ L1 rtrimulative errors, a particular type of correlated errors,occurred 97 because any loss of the product at the measurement 1 affected all subsequent measurements. Also a timing error made at the measurement 1 did cause a compensating error at time i + 1. (Figure 17). These violations plus the assumption that the density (D) and geometrical properties (P and S) did not affect the estimation of the ambient parameters limit the value of the statistical tests regarding the estandard error, and consequentially the confidence intervals. An alternative method of testing the value of the statistical tests and the confidence intervals was chosen in this study: the predictions of the model were compared with the experimental data in all ranges of the independent variables. The tests are described in the first section of Chapter VI. 5. 3. 2 Layer Densities The estimation of the ambient parameters assumed product uniformity in their density and equality of the particle geometry. In this section the experimental data is analyzed by fixing the geome- trical variables only. The fourth of the right-hand side of equation (5. 1) was fixes to 1 . Under these assumptions, equation (5. 1) can be written in its finite form as 98 where -1 '15. = K (5.13) a0 + 8‘1; + a2(é-S'éa)-I:’I—+ a3(és'éa) I—(' values were calculated by equation (5.9). The new parameter estimation problem (equation 5.12) is one of simple linear regression, Partial information of the imput data is summarized in Table 10. The results are shown in Table 11. All the test statistics were shown to be significant at the 0. 01 level. Two observations are worth noting: (a) the simplicity of the density linear factor does not mean that there exists a linear relationship between the drying rates and the layer density because of the moisture ' content depending term in the right-hand side of the equation (5.1). In thicker layers, for example, the average moisture content is higher than for thinner layers, if all other conditions are equal. This weights more the a2(‘§s - Ea) M term, and the apparent linearity does not hold, (b) the linear density term was nearly the best one that could be given In effect, when a parabolic function (a4+a5D + a6D2) was used, no improvement in the fitting was achieved, as it is indicated by comparing the F values of Tables 11 and 12. 5. 3. 3 Geometric Properties Equation (5.1) in its finite-Lapproximation form is 99 Table 10 Density Characteristics for each Drying System Drying Density Number Descfiption Geometrical System (kg/m2) Observ. Drying System Form 16 29 l 20 83 vertical tray 1x1x5 cm 24 63 28 38 213 16 22 2 20 94 hor. tray 1x1x5 cm 24 26 142 16 53 3 24 49 vertical tray disc bars 28 36 177 12 6 . hor. tra small chips 7 16 __6_ Y 12 8 6 8 12 13 hor. tray large chips 16 6 25 9 8 18 on the floor 1x1x5 cm 20 8 26 Table 11 Density Coefficients and Associated Statistics / Drying Estimated Standard Calculated Mult, C. F System Coefficient Error t value Coeff. value 1 a4=1.5396 - — 38.5** >:<* *4" a5=-.0221 .0357 -6.205 100 (l Table 11 Density Coefficients and Associated Statistics (Continued) Drying Estimated Standard Calculated Mult. C. F System Coefficient Error t value Coeff. value 2 a4=2. 3996 - - >:<>:< > a5=-.0615 .0891 -6.890** .504 47.59"?k 3 a4=l.5585 - -** k a5=-. 2526 .0405 -6. 233 .426" * 38.85** a 23.2536 - - 4 >1: 33* 7 a5=-. 1409 .0226 -6.238** .892* 38-92 8 8431.8266 " " >1‘* a5=-.0695 .0056 -12.399** .933** 153.68 34:2. 6564 " — '<'< >'<>’ 9 a5=-.0838 .0139 -6.051** .777” 36.62' “ Table 12 Density Coefficients of a Parabolic Function Drying Estimated Standard Calculated Mult. C. F . System Coefficient Error t value Coeff. value 514:1. 7838 - " *9. ' >'.<>:< 1 a5=-.4497 .4075 -1.103 .393 19.35 a6: .0513 .0912 .562 R'” = a6 + a7P + a8S (5. 14) where E111 K” (5.15) 84 + aSD S is given by equation (5. 2) . The porosity of rectangular bars (Figure 21) was fitted to the equation 101 P=(0.420+0.016L)(1.1609-0.144mn (5.16) where L is lengthof the bar and W the thickness of the square section of the bar. R" values were calculated by equation (5.13) for drying systems 1 and 2 (Table 8). During the R'” calculations no restrictions were made. The coefficients a6, a7, and a8 were estimated by ordinary multiple linear regression. Characteristics of the input data and the estimation results are given in Table 13. The previous discussion of errors applies as well to this final stage for the estimation of parameters. In effect, all the violations to the standard assumptions that were mentioned in the previous stages are applicable to this case. Table 13. Geometric Coefficients Characteristics and Statistics \ Drying Number Estimated Standard Calc.t Mult. F System Observ. Coefficient Error value C. C. value 362‘100633 - - I: 3k)? I), 1 613 a7: 1.8630 0.386 4.831** 0.614 184.8w a8: 0.5245 0.028 18.677** 363-0. 8093 - - .“ 1 >::* ** 35* 2 232 a7: 2.6647 0.394 6.761 0.506 39.4 a = 0.2125 0.027 7.912** 8 IV ANALYSIS 6.1 Comparison of Experimental and Calculated Moisture Contents A complete testing of the mathematical model is given in this section in order to answer the questioned properties of the confidence intervals of the estimated coefficients of the model given by the equation (5. 1) . An explicit moisture relationship was desirable and readily obtained by using equation (5. 1) in its finite form: t : - a0+ a1u+az(es- ea)(__12___) +a3(es- ea) a4+ a5D X Mi+1+Mi (6'1) soving for Mi+1 withAt = 1 c1 (c3 - 4c0c2 )O'5 M1+l : " + - (6.2) ZC 2C0 0 where C0 = 0.5b1b2 CI: 0.5 bObZ + b1b2b3 +1 c2 = b0b2b3 - Mi and b0=a0+a1u+05a2(‘éS - ea) Mi + a3 (es - éa) b1 Z0.532 (és " éa) 102 103 b3 :O.5Mi - Meq A subroutine (LAYEQ), listed in Appendix A4, was programmed to perform the moisture calculations in a discrete hourly form. The single subroutine was made applicable for all drying systems by giving a selected value of one to the non—estimated parameters a4 and a6 and zero to the non-estimated parameters a5,a7 and a8. The calculation procedures were: 1. 40 the equilibrium moisture content and the saturation water vapor pressure deficit were calculated by the subroutines EQEQ and VPDIFas function of the given average hourly weather conditions. the first moisture content values M1 were calculated as a function of the given initial moisture content M0’ the calculated Meq' the (6's - ea) values, the given average value of the air velocity during the first drying hour, the product densities, and the geo- metric properties. The apropriate set of estimated parameters was used in equation (6. 1) for the corresponding drying system. the calculated moisture content values of M1 were stored in place of M0 to be used as the initial moisture content for the next calculations, which were performed in the same form. the iterations continued until the last values of the drying day. The main computer program performed the general comparison as follows; 10 all the information necessary to identify the drying experiment was read in. 2. 3. 9. 104 field measurements were read in and some readings were corrected because of non-calibrated instruments. experimental moisture content values were calculated for the second experimental period. The moisture content values corresponding to the first experimental period (calculated with the oven set at 75° C) were read in and were normalized to the moisture base corresponding to the oven used for dry matter content determination in the second experimental period (100°C). the geometric properties of the bars were calculated. the hourly average ambient values for each drying day were calculated. subroutines EQEQ, VPDIF, and LAYEQ were called to cal- culate - using the model - the moisture content values for each hour. experimental and calculated hourly moisture content were compared in dry and wet basis, and moisture ratio forms. a last moisture content value was calculated using only average weather condition of the day and was compared with the final experimental moisture content value. a comprehensive output of the results was printed. The listing of the main program and a short example of the output are included in the Appendices A5 and A6. 105 A summary of the comparison results follows: 1. the particles lost a daily average of 54 percent of the total possible removable water. The standard deviation about the mean was 20.4 percent, i.e. , almost all the posible range of dehydration was covered. The average recorded drying hours was 6. 7 hour per day. The hourly average moisture content was 48. 6 percent, w.b. , the complete practical range of moisture content was recorded (70. 0 to 12. 0 percent, w. b. ). the coefficient of determination of the calculated moisture content with respect to the experimental values was 0.983 when the moisture was expressed on a wet basis. This means that the single model predicted 98 percent of the moisture content changes during the 1691 observations supplied from the 9 drying systems. ., the hourly average moisture content error for all obser- vation was of 2 percent, w.b. the final moisture content error calculated based on the average weather condition for the drying day was 3 percent w.b.‘ -- average value of 152 observations-- This result indicates that the enviromental conditions for each day did not vary too much. the model worked equally well for the nine drying systems. The highest hourly average error was of 2. 3 percent,w.b. 106 and corresponded to the drying system 1 (Table 8). the errors seemed to present a uniform distribution within the ranges of the weather conditions, the densities and the geometric values of the drying system. The errors were slightly higher for the vertical drying systems compared to those of the horizontal ones. the most severe tests of the model were the following compari- sons: 3. more than 1100 comparisons of moisture content values of drying systems 1 and 2 were made based on only 6 ambient parameters estimated from 133 observations. a hundred fifty— four comparisons of drying system 2 (Table 8) were made with an hourly average error of 1.5 percent, w.b. , and average drying day of 6.4 hrs. None of the experimental values was utilized for estimating the coefficients of the model. Furthermore, more that 50 percent of these observations had densities of 8 kg/m2 , which‘value was not used in estimating the density coeffi- cients. ninety-six comparison were made from data obtained at night. The hourly average moisture error was 1.6 per- cent, w.b. for 12 hours. The weather conditions were significantly different from the average prevailing condi— tions during the study. During this period a peak relative , 107 humidity of 93 percent and an air velocity of 0.1 m/sec were recorded. Typical comparison results are shown in Figures 25, 26, 27 and 28. Three curves are shown in each graph : (a) the experimental moisture content ratios, (b) the calculated moisture content ratios based on hourly average ambient conditions, and (c) the calculated moisture content ratios based on average daily conditions. This summary permitted establisment of the excellent properties of the estimated coefficients of the model and their wide applicability . The violations of the standard assumptions of least squares were not strong, and the model is adequate to predict or simulate drying performances in most practical ranges of the independent variables. Simulation is one of the main objectives of the remaining sections of this chapter and the following. 6. 2 Comparison of Different Natural Drying Systems Comparison of the performances of the different drying systems can now be made. The good model and the use of average weather conditions permit these comparisons. 6. 2.1 Simulation Computer programs were written to predict or simulate drying of the nine systems under wide ranges of environmental conditions and different layer densities. A listing of the program used for six of the nine drying systems and a short output example are included in ov’U awVH ,U ‘.I. Clo TF4 108 . Experimental 4. Calculated based on average hourly conditions Calculated based on daily average conditions O 1. 0 1.0 .9. 13 0. . ad 8 0 8 {J 5 +5 0.6 0.6 o O 80.4 March 15, 0.4 Jun 2,1973 3, Tray No 36 "Vertical drier \ .3 Drying System 1 Drying System 6 k g 0.2_ 1x1x5 cm bars 0.2 __Disc bars 5&0 0. 0 Efrorzll’lo w.bl. (av.lliourly) 0. 0 Errqr:0. 6'70, w.l:.(av.liiourly) . 1 0 Z 4 6 8 O 2 4 6 8 Drying Hours Drying Hours l. 0 .3 a: at: 0.8 _ \ C‘m ‘5 3 0.6 c: \ \ - 8 Sept.1,l973 Apr.l7(night),1973 20.4—Tray No l 0.4 Tray No 33 3 Drying System 2 "' Drying system 3 .33 1x1x5 cm bars Disc bars § 0.2_D=8;M6=48%,w.b. 0.2 D=24:Mo=40%,w.b. Error:1%,w.b.(av.hourly) '- Error:0. 3%w.b.(av.hourly) O. 0 L I l L 0.0 l l J 1 l 0 2 4 6 8 0 2 4 6 8 Drying Hours " , Drying Hours Figure 25. Comparison of Experimental and Calculated Values. 109 0 Expe rimental “’ Calculated based on average hourly conditions 0 Calculated based on average daily conditions 1.0 1.0 0.91.. \ 0.9 0.8.. x. 0.8 \ .9 007_ °\‘ 007 . *5 0'61. O 006 +- \’ 3 1 g 0.5,. May 26,1973\o 0.5 _Apr 12,1973 °\ 0 Vertical drier Tray No 33 0 2 0.4__ Drying system 6 o 0.4 _Drying System 3 f .3 Disc bars \‘9 Disc bars \ '8 0.3 __ D=25.3;Mo=40%w.b. .3 D=20; Mo=30%w.b. \, 2 Error=1.4%w.b.(av.hr) _Error l.3%w.b.(av.hr) q 0.2_ 0.2 _ 0.1 1 1 1 1 1 10.1 1 ; 1 1 1 1 1 0 l 2 3 4 5 0 l 2 3 4 5 6 1.0 Drying Hours 1.0 Drying Hours 009 I— , 0.9 0.8 r- 0.8 o. 7 f 0.7 I; 0.6 )- \ 0.6 ’ 9: Sep.l4.7 ? "Mar 21,1973 \ 8 0.5 Tray No 2 0.5 Tray No. 35 \\ *5 ‘t" Drying Sys "Drying System 4 .\b 8 1x1x5 cm bars Disc Bars ., 0-4 - D=8, Mo=6l%wb.° 0-4 _ D=20,Mo=65%w.b. S Error=l.6%w.b. \ ' Error=0. 5 % w.b.(av.hr.) 3,3 0.3,__ \ 0.3 _. o O 2 0.2... 0.2 __ 0.1 1 L 1 1 1 1 0-1 1 '1 1 1 4 1 0 1 2 3 4 5 0 1 2 3 4 5 6 Drying Hours Drying Hours Figure 26. Comparison of Experimental and Calculated Values. Av-u-oN- up-nid-utvn.1v .01--?L-Avfiz PV—ud‘Vn nay-fihfihei. V .Huo-.~ni..-A..§HI~ Moisture Content Ratio Moisture Content Ratio 1.0 0.9 N.» 110 Experimental 4- Calculated based on average hourly conditions 9 Calculated based on average daily conditions 1.0 0.9 0.8 __ Mar 8,1973 Tray No 25 ° __ Drying System 1 0.4 l.2xl.2x7 cm bars D=16;Mo=51%w.b. 0.3 H Error=1%w.b.(av hr) _ 0.2 1 1 1 1 4 0-1 0 1 2 3 4 5 6 i— Drying Hours 1.0 0.9 0.8 0.7 0.6 0.5 — ”Max-21,1973 Tray No 33 Drying System 1 x lxlx7" cm bars D=20:Mo=67%w.b. Error=3. 5%(avhr.) Figure 27. 1‘2 3 4 5. Drying Hours §\ .1. .. \§+ _ \ §+ - I \O\+\ \ {- _ Mar 8,1973 \ Tray No 6 \b __ Drying system 2 lxlxl cm bars D=16;Mo=537o w.b. Error=l%w.b.(av.hr) - — p 1 1 1 0 1 2 3 4 5 6 Drying Hours Mar. 10. 1973 Tray No 22 Drying system 1 ' 0.8x0.8x1.0 cm bars D=20;Mo= 65% w.b. Error=5%w.b.(av.hr) g \ 0.2 _. q 4 0.11 1 1 l 1 1 6 0 1 2 3 4 5 6 Drying Hours Comparison of Experimental and Calculated Values P .1 . u n... V- f, v A onc1U'aufidu. a V Univ AIIJ nal-91FZ City. A11J Pv. ad... V. P1.- rIIv un-L.U.H~.-A.H.v LUth-ustAiV‘ 0 Moisture Content Ratio Moisture Content Ratio 1.0 0.9 0.8 .7 0.6 Figure 27. 110 Experimental 4- O \. \ ° + .\+ // 1.0 0.9 0.8 0.7 Calculated based on average hourly conditions Calculated based on average daily conditions \\ c’§.\+ —. \0.6 — o \ . \ . __ Mar 8,1973 0.5 _ Mar 8,1973 \ Tray No 25 O Tray No 6 \; __ Drying System 1 0.4 __ Drying system 2 1. 2x1. 2x7 cm bars lxlxl cm bars D=16;Mo=51%w.b. 0. 3 __ D=16;Mo:53% w.b. .. Error=l%w.b.(av hr) Error=l%w.b.(av.hr) .. 0.2 ,_ 1 1 1 1 1 10-1 1 1 1 1 1 1 O l 2 3 4 5 6 0 1 2 3 4 5 6 r Drying Hours 1.0 Drying Hours 0.9 Mar. 10. 1973 Tray No 22 0'8 - Drying system 1 0.8x0.8xl.0 cm bars 0.7 __ D=20;MO: 650/0 w.b. Error=5%w.b.(av.hr) 0.6 __ . 0.5 " ”Mar21,1973 " Tray No 33 \ 0.4 " Drying System 1 \ _ a lxlx7_ cm bars \, 0.3 \ "D:20:Mo=67%w.b. \ "' \. Error=3. 5%(avhr.) \ __ 0.2 _. q 1 1 1 1 _1 0. 11 1 1 1 1 1 m- 012 3 4 Drying Hours 6 5 Drying Hours 0 1 Comparison of Experimental and Calculated Values -...u-.....x .v 1:1. .4... _nvw./— i u... ~ u»~rV--~HV .v.-.~ufl.~.~¥< Y... lll ' Expe rimental + Calculated based on average hourly conditions 0 Calculated based on average daily conditions 1 0 ( 3 1.0 o\. 0.8 .. o\§\0.8 .— o§ 0. 7 __ - 7 .— .9 +5 0 6 __ 0 6 __ \ m . *8 o 5 0 5 _ °\ 8 - . \ g 0.4 Sept 1,1972 0.4 _ Oct 17,1972 3\ a) ' '- Tray No 3 Tray No 5 \ S 0.3 Drying system 9 0.3 _ Drying Sys. 7 \. ‘3‘; " 1x1x5 cm bars Large Chips '5 0 2 D=20;Mo=60%w.b. 0 2 D=12;Mo=66%w.b. 2 ° '- Error=0.5%w.b.(av.hr) ' " Error=l.5%w.b.(av.hr) 0.1 1 l 1 1 1 LO.1 1 1 I I l 1_ O 1 2 3 4 5 6 0 1 2 3 4 5 6 1- 0 Drying Hours 1. 0 r. FDrying Hours 0.9 i__\ 0.9 0.8 0.8 4 0.7 0 7 ¢\ .9 ' » " \ *‘ + *5 Oct 27, 1972 Oct 27, 1972 \ .. ‘, 3 0.5 Tray No 8 0.5 Tray No 4 \ g '- Drying system 7 0 'Drying system 8 \ 0 Large chips Small chips 6\ 0.4 2 - D=16;Mo=64%w.b. 0'4 "D=12;Mo=65%w.b. \O 3 Error=0.5 %w.b.(av.hr) Error=l.4%w.b.(av.hr) . .33 0-3 0.3 _. o - 2 0.2 _ 0.2 .. 0-1 1 1 1 1 1 L 0,1 1 1 1 1 1 1 0 1 2 3 4 5 0 1 2 3 4 5 6 Drying Hours Drying Hours Figure 28. Comparison of Experimental and Calculated Values 112 the Appendices A7 and A8. The systems simulated are described by the computer listing COMMENT cards. The values given to the variables were : densityl : 10,25, and 40 kg/m2 wind velocity: 0. 5,1.5, 2. 5, and 3. 5 m/sec. air temperature: 5,15, 25, and 35°C air relative humidity: 40, 50, 60, 70, 80 and 90 percent Thirteen hours of a drying day were simulated for all combinations of the variables and for each system. A similar program was run to simulate all the drying systems, including those models that did not fulfil the statistical tests (section 5. 3.1). Results of these models were analyzed only for the conditions in which the experiments were performed. 6.2.2 Solar Cabinets The best performance of the solar driers is shown in Figure 13a. The solar cabinet loaded with 8 kg/mz, removed about 4 percent more of the total removable water than the horizontal tray with the same load. Simulated results were used to compare the cabinet with a vertical tray drying under the same conditions. The comparison resulted in 4 per- cent higher dehydration for the vertical tray. The difference could be {lbout _25 percent or higher if a more practical density had been used 1density coefficients for the vertical drier were estimated based on those of the vertical trays for the same product. 113 and a more common wind velocity had ocurred such as 20 kg/m2 and 2. O m/sec. A simple energy balance shows the limitations of a solar cabinet that uses only incident radiation to dry high moisture content products. From the 4.24x106 cal/m2 recorded radiation during 8 drying hours (Sept.21, 1972), about 60 percent was collected by the black surface. The estimated drying efficiency of 60 percent reduces this amount to a net of 1. 52x106 cal/m2 . About 0.58x106-calories are necessary to evaporate one kilogram of water. The cabinet, based on these figures, was expected to evaporate 2. 62 kg/m2 of water during the 8 hours but actually evaporation was 3. 84 kg/mz. Simulated results indicate that a vertical tray loaded with 25 kg/m2 and an average wind velocity of O 2.5 m/sec, all other conditions equal, evaporates about 11. 5 kg/mz. The facts that this cabinet was the best among all solar driers are explained by examining the relative position of the cassava layer be- tween the collector and the free air underneath (Figure 12) : the 10 cm distance for the collector and the contact with the air allowed the the product to use both the collected solar energy and the sensible energy of the air. The efficiency was still very low compared with the vertical tray because the air movement was restricted. It seems difficult to design a more efficient unit for natural drying of high moisture content products because attempts to collect the solar energy imply the restriction of the air circulation, which has 114 more energy available for drying the products during the early periods of the dehydration process. The cabinet drying rates for this day and for the very small density of 8 kg/mz were higher than the highest drying rates for drying yams reviewed by the author: 2. 8 kg/m2 in 20 hours (Headely and Springer, 1973) and 1. 2 kg/mz in 24 hours by Nahlawi, (1960). The drying rates of CIAT's cabinet could be increased without diminiShing the product quality by just using higher densities. 6.2. 3. Product on the Floor Figure 5 shows the drying differences between cassava bars ele- vated from the floor in perforated trays and the same product on the floor. Figure 23 shows the quality differences of the end product for the same experiment. Figure 29a shows a similar comparison by simulation with the addition of the performance of the vertical tray with the same product. The importance of the air circulation through the product is clearly evident. Ambient conditions were chosen to match the ambient conditions of one day in which the experiment of the product on the floor was run (the statistical tests were not significant for the drying system 9, see section 5.3.1). $2.4 Cassava Chips The drying characteristics of the conventional cassava chips were irlferior to those of the rectangular bars as is shown in Figure 14 and 115 2.0 1 §§~ 1.8 _- .\ \~~~§~~ (a) o. \ ~s“ 21 6 \ \ 7 ~ 0) . — .' \ ~~\a~ 1.4 o. \ \‘ f; - _. \ \ 'U \ . \ \ 111-2 .. \ 8 \. \ 1.. \ 31:0 F---on the floor ~\ E: --- Horiz.e1ev.tray "\ 30'8 —"'"""" Vertical tray ”\ 8 '\.. 00.6 _. 13:20 kg/m2 8 u = 0.5 m/sec .30.4 _ T = 30°C 3 RH = 60% 2 0.2 _ 0 0 1 1 1 1 1 1 1 1 l 2 '3 4 5 6 7 8 Drying Hours 2.0K 1.8 _ “ \~ .31) 1.6 ‘\\\ m ' \\ ( b 8 \3. ’ \ :4 l 4 ,_ \ \\ "U ‘\ ‘\ .5: 1.2 _. \. \\ 8 ‘ \ H 1.0 \ \\\ a) 1'" ‘ \\ 0“ S \\ . ---- Small chips \ ‘s *5 0 8 " Large Chips “ .3 _.._.. 0.9x0.9x5.0cm bars\‘ \ O 0.6 1’ 1 ‘\ U .‘\ 2 0.4 Horizontal tzray a "' D: 15 kg/m m .— '8 0.2 ”_l'im/Sec 2 - T = 30 C RH 40% 0.0 1 l l 1 1 l l I O 1 2 3 4 5 6 A 7- 8 Drying Hours Figure 29. Comparison of Drying by Simulation. 116 confirmed, in a more general form, in Figure 29b. The ambient conditions chosen to make the comparison are those of a drying day of the large chips. Larger chips were slightly better than small chips for drying in thick layers because of theirfirmer structure and higher porosity values. (Figures 14d arri 29b). 6.2.5 Disc Cutter Bars The efforts to produce equally efficient rectangular bars with the disc as with the manual press were not succesfull as is shown in Figure 30. The manually pressed rectangular bars were consistantly superior because they permitted air to circulate more easily and because they were more uniform in size. The differences in perfor- mance are higher in vertical than in horizontal trays. Fines, the weak structure of the disc bars, and the non uniform bar's sections make them lose the desirable aerodynamical properties sought. Multiple indirect observations showed that the disc bars performed better than the conventional chips. However, no direct experimental comparisons were made, and comparisons by simulation could not be made because of the poor estimated coefficients of'these models. The disc bars are analyzed only from a practical point of view in section 6.4. $2. 6 Rectangular bars The bars produced by the manual press were the best geometry 117 l O k 1.0K \ 0.9 '- \\\ 0'9 _ “\ \\\ \‘\ O 8 \‘\ 008 \ \ r- \\\ "' \‘x o 7 ‘\\ 0.7 \‘\ £3 0 6 0.6 \ \\ a: - ~ \ 8 0‘5 -_._,-- Disc bars 0'5 --.._._ Disc bars 5 —— 1x1x5 cm bars ___. 1x1x5 cm bars 0 0.4 .. 0.4 .— ' 8 Horizontal tray Horizontal tray 3 0.3 __ 13:20 kg/mz 0.3 __ D =20 kg/m2 .3 =O.6m/sec u=2.16m/ sec g o z __ 0.2 _ 0.1 l 1 I 1 P 0 1 1 1 1 1 O l 2 3 4 5 O l 2 3 4 1'0 R\ Drying Hours 1.0 \ Drying Hours 0.9 _\~\ 0.91—\\\ \ ‘~ \\ \\ 0.8 _. \ 0.8 .. \ \ . \ \\ \ \ O \ \\ 4': 0.7 _— \ 007 — \\‘ m \ ‘\ m \ \\ \\ +5 0.6 __ \ 0.6 __ \ 3 \ c: 8 0'5 -—____ Disc bars \ 0'5 -- ___ Disc bars \ Q ___. 1x1x5 cm bars __1x1x5 cm bars 3 0.4 0 3 _ 4;, Vertical Tray Vertical Tray 8 0.3 D: 20 kg/m‘?‘ 0.3 D =20 kg/m2 2 ,_. u: 0. 6m/sec "‘ u=1. 6m/sec 0.2 _ 0.2 __ O l l 1 J 1 1 0 1 1 l 1 1 O. 1 2 3 4 5 O 1 2 3 4 Drying Hours Drying Hours Figure 30. Comparison of bars produced by the Disc and Press 118 tested because of their drying characteristics, good handling properties and general appearance. Changes in the bar dimensions were very critical as is shown in Figure 31 and in the sensitivity study of the last section (6. 6) of this chapter. The geometrical properties were expressed by the equation. F=a6+aP+a8S (6.3) 7 where the porosity P and the geometric property S are given by expressions (5.16) and (5. 2) respectively. Expression (6. 3) was succesfully applied in the model (6. 2) for 1174 comparisons with experimental data. One way of increasing F was obtained by increasing the porosity. Higher porosities were obtained by enlarging the bars (Figure 21). No further improvement occurred after a length of 7 cm. A more effective method to increase F was to decrease the bar dimensions. Again, practical considerations restricted the procedure: (a) there exists a critical minimum characteristic length of transition between cassava bars to cassava fines. The phenomenon is related to the critical mean free path of the natural air flow through the layer, and (b) small bars with section less than 1x1 cm can hardly be made with low-cost cutting devices. This limitation does not seem too restrictive if more sophisticated type of machinery -- like industrial dicers for fruits, roots, and vegetables -- are used (FMC, 1960). The smallest particle tested in the study was a bar with the 119 l.2xl.2x5.0 cm 1.0x1.0x5.0 cm ._.--..— 0. 8x0. 8x5.0 cm 2.0K. 2.0 1.8 _\\§~\ 1.8 \ \‘~\ 3 1.6_ \ \\‘~\ 1.6 3 \ \ ‘\ .0 1.4 \ \ ‘\ 1.4 >~ - \ 3 \~. \ .J 1.2 .2 a _. \‘ \\ 1 '8 1.0 _ \ 1.0 a) s “U s *5 0.8 __ \ 0.8 G) E 2 U 0.6_D=10kg/m 0.6 a) T = 2.5 °C 5 0.4 1. RH = 40%(fixed) 0.4 ,2? u.= 0.5m/sec (fixed) g 0.2 1 1 1 1 10.2 0 1 2 3 4 6 2.0K Drying Hours 2.0 U) ’5 1.8 ¥{\ 1.8 16 1-‘ \ ,0 \\\\\ i 1.6 , \ \ 1-6 PO _ \ \ \\ Ft; 1.4 \ \ ‘\\ 1.4 .g - x \\ U ‘\ 8 1.2 _ \ \ 1.2 “ \ *E ‘ \ g 1.0 _. \ \ 1.0 8 “ 0 0.8 __ D210kg/m2\‘ 0.8 ; T235 °c \ _‘J. 0.6 __ RH 40% , 0.6 0 u = 0.5 m/sec ‘ 2 0.4 \ 0.4 0'2 l 1 1 I 10"2 0 l 2 3 4 Drying Hours F"Sure 31. (x. - ‘\\,{‘~. \\ '- s \ \ . \ c‘ \. ._ D = 25 kg/m2 T = 25 °C RH=40% u = 0.5 m/sec l l L l l l O l 2 3 4 5 6 L Drying Hours \\‘\ L—- ‘ \‘ss \ \ ‘x F— \\ \ \\\ , \ ‘x __ . \\ \\ \ ‘\ x \\ F \‘ \ _. \ \ D-25 k 7— ‘ ._ - g/m ‘ T : 35 °C \‘ __RH=40% ‘\ u=0.5 m/sec l l l 1 I L Drying Hours Comparison of Rectangular Cross Section. 120 dimension 0. 8x8x1. 0 cm (P=O.456 and S=4.125). The particles were tested in a vertical tray with D=20 kg/m2 on March 10,1973 (Figure 27d). This was the highest desorption rate during the study, higher than the dehydration of the black dusted particles on a good sunny day (Figure 13c) . In both experiments the individual particles reached approximately the same moisture content ratio but the black cassava layer had only a density of 8 kg/m2 . Figure 31 shows the importance of the section of the bars for two densities and for two ambient conditions. 6. 2. 7 Vertical Driers The vertical drier was a commercial extension of the scaled vertical trays. Simulated performance of the two driers,together with the vertical drier modified with the wings, are shown in Figure 32. Two main conclusions can be be made from the graph: (a) the plain vertical drier has an advantage over the trays, and (b) the plain vertical drier has an advantage over the modified drier. Both conclusions are very practical because they result in reduction of cost in natural drying of cassava. The better performance of the vertical drier over the small trays can be attributed to smaller effects of the big, flat, and porous plate in changing the air current direction due to higher cohesion forces of larger air masses. Also, the larger the flat plates, the more air turbulence exists when the air flow is parallel to the plates. Higher turbulences result in Moisture Content Ratio 121 1. O 0.9 O. 8 O. 7 O. 6 0. 5 0.4 _____ __ Vertical Tray _ __ Vertical drier modified with wings \ —---— Vertical drier 0. 3 Disc bars D=25 kg/mZ u=1. 5m/sec T= 30 °C RH=60% 0. 2 1 L 1 1 0 2 3 4 8 Figure 32. Drying Hours Vertical Drier Performances Moisture Content, decimal, dry basis 1 122 w 2.0 L. ~ 1 9 _§:'\.,\ 1 9 \\:>‘ o . °'.\ F \. \.'\‘\ 1 7 \ \\ _ \. \.., \\ \ \ \x 1’6 r- .\ \ .3. \\ . \ \\\ l 5 '- \. \-.. \\\ \ \ \'- ‘\ 1.4 \-. ‘\ - \ \ \ \ \. \ l 3 \ ‘\ — \ '-\ ‘x - \‘ 1 2 t- \. °\\ \\\ \ \ Drying SYstems \ \ 1.0 _ ' '° \ \. \ 0.9 __ \. \ \, 0.8 _ ————— Hor.Tray 1x1x5 cm Bars \-\ .\. 0. 7 _ mum-m-Vertical Drier, Disc Bars \ \ 0.6 ___. _Vert.Tray l.2xl.2x5 cm bars '\ \ 0.5 _____ Vert.Tray, 1x1x5 cm bars 0.4 " u=1.5 m/sec 0.3 T=25.0°C " RH: 70.0 070 D=25k m?- 0.2 _ g/ 0.1 _ 0'0 1 1 1 1 1 1 1 1 1 1 1 O 1 2 3 4 6 7 8 9 10 ll 12 13 Drying Hours Figure 33. Comparison of Performances of Drying Systems 123 higher heat and mass transfer (section 2. 7. 3). These implications are more important than the disadvantage of the drier height (2 meters). In fact, the product dried slower at the top of the drier because of the diminishing effect of the moisture released in the bottom and central parts. The released water vapor moves upwards because of the buoyancy forces caused by concentration differences (section 2. 7. 3). The phenomenon of slower drying in the top was observed by the color gradient established along the height of the drier in two experiments when the weather conditions were poor. The wings do not accelerate drying as was expected because (a) when the wind is blowing along the plane of the drier, the wings obstruct its movement, and (b) the beneficial effect of a percentage increment in wind velocity through the layer, when its direction is perpendicular to the drier, is not very large (as is shown in section 6.6). Figure 33 shows a more complete comparison of the vertical drier with wings loaded with disc bars and other drying systems. In summary, the vertical tray with neat rectangular bars dimension 1x1x5 cm is much more efficient than the vertical drier. In turn, the vertical drier is slightly superior to the tray with bars of dimensions l.2xl.2x5.0 cm. 6. 3 Thick Layer Drying Eguation Having tested the goodness of the drying model in its finite form and the accurate results obtained using average daily weather conditions, 124 it was desirable to integrate equation (5.1) to be applicable for any pro- cess time. Equation (5. 1) can be written in the form dM f1 f0 =f2f3(a4- aSD) dt (6.4) M 4—M +_ f2 f2 where f0 = [a0 + alu + a2(eS - 6a)] Meq f1: .. [a0 + alu + a3(e53 - ea)- a2(eS-ea) Meq f2 = - a2(es - ea) f3 = a6 +a7P +a88 or in the form dM 6 =(g+g D) dt (.5) (M + go)(M + g1) 3 3 where f1 so =-—- - g1 f2 2 0.5 0 5.11. _f_‘_ —4_{9_ f 2 g3 = a‘(af2f3 which can be integrated by partial fractions 30(M0+g1)-g1(Mo+so) exp [(gl-goxgz + g3D ) t] (6.6) M += J -(M0 + g1) + (M0 + g0) exp [(gl-go) (g2 + g3D ) t] 125 or solving for the density D M+g1 MO+ g0 g2 D: — (607) where all symbols are the same as above: Expression (6. 6) is an empirical thick layer drying equation for cassava, valid for (a) the total range of moisture content, (b) fixed or variable ambient conditions, (c) all drying systems, (d) variable ‘ dimensions of the rectangular bars, and (e) variable layer densities. The accuracy of equation (6. 6) with respect to the finite form (5.1) depends on the discretization or truncation errors (Carnahan et al. , 1969) created in the approximations given by equations (5. 7) and (5. 8). Although an analytical expression for the truncation errors could be calculated based on the Taylor expansions of both expressions, a direct comparison using equations (5.1) and (6. 7) is preferred in this practical study . The comparisons are given in section 6.4. A preliminary test of equation (6, 6) was made by applying it to a deep bed drying experiment consisting of a plexiglass cylinder of about 15 cm of diameter and 25 cm in height, filled with cassava slices of about 0.5 cm thickness subjected to forced air at 23. 8 °C, 65 percent relative humidity and approximately 10 m/sec under controlled conditions. 126 Experimental average moisture content values were used to calculate the drying proportionality IE values (equation 4.1). The relevant coefficients of the model (5. 1) were estimated in the same way as described for the natural drying analysis in section 5.3-1. Non—esti- mated parameters were fixed to values of one and zero in order to use equation (6. 6) unchanged to predict the bed average moisture content values (Figure 34). The good agreement between experi- mental and predicted values tests, once more, the goodness of the model, but the simple equation is not adequate to predict general performance of deep bed drying. The residuals (Figure 34) are all of the same sign. This is explained by the cummulative type of errors (Beck, 1972) found in the residuals of the .12 values. In effect, the sign of these errors changed only in about 10 hours of the drying process (Figure 34). Other discussion relevant to the practical value of equation (6. 6) follows. Equation (2. 7) with proportionallity "constant” given by equation (2.8) is a particular case of equation (6.6 1) when (a) it is applied to a thin layer, (b) the humidity of the air does not effect the drying process (only approximatelly at high air temperatures), (c) air velocity does not affect drying (only true when convective transfer coefficient is infinite). Under these conditions equation (5. 1) takes the form de dt =a3eS(M-M (6.8) eq) 127 __ Experimental 0.1 ,_ o .H Calculated *3 0.08.... A Dd § 0.06- C A 8 T: 23.8°C \ 8 0.04_ 3 RH=65°70 .Y.’ o 2 0.02_ 0.01 l 1 1 1 1 I 1 1 0 4 8 12 16 20 24 28 32 Drying Hours Figure 34. Cassava Deep Bed Drier 128 where e the saturation water vapor pressure, is given by the 8’ Clausius-Clapeyron equation (Lay, 1963). C12 e : di exp( _ ) (6.9) 3 Tabs No functional relationship for the changes in the diffusion coefficient and shrinkage of the cassava bars were used to derive equation (6.6). Diffusion coefficients decrease with moisture content as the dimensions of the bars do. Equations (2. 3) and (2.5) suggest that the two effects are dampered. The practical results obtained justify assuming constant diffusion coefficients and no shrinkege . 6.4 Maximum Density Allowable This section is devoted to (a) developing simple graphs which provide the information needed to select the maximum density which can be dried without quality deterioration as a function of the drying conditions of the first day of drying, (b) studying the influ- ence of the indep‘endm’t variables on natural drying, and (c) compar- ing the drying systems from a practical point of view. The quality criteria established by deterioration observations (section 4. 7) were introduced in the model by fixing the initial and final moisture content values. Initial moisture content of cassava was assumed to be 66.67 percent,w.b. (A sample mean of 66.10 129 percent,w.b. and a standard deviation = 1.6 percent were calculated from 126 observations). The final moisture content was fixed to 50.00 percent, w.b. for the untread cassava, and 54.00 for cassava dipped in alcohol solution. Equation (6. 7) was solved for a wide range of the independent variables. A FORTRAN subroutine (CRITD) was written for this purpose. A computer main program controlled the calculations. A listing of the subroutine, main program and a example of the output are included in Appendices A9, A10, and All. Results for the vertical drier with disc bars and an average wind velo- city of 1. 5m/sec are summarized in Figure 35 for different effective drying hours during one day. The effective drying hours depend on the geographical location and the season of the year. Figure 36b was developed for different combinations of air temperature, humidity and velocity. Eleven effective drying hours were assumed to be a reasonable drying time for the tropics. The x-axis of Figure 36b is the saturation water vapor pressure deficit which is obtained from the average tempera- ture and relative humidity (Figure 36a). Equal values of satura- tion water vapor pressure dificit can be obtained from different combinations of temperature and relative humidity and consequently, for different values of equilibrium moisture content. This originates a maximum error of 3 kg/m‘Z from the reading of Figure 36b ( The maximum differences due to differences of the equations (5. 3), (5.6) 130 A: *1”. mpsom METAMQ .wogo:< KSECMQ Esgwxmz mm mo EEJEGov opdmmoum pong, .833 0H m o v M NH .mm 3:3 .oom\E m4 0 5 mumn 0mg fir,» aware. .w “3.36 fidofiuo> ON mm om mm ow may om mm 2111/8» ‘Aqisuaq IsA'erI Maximum Density kg/m2 Air Temperature ° C 40 35 30 25 20 15 10 5 Saturation Water Vapor Pressure mm Hg Figure 36. Maximum Density Allowed. Weather Conditions 132 was 1 kg/m‘Z in the same range of the independent variables. Results of the maximum allowable density were used to investi- gata the order of magnitude of the truncation errors due to the appro- ximations implied by equations (5. 7) and (5. 8). Nine comparisons between fixed density values using equation (6. 2) and calculated densities from equation (6. 7) , for the same independent variables, gave an average error of only 0.2 percent. Truncation errors were therefore, negligeble. The same computer program was used to compute the total number of hours necessary to dry the product as to 13 percent,w.b. , or 1. 2 times the equilibrium moisture content (in case value was higher than the specified 13 percent value). The results obtained and the practical observation made during the study indicate that the total drying process, for maximum density designed layers, occurs approximately during three or four days. Curves of the maximum allowable density also permits practi- cal comparisons to be made of the drying systems. Figure 37 shows the performances of 6 different drying systems. Wind velo- city was assumed 1. 5 m/sec. The following conclusions are drawn: 1. The vertical trays allow drying of at least 15 kg/m2 more cassava bars that the horizontal trays. 2. The clipping of the product in the alcohol solution increases the allowable density from 5 to 10 kg/m2 . 133 .mEBmKAm wGTCD . 60302.4 .35200 858332 .wm 03.3mm mm mo ES #3330 0pdmm0ua Road; ~30? A: 0H NH 510 w w o v N o _ _ . _ _ _ _ xx _ \ l...l mama Eu mu: «A Hayfiumuom 9:3 036.33.23/ 111111 I 9:3 80 03 .zxm .2 3:20.063, Ill made. 00% .mwcwkfiw .0qu .20? Il1||1 c0330...“ 3:030 5 @256 mama ommviwcwg 0w .0qu ~003M0> Illl nude. 50 mxHxH .>0uu.uu0> musofi waffle 039.0030 Han» o0m\8 m . Hus O .--1 L!) 0-0 cm mm om Ln M ztit/Bx ‘Aqisusq Jsfieq O V!" in ‘3‘ om. mm 134 3. the vertical drier allows more drying than the vertical trays, the amount depending on the weather conditions. 4. the disc bar performances are inferior to the 1x1x5 cm bars but approximately the same to the 1. 2x1. 2x5. 0 cm bars. The above points on maximum allowable density assume that the average weather conditions are known or can be predicted. Since weather prediction at present is not practiced in the developing coun- tries, safer densities should be used. The problem is a subject of a simulation study based on risk functions and benefit-cost relationships. 6. 5 Limitations of Natural Drying Figure 36b shows the range of environmental conditions in which it is not feasible to dry cassava without deterioration for a fixed velo- city. Similar curves can be make for other values of velocity. The product might or might not reach a moisture content low enough for long storage, after the recommended three days, because of hygros- copic relationships (Figure 22). Solar collectors seems to be very adequate to obtain the supplemental heat needed. 6. 6 SensitivityAnalysis Based on Maximum Densities Sensitivity analysis has in engineering equivalent importance to that that of the elasticity in economics. In fact, the mathematical relationships are the same but the results usually expressed in different manners. The sensitivity analysis applied to the maximum density allowable 135 to dry without deterioration is used in this section to study the importance of all the independent variables in the process of drying of cassava naturally. The analysis provides also adequate answers to the very practical questions (a) under a typical weather condition what would be recommended to increase the maximum density, or (b) what would be the relative degree of improvement under several wether conditions. Sensitivity coefficients Xi of a function h with respect to the variable x- are defined as the first derivates of the function with respect 1 to xi (Beck, 1972). x.% 19x1 The coefficients measure the change in the function caused by a (6.10) change of the independent variable. In order to compare the sensitivity coefficients of one function with respect to several independent variables they are expressed in a normalized or percentage form of the indepen- dent va riable : _ 9h _ ”9h x. 1 Xi (6.11) ' A FORTRAN program was written to calculate the sensitivity coefficients of Drn with respect to all independent variables, and ax for each of the drying systems. The coefficients are : 136 9Dmax ,.; ODmax gDmax oDmax XL=L———-—- E W=W —— XT RH = T Xu: _— ?L 2 Q W 7 ’ ’3 T 9 ’3 u (6.12) Finite approximations of the derivatives were preferred to the analytical expression. The geometric properties of thee rectangular bars were written in a subroutine (DIMEQ) to facilitated the derivative calculations (See Appendix A13) . Some practical considerations enter in calculating the sensitivity coefficient with respect to the air tempera- ture,Changes in this variable asually result from modifying the solar absorptance of the surfaces surrounding the drying system. In this process the air temperature increases at constant absolute humidity, i. e. , the temperature increases and the relative humidity decreases simultaneously. The calculations of the sensitivity coefficients were made assuming this kind of change with the aid of the psychrometric model written in the VPDIF subroutine. Evaluation of the sensitivity coefficients were made at different and representative values of the indepandent variables. The computer main program listing, and a result example are included in the Appendices A12 and A14. Results of the sensitivity analysis are summarized in Figures 38, 39, and 40. Figure 38 compares the sensitivity coefficients of four typical combinations of temperatures and relative humidities for four values of the wind velocity. The chosen "pivot" drying system is a Sensitivity Coefficients , kg/mz Sensitivity Coefficients , kg/mZ W ___—X)? \ —"'_"’ L \ -. x \ L10 - \ 20 200 \\ u=0 Sm/sec u=1.5 m/sec 175 __ \\ 175 \\ W21. 2 cm \x \ 150 __ \ L=1.5 cm 150 \\ \\ (fixed) \ 125 ‘ 125 \\ _. \ \ \ \ 100 \\ 100 \\ >— \ \ \ \ '- / \ \ \ / \\ \\ 50_ \Z“ 50 /'—-~\\ \ I \‘~ // \ \s‘ 7‘“ \ 25 ._ \“ 25 /'n..,. ~.\. --“--..._ ~-.- . "’~...... \ 0 l 1 "-|---...... 0 l 1 1""l 5 15 25 35°C 5 15 25 35°C 90 8O 60 4070RH 9O 8O 60 40 070 RH 200 ,_ 200 175 _ u=2.5 m/sec 175 u=3.5 m/sec 150 150 h. x \\ 125 _ \\ 1255__ \\\ \\\ 100 .. \\ 1.00 \\ \\ \\ \ \ 75 __ \\ 75 \\ \ \\ \ \ . \\ \\ 50 ._ \ 50 ‘x / q.— — —§~\ _ \ - 2' ~~~~~ “ ._ M,t / -~-:-:-~:\“\ / .~‘.-::‘~\_- \ 0 J 1 l “T 0 1 1 1 ~"‘1 5 15 25 35°C 5 15 25 35°C 90 80 60 40%RH 9O 80 60 40%RH Figure 38. Sensitivity Analysis, Typical Weather. 138 Pivot conditionsz‘u=1.5 m/sec2-;T=25°C; RH 60%;L=5cm;W=1. 2 cm ............. X _-(_Y.erti<=a1 Tran.-- _.__._..___ l W XT Xu XL; I 200L 200 __ [.9 N s. 3" E 175 175 ,’ DD _- F' a I M ' I a; 150 _ 150 __ I E’ ,’ ~93 125 125 I U r— - I E "s. I, 8 100_ 24/00 __ ,’ U , / 3‘ // . 1’ .g 75 __ ,I’ 75 __ I” r; / ’ I?) 50 ’l 50 I” s: - / -,/ an / U) ,l 5 25 / Z _\ / _ .—-—- / / _.... ._"‘"‘.:_:,\ ___. 1::._._-_... 0 ’1 1 1 1 ~E“ 0 i 1 1 1 1 5 15 25 35 45 55 65 75 85 Air Temperature, °C Relative Humidity, % ' N E m 200 .. 200 .- b4 - 175 175 m _- 3‘3 1‘ 3 150 __ 150 _ E g 125 _ 125 _ U o r? 100 _. \ 100 __ > \\ -... '3 \ ‘5; 75 \\ 75 c: "" s — .. a) \\ ””””” m 50 ’_ ‘\\\ 50 __ —-"" 25 “25 1— r- \. 0 h“ -— ‘1:.:,__ O ___. ___—‘—'~c.— {’1 '1 1 1“ 1 1 1 L 0.5 1.5 2.5 3.5 1.5 5.0 Wind Velocity,m/sec Bar Length,cm ' Figure 39. Sensitivity Analysis. Independent Variables X ___ W ___.— X)? ---—--~~ u NE 200 __ , Z 200 _ I \ Vertical tray ‘Horiz. Tray 20175 _ l.2xl.2x5 cm bars// 175 l.2xl.2x5 cm bars/ a; I/ 15 / *" 150 O —— / - u / E 125 ’/’/ / 125 — / o _ 8 v” / u=1.5m/sec / >100 .. T=25°C 100 .._. E L 5cm / E 75 __ W=1.2 cm75... / g 50 / (fixed) / // / ,I 25 ” 25 / a" ’ ’I’ r—i “..a"" _-—-.‘-” ”” 0 T 1 1 l 1 L - o 1----+—-“l' 1 l 1 4O 50 60 70 80 9O 4O 50 60 70 80 .90 Relative Humidity, % Relative Humidity, ”/0 NE200 _ / 200 1.. E175 L. Vert, Tray :175 Vert. Tray / '5‘ Disc bars / 1 — Disc bars " I 3150 1150 / C‘. —- / I .. .2 ’ ’ .2125 ’ 125 ’ a: — / ,: - g I 0100 __ / 1' 100 _- § / .’ / Z 75 __ I 75 __ .3 / 1’ / I 5 50 _/ ’l’ 50 .... ‘ / U) 25 _- a” 25 _- ‘L’ ” ‘-"’/" ””” v 0 1 1 1 1 1 1 0 'T'""'1' l 1 1 l 40 50 60 70 80 9O 40 50 60 70 80 90 Relative Himidity,% Relative Humidity,% Figure 40. Sensitivity Analysis. Drying Systems. 139 140 vertical tray with rectangular bars 1. 2x1. 2x5. 0 cm. air temperature of 25 °C and relative humidity of 60 percent. The sensitivity curves show that the order of effectiveness of the improvements is: (a) reduction of the bar section, heating of the air, reduction of the bar length, and increment of the wind velocity. It might appear surprising that the least effective form of increasing the maximum permissible density is achieved by increasing the wind velocity, but the result is understood by interpreting change of Dmax caused by the change of the wind velocity in percentage form, as the coefficient was calculated. Consider, for example, air at 30°C, 65 percent relative humidity, and 0.5m/sec. This gives a (es - ea) value of 11 mm of Hg. The Dmax obtained is 30 kg/mz. The same increment could be obtained by heating the air 2 °C . The percentage increment of the air temperature es 5 percent, while the percentage of the wind velocity is 200 percent. Figure 39 compares the sensitivity coefficients calculated as function of the different values for each of the four independent varia- bles. The pivot drying condition is a vertical tray with l. 2xl.2x5. 0 cm bars subjected to air at 25 °C, 60 percent relative humidity and l. 5 m/sec of wind velocity. It is clearly shown from this figure that the first attempts to increase the efficiency of the drying system should be directed to reduce the bar section and second, to heat the air with an appropriate surrounding floor. The conditions most 141 susceptible to improvements are those of high humidities. This finding can be generalized in the sense that for a given system higher sensitivity coefficients indicate low performances due to the .asymto- tic form of the maximum density functions (see Figure 35, for example), Figure 40 compares the performances of four drying systems based on the sensitivity curves. Curves (a) and (b) show that for a vertical tray, reduction of the bars section is the most effective improvement . For horizontal tray, however, heating of the air is the best choice. Curves (c) and (d) show that the performances of the vertical tray and the vertical drier are similar. VII COST ANALYSIS Cost analysis of cutting and natural drying gives the relative economic efficiency ibr the different systems. This subject is very important since (a) the most efficient methods are not being utilized at present and the drying systems are basically different with respect to the capital and labor inputs, (b) the selection of a given drying system will be determined by the availability of the resources of the entrepreneur. This study, although not designed to perform cost comparisons of commercial types of operations, provides the preliminary infor- mation needed to estimate and to discriminate, with respect to the inputs, the main costs involved in the processes of cutting and natural drying. Mathematical simulation is again of paramount importance in cost estimation since average weather conditions will determine the maximum layer densities -- minimum cost -- for each of the methods of layer drying . Natural energy to dry the product does not involve any cost. Three types of natural drying systems are analyzed : (a) drying on concrete floors, (b) drying on elevated and perforated trays and (c) drying in vertical driers. The following are given as facts and assumptions in order to 142 143 provide meaninful comparisons between the systemszl 1. the cassava particles are produced by the disc cutter. 2. drying rates for commercial drying operations are the same as-those of the individual experimental models if (a) stirring of the product is performed continuosly by one man on concrete floors, (b) the horizontal trays or vertical drier are separated by a distance equal to their lengths. 3. no risk functions are considered . This implies the use of a common safety factor in selecting the maximum density recommended by the simulated results (sect ion 6.4) . 4. the vertical type of drier allows 15 kg/m‘2 more drying than the horizontal elevated trays and 25 kg/m2 more than the system of drying the product on the floor. This assumption is a conservative estimate for the vertical drier and is based on simulated results of maximum densities permissi- ble for different weather conditions (section 6.4). 5. cost of the driers per unit area of the drier do not depend on the drier sizes. 6. total drying time for each operation is of three days (section 6.4) . Costs of further drying (if it is needed) to obtain safe moisture content values for long term storage (section 6. 5), are not considered. 7. five hirdred. kilograms of fresh cassava are loaded on Mondays, 10. ll. 12. 13. 144 Tuesdays,Thursdays, and Fridays during 48 weeks of the year. This gives a total of ninety- six tons to be pro- cessed per year, the production of a farm of about 5 ha. The drying capacity of the system should be 1500 kg/week. the vertical drier includes the roof cost. rent of land'for drying is not considered because (a) there is no experience to estimate the real area needed, and (b) these costs are known to be small compared with the drier costs for the same area. two densities, 5 and 15 kg/mz, are fixed for the concrete drying system. This gives (assumption 4) 20 and 30 kg/ m2 for the densities of the horizontal trays, and 30 and 40 kg/m2 for the vertical drier. The low densities (for all systems) indicate poor drying conditions due to the weather. The high densities indicate good weather condi- tions. costs are based on current material and labor prices in the Cauca Valley, Colombia (one dollar equal to 23. 80 pesos, 1973 exchange rate). Figures are given in dollars. the required labor for drying is assumed for each system in Tables 15 and 16. Daily wage is $1.00/day. depreciation costs are different for each drying system. Actual values are given in Tables 15 and 16. Interest charge is 12 percent per year. 145 7.1 Cutting Data Cuttingcapacity (two men working) 96,000 kg/year l man-days Labor = x- ___x 120 kg/man—hou. 8 man-hours machine utilization 1 probable life of the disc cutter cost of cutter annual maintenance cost (6%) 7. 2 Drying Data 7. 2.1 Concrete Floors concrete floor (1:2:3), 10 cm thick probable life labor in handling and stirring 7. 2. 2 Horizontal Trays tray cost probable life ma intenanc e 15% tray support cost 240 kg/hr = 100 man—days/year 2.08 hours/day 10 years US $150.00 $ 9.00 year $ 1.50/m2 25 years Tables 15 and 16 $ 3.00/m2 7 years $ 0.45/m2-year $ 1.00/m2-year 1 This is a good practical estimation since the cut product should be ready, for drying, early in the morning. probable life maintenance 10% labor in handling 7. 2. 3 Vertical Drier drier cost probable life maintenance (7%) 7. 3 Cutting Costs 146 10 years 35 0.10/m2-year Tables 15 and 16 $ 20.00/m2 10 years $ 1.40/mZ—year Cutting costs are summarized in Table 14. Calculation of the costs per unit dry weight is based on a ratio between fresh and dried weights equal to 2. 5. Table 14 . CuttingCosts Item Costs Percentage Depreciation = $150/10 years $15.0 11.3 Annual interest charge=75x. 12 9.0 6.6 Maintenance = 150x.06 9.0 6.6 Labor= 100 man-days .OO/day 100. 0 75.1 Cost per year for 96 tons 133.0 100.0 Cost per year per freshton 1.4 Cost per year per dried ton 3.5 147 7. 4 Drying Costs Tables 15 and 16 present the distribution of the drying costs for the three systems and for the two, weather depending, densities. 7.5 Total Processing Costs The total processing costs of cutting and drying are presented in Table 17 for the high and low densities, and for fresh and dry weight basis. The following conclusions can be drawn from this "case study": 1. drying and cutting costs are approximately the same for the three systems and equal to $4. 00 per fresh ton or $10.00 per dry ton. This cost represents about 12.5 percent of the present c.i.f. (cost plus insurance and freight charges) of dried cassava in the European Economic Community. 2. labor costs constitude about 90 percent of the drying Table 15 Dging Costs for Low Densities I Concrete Horiz.Tray Vert.Tray tem (300 m2) (75 m2) (50 m2) Cost of drier $ 450.00 $ 225.00 $1000.00 Cost of supports - $ 75. 00 - Labor (man-days) 276 150 70 148 Table 15 Drying Costs for Low Densities (Continued) Item Concrete Horiz.Tray Vert. Tray (300 m2) (75 m2 (50 m2) Costs for 96 ton/year $year % $/year % $/year % Depreciation of drier: new cost/prob.1ife 18.0 5.6 32.1 12.9 100.0 33.3 Depreciation of supports - - 7. 5 3. 0 - - Annual interest charge 27.0 8.4 18.0 7.2 60.0 20.0 Maintenance of drier - - 33.8 13.6 70.0 23.3 Maintenance of supports - - 7. 5 3. 0 - - Labor 276.0 86.0 150.0 60.0 70.0 23.4 66.66 ----------------- 366 6 6' 61.666 ' Eli's-.6 ' ' '6 6 6 f6 ' ' 366.6 ’1' 6 6 f6 drying cost per fresh ton per year 3. 4 2. 6 3.1 drying cost per dry 8. 5 6. 5 7. 8 ton per year Table 16. Drying Costs for High Densities Concrete Horiz.Tray Vert.Tray Item (100 m2) ( 50 m2) (37.5 m2) Cost of drier $ 150.0 $ 150.00 $ 750.0 Cost of Tray supports - $ 50.00 - Labor (man-days) 193 112 56 149 Table 16 (Ccntinued) Drying Cost for High Densities Cost for 96 ton/year $/year % $/year % $/year % 63......666121666 BELL: ""6-.-0"-2- ’6 ----- 66.-4' "”6176 ""660 """ 3 '2’. 7 new cost/prob.life Depreciation of supports - - 7. 1 3.9 - Annual interest charge 9.0 4.3 12.0 6.7 45.0 19.7 Maintenance of drier - - 22.5 12.5 .0 23.2 Maintenance of supports - - 5. 0 2. 8 - - Labor ' 193.0 92.0 112.0 62.2 56.0 24.4 ilinnmm-m"6-6366666666666666m666:6"-2.2666676666 drying cost per fresh ton per year 2. 2 .9 2.4 drying cost per dry ton per year 5.4 4. 7 . 0 Table 17 Total Processing Cost Concrete Horiz.Tray Vert. Tray Cost Density Low High Low High Low High $ $ $ $ $ $ cutting cost/fresh ton-yr 1.4 1.4 1.4 1.4 1.4 1.4 drying cost/fresh ton-yr 3.4 2. 2 2. 6 1. 9 3.1 2.4 processing cost/f. ton-yr 4.8 3.6 4.0 .3—3— 4—5 W cutting cost/dry ton-yr 3.5 3.5 3.5 3.5 3.5 3.5 drying cost/dry ton-yr __8_.__5_ 5.4 é._5_ i2 _7_._8_ 6:2 processing cost/d.ton-yr 12.0 869 10.0 8.2 11. 3 9.5 150 costs on concrete floors, 61 percent of tray drying costs and 24 percent of the vertical drying system costs. 3. unfavorable weather conditions, indicated by the low and high densities, increased drying costs by about 40 percent in compa- rison to the costs incurred under favorable weather conditions. 4. cutting costs are approximately 35 percent of the total processing costs. The acepted facts and assumptions might limit the real value of these figures because of the possible errors. When more realistic experimental data on commercial operations become available, more reliable cost figures will be obtained using the same framework of analysis. VIII SUMMARY AND CONCLUSIONS Traditional forms of drying cassava chips on concrete floors or wooden trays can be improved substantially without incresing the costs but making the operations less risky and more feasible, practi- cal and attractive. Vertical layers of rectangular cassava bars, produced by a modified conventional disc slicing machine, allow drying without deterioration of at least 20 kg/m2 more than the amount current] y dried safely by traditional methods. The vertical layers can be covered by a roof to protect the product from the rain. They can be left outside overnight to continue the drying process. The dehydration efficiency is not diminished by the shade from the solar radiation. Drying of the product in horizontal, elevated, wire trays is also a more efficient method than the traditional forms but less efficient than the vertical drier system. Regardeless of the form or position of the product, the energy required for the evaporation is taken from the air enthalpy. The air circulates more easier in vertical layers of cassava with adequate geometric forms than in horizontal layers. Also higher air turbu- lences are created in vertical layers than horizontal layers. The 151 152 turbulences are created by the wind velocity and by buoyancy forces caused by the evaporation. The turbulences induce higher rates of heat and mass transfer. It was possible to model the different drying systems mathema- tical with a simple equation whichipredicted all the extensive and varied experimental data accurately. The equation, empirical in nature, includes all the variables of importance in natural drying of thick layers of cassava. One of the most widely used empirical thin layer equations was showed to be a particular case of the proposed equation. The model was used (a) for recommending maximum allowable layer densities to safely dry the product as function of the drying system, weather conditions and the effective drying hours of the first processing day, (b) for recommending the most appropriate form to improve the drying efficiency of a given natural drying system as function of the independent variables. Results indicate that the prima- ry efforts should be directed to produce a neat, uniform and firm rectangular bar (or ideally a cube with a square section of 8 mm of size). Secondary efforts should be devoted to improving the solar absorptance of extensive area around the vertical drier, and (c) for estimating and comparing costs involved in three drying systems. IX RECOMMENDATIONS FOR FUTURE RESEARCH Results of this study suggest that new natural drying systems of cassava can be implemented for commercial operations. The proposed systems should increase the cassava drying industry by: (a) improving the quality of the end product, (b) making the process more economical, less risky and, in general, more attractive, and (c) providing different, low-cost, drying alternatives for different types of entrepreneur. Research is recommended to implement commercially the proposed drying systems. The disc cutter assembly can be improved to produce firmer, smaller and more uniform rectangular bars. In order to obtain these desirable physical properties, the movement of the root, when being cut, should be eliminated, and the disc modified to avoid the bending stresses in the bars when they are cut and released by the disc. Research is also suggested to design other mechanisms for producing the desirable geometrical properties at low cost. The feasibility of reducing the initial moisture content of the roots (by using a mechanical press) prior to drying should be investigated. Drying performances of layers in intermediate positions between the vertical and horizontal should be investigated together with (a) the 153 154 possible reduction in costs of the drier structure, (b) the practicality of loading and unloading the drier, (c) the protection of the product with shade, and (d) the type and availability of construction materials. Implementation of solar collectors to produce the supplemental heat needed to reduce the cassava moisture content to a safe long storage value would be the logical complement of the natural drying system studied. The collector might be design to complement the design of the natural drying system in order to reduce costs. The applicability of the new natural drying technology to other products which are presently dried using the same conventional me- thods should be investigated. The mathematical model can be genera- lized to products in which solar absorption is significant. The general drying equation would be adequate to perform sensitivity analysis which, in turn, would indicate how to improve the drying methods. The proposed drying equation seems to be applicable to give a practical solution to the diffusion equation with convective boundary conditions. The equation might result in a general thin drying equation. Also, simplified deep bed calculations, using the density function, are promising. Hygroscopic data of any product seems to be predictible with acceptable errors by using the presented double polynominal function. APPENDICES APP EN DIX A APPENDIX A COMPUTER PROGRAMS Page Legend of Notations . . . . ........ . . . . . . . . ....... 156 Computer Programs, Subroutines and Example Results . . . 160 Al Subroutine EQEQ . . . ............ . . ....... 190 A2 Subroutine KEXP . ....... . . . . . . . . . ..... . . 160 A3 Subroutine VPDIF . . . ..... . . . . . . . . ...... . . 160 A4 Subroutine LAYEQ ...... . . . . . . . . . ....... 161 A5 Program to Predict Natural Drying of Cassava and to Compare with Experimental Data . . . . ........ 162 A6 Output Example of Predictions and Comparison . . . . 166 A7 Program to Simulate Natural Drying of Cassava for 6DryingSystems....................... 170 A8 Output Example of Simulation . . . . . . . . ....... 172 A9 Subroutine CRITD . . .......... . .......... 173 A10 Program to Calculate the Maximum Layer Density Allowable to Dry safely 0 o o o o o o o o o o ooooo o o 174 A11 Output Example of Calculated Maximum Densities . . . 176 A12 Program to Calculate Sensitivity Coefficients of the Maximum Density Function . . . . . . . . . . . . . . . 177 A13 SubroutineDIMEQ................ ....... 178 A14 Output Example of Calculated Sensitivity Coefficients 179 155 AVMC AVRMC AVWMC CM CMC CMCDl CMCD CMCR CMCW COULS COUNT CRITD CRTD DATE DC DEN DENPT DIMEQ COMPUTER PROGRAMS LEGEND OF ANOTATIONS Calculated moisture content using average daily weather conditions, decimal, dry basis Calculated moisture content ratio using average daily weather conditions Calculated moisture content using average daily weather conditions, decimal, wet basis Calculated moisture content, decimal, dry basis Critical moisture content, decimal, dry basis Initial moisture content for each hour, decimal, dry basis Calculated moisture content, decimal, dry basis Calculated moisture content ratio Calculated moisture content,decimal, wet basis Counter of number of experiments for each drying system Counter of total measurements fo each drying system Subroutine to calculate the maximum layer density allowable to dry safely Maximum density allowable to dry safely,kg/mZ Date of experiment Difference between calculated and experimental moisture content Density, kg/m‘2 Fresh cassava weight per tray, kg Subroutine to calculate geometric properties of rectangular cassava bars 156 EA EQIOO EQEQ EQMC ES ESMEA FE 1P1 ITYPE KEXEQ KEXP LAYEQ LDIM NCLAS NDAY NM EAS NN NTRAY PAR Water vapor pressure, lb/in2 Equilibrium moisture content, percent, dry basis Subroutine to calculate the equilibrium moisture content Equilibrium moisture content, decimal, dry basis Saturation water vapor pressure, lb/in2 Saturation water vapor pressure deficit, lb/inZ Mean error of final moisture values calculated using average daily conditions Index for hourly measurements I + 1 Form of input data : 1: tray drying in 1973; 2: tray drying in 1972; 3 = vertical drying; 4=vertical drying with correc- tions for the RH measurements. Index for trays Subroutine to calculate the drying proportionality constant Experimental drying proportionality constant, hr"1 Subroutine to calculate discrete moisture content values Length of the rectangular bar, cm Drying system Drying system Day of the experimental: 1=first day; 2: second day Number of experimental measurements per day Drying system. Number of drying tests in a drying experiment Coefficients of the thick layer equation 157 POR RHlOO RH RHER RSOD SCTAH SCU SCWl SCWZ S DIM SIGD SE TEMPC TOTH TN UM TPOS UMPS UNOTS VPDIF Porosity Relative humidity, percent Relative humidity, decimal Relative humidity measured with calibration errors Total coefficient of determination Sensitivity coefficient of the maximum density with respect to heating of the air, kg/mZ Sensitivity coefficient of the maximum density with respect to the wind velocity, kg/mz Sensitivity coefficient of the maximum density with respect to the length of the bar, kg/m2 Sensitivity coefficient of the maximum density with respect to the thickness of the bar section,kg/mZ Thickness of the bar section, cm Rectangular bar geometric property, cm'z Moisture content error for each system Dry bulb temperature,°C Total hours needed to dry the particles as to 13 percent, wet basis, or as to l. 2 times the equilibrium moisture content, hours Tray or test number Position of the tray: l=vertical; 2=horizontal Wind velocity, m/sec Wind velocity, nautical miles/hour Subroutine to calculate the saturation water vapor pressure deficit 158 W100 WBLOC WD WDIM WDRYR WFRAM XMCD XMCI XMCR XMCW XMER WPL WT WTRAY Weight of the cassava dry matter plus the tray weight and the tray frame weight, kg Weight of auxiliary blocks for measuring (,kg Dried weight of cassava, kg Thickness of the bar section, cm Weight. of the empty vertical drier, kg Weight of the vertical tray frame, kg Experimental moisture content, decimal, dry basis Initial moisture content, decimal, dry basis Experimental moisture content ratio Experimental moisture content, decimal, wet basis Experimental moisture content determined with oven set at 75 °C Weight of an auxiliary plywood used in the vertical drier,kg Total weight measured every hour, kg Weight of the tray, kg 159 UH MOISTURE ELAIIVE HUMIDITY I R APPENDD( A .A1 GIVEN DRY BU A C.**“ SUBRDUTINE T0 CALCULATE T C“*“ CONIENT AT scoot ttttt Cttt$¢ costs: 0 1 I. .0 I P .1: V. \D ‘ '2 II It 0 T 0 C 56 D t l .1 I H 04..l R 1| L 1| 0 DA E 0 1| P N A N E E 6. N H 3 1.. r. N E .3 TT. 2 o. E E 0 30 0 D 0 AA 44 D T . 5 1 S I. 1 S 2 R 1. 1 S 1‘ E 2.1 P T 1 D. . UE 6E I: P I 4 80 v R 0 1 1 TR 34. D O \1 5 6.1 .L U .l I. J AU 35 I. l I: 8 a: D D O. O D 0 SS 53 n. 0 \l 5 DU C O 0 C I S 7.6/0 C \1 b .2 H R 2 M 0. EE 5522 H E 5 7‘ C D. .l C I. HR 56.1 C D. . Q.U 1 D 0 1| TIP OIED 9 C . 2... D G C D D v. 495C D R 1 13 G N H pu C NR¥1 1:13H nu P I. 7.; I. I X I H EDI. 210x .1 H 0 1: b S V. t 5 x EPD .26 O S E . Cl 1 R \1 t .1 HA1. .301 1 T- E .r. R D D R I TVM 1570 R O 1. .2 U 2 D J E U 4.162 D D 3 1 lo. l. I)? v BRH OZIIIP P 2 2FO v A CO v .1 E E .5C0 1 l. o. 8%ch T. HZN 1.. ETF 2 vaZN t 2 5C1IE N 01E 0 CAV 31901:... R 3 IESD E ESD C NH... 2 . 5350 D. o 2 up 1 H ’0. 1 H E T 2E1 9? 1 H 1 21. 10 K I. 1 D X RLA 8521 D E 6 001C P R 01C 1| EAL ISIDIC T. 4 .ZOH H 2 E 20H I .3 FUE 66.20H + 9 oLZX 1E A“ P (2X 1 A FTR 029(2x C 2 CJAII D. ,T x A‘ 9 \0 IC 211A1‘ 9 p 9 ZESC It . E ESC 1 DAD 310ESC 11 5 5H M E10 MPH J N oQEMPH t . 95 ..Q #10 E SHQ o EEA [drwSHQ9R . IEUE U11. H EUE 1 HH 537EUE6P 9179-. RU fl 9990. TITC. 9.08919." 1 011A +R/ \1 11A .1 R 7911A9E 0 .OcUE 0.. E P DOE .1 DU F3OOOEST E .ZIH all, r. X 21M D ENI P1221H «.4 5 1.1.15 t + A E 11.5 C TAA 1cJTllb+B .l 9 BHIE U52 L K HIE M A R E42H1E.P A .1 “RD 9 R10 U 9 RD 0. X LEE 0. BIRD 7210 E 5 5 9C5 +tE C J vCS . UR? I. 1. 6 C593! . 1 01M? 0 CU L I 1M0. 1.. CUM ID 111MP+R s It“ (MUCH); (R1! A I OCH J LSE FZQOCHBP E [.8 .2 9.1.11. t +9. C .1. 7.. 9U v AST. 1| 0022 9U a" 1| at o 211) 92 URX Q I.) 9 .1 CE FCE .11: 91E Q Q/ ILDH+ RIE O E CUH 1 RB IP11CUH$T 1 EE T91R11 +* T. o X 91R D DPL D 158P1R1+ 7. 01/ 9M11 DU. 1 E H11 C T- U PBQ..H(1I.A\1 o ED5SEDC‘ (R K K EUC H RB VPBEEDCIP’ l 90 llrij t +1. EC .IPuOr x E0 OZZTnoPC‘) 5 EC.R IMP UQQ N E IN 1| NPY EA38 IHPCR N 1E 1NSEM RIE IT NPNSE t IAR NP69NSEHPP z [.8100 IE1++ 2 TN 1x0 9T 0 TVD I 0.790 OTEXHS’UII T. ’1». 9!...) TIAPII UA TEI, 12 U TROII) TEEEIIRI ”UA13§SONIT( .IN HUT “UKCXUN+)\ N nfinN UDLEUSnflw=trnsltLIN D at N1AUKHI.:(nu RC. 0 “RIDIZ. R Rcht nu 9afimlnfinRtichfnR RA?JAFTLMPRH .LU 8N" RIEfilflzor U n$IV .KAREflFlMDBEbIREth 8T3THRHH:12HTD U0 BAMRHIX TD UAI BleHRHH:P1==HTD UA .AIDDEUQQQEN SC UEIDDPEIEN SHG UA“6100E$.SUASEN SD DDPCTREEERE SRDPCIK’RE SDSZDPCTEFPREERE l 1 tit... 1 .1 .ttvtttt .12 1 l fitttti Otttttt t$trtt tttt¢tt fittttt ttttttt tttttt ttttttt CCCCCC CCCCCCC 160 APPEN DIX A A4 2 '55 . .00 I .I R l 0150 1.0.. 1 9 A 9 It I O '0 '00 0 In. p ll. . 71.— 7. ’0 o O .14 6 6. n.” 99 o O 6 o .10 1| R . A 6328. 011.. v . N A 7.. n. 8 .111 0 9 0.91 E D. I. 1. 6230 1753! D a 1 - 3 11. 0 07524 I 1 S T. ,1. 5202 .2859 1 9 D: 1 .1. .9 . 9 70098 0 1.. .. 1n 1.1 10 9|. 6 06.107 1 5 1.. 1C .. 036 6.1.03 1 R 0 .11. -1 2018 9 9 . .8 0 A. C r.” 5 .50 31. .0 .2 D. H L 1 7 900 49 I 1 o .1. 9 C t A. 08 o I. 0756 9 C 9 D H v .11.? . .366. H 1.. G N 8 0.0 '1. .1526 x I“ .1 1| 1| 1.02). I. 0.285 a. R S 1 R 3 .80 58 . .6 1 A 9 0 A 2. 40 7731. . 0 P R L P 0 '2 o 6.2 v 2 2 v 0 Mn 9 060. 319.1 0 (.11 P C 1 .8 . 0 50505 C09 1 I N .196 0.599 H21 N 1 N 9120 o 9156 01.4.. 2... N .. 908.... 6665 ESR 0 N 7 0 .30 70912 PA 9 0 l1 1 8 1.10 10000 1 ID. 0 3 R 0 160 o 3 .000 01 o. C .1 A C 02.. 2.0.. 201 H R P t .0. I 0 I. o O 9 129 x A It . 1 0 12 .6. 173 A101 a. P t z "7 .86 .4166 E52 C O 1 1| N5 . 44. [1662 NPR H 1 1 I '7 '20 90161 SHA Q In K 1 K4410 R.219 EUP E 1 1 1 1052. A1720 1!! D S N 2 n o“. o- P8000 111 A P E c C/ZO! 97000 009 E H .0 I 04580 810 . . 2111" U 2. 0 NR.6. R0... 11195 t ’1 1 . C NA140 A..11 H1R(E 1 1N I 1 t P560. P156 RDAQ... N IN I. +1. Iv 7960 Q. .861. 'PUPRS N .1 1 re ..1.H.1V 132 . . 701.17 1M AD 9 A») H 89. 1R620 R 1951.. P1C1Du 2 .1.-. C '11 1A8 9 9 A .974 9.. v9 10 1 Min E 7.1..“ cp 0.00 p0240 (1. O1 is). 1,111,), )u r AP _ 8.100 E 112 ./ 1 930 . 1.0.. 4 .t .. LLLLLLLLL A15... . t , .1 Y2 99106 O,“ o D .IcuL. 1 5.. 1|.l.al\l|l\‘1l|'|l-| p18. 4. 1L 1.3..» ARVIU .. 0R1 . 1.. .._...1. .. 1....‘3/1RJ10789 +111 I! .H.1UI\ LAIJBSDA 9 It... . 1.5., fihDHRRRRRRR 1Awi.i.11 » 1.1“ lb Uh . . R _I. 5.1.0.950. 1... 91(AAAAAAAA M.C.WN1H.443RC .. 70 . 1 n. 1 1.. tpPPPPPPPP NH O tJNBBUflua (0 {uh/5N LL. 1.. = .. = .. x x 3 a 53511::- #51 IR.52DRD!1. D901TUE:111111111EE1511012221H TA170 1A .0 . 1 61.119 AUL123456789UU1tRRGDBBBIN.’ Up.1*o0p. .90 BSOS‘NLN 9"!!!OOONNR1AAIPUV$VCI|IN D 11. . 1 10 ./ N1N7DFIOLLLLLLLLLIIANPPSH100. 16R RA96 1A10 .00AE1F,RH111111111111TIPN (thHLO‘DAU 8.1308 9.19 .0 9 .IHRHAyiN RRRRRRRRRNN: 12:1 x .. z : 2.11.1310 UAI. .45A00 100AIUIPUFDDAAAAAAAAA000412N5012MMFEN $02 . 8207 0 . DDPD CICDPPPPPPPPPCCB‘BBNDCCCCCIRE 1231 12345 I. 1. I. 1 5 m6 161 Y A SIMPLE THICK LAYER .AS RYING OF CASSAVA - PREOICTEO RESULTS L D ENTAL VALUES APPENDIX A ARE C C***.‘ PROGR c1..11 IHE C11... AS c.1111 c.1111 c.1111 c1111. c.1..1 c.1111 nay c1111. PLACED ON E OXHENSTONS ON C CUTTER ON A PERFORATEO DISC CUTTER ON A T G O L CASSAvA CHIPS ON PERFORATEO Y A DTSC CUTTER 0N Y A DISC CUTTER 0N 2011XHC012011011DEN11011 6 9 1 D 6 BLE OIHENSTONS 1 H l l S C 9 OIHIJ11TPOSCJ11TNUHTJ11H1001J11H L1 FDFTRLRTR RIC OFKUNPMQVND..PD T 0 C 0 0E SASZSISZS SHGSLSS SMNHI 11 00 RRRIRTRIR R RYAYR EU C019 F. . AOARDRARARARAAHAA 1111561 11 BFBOEBUBEBELRSRB 1101 1115 A 1 R H V H 1 I T T 00151CL E0 RER R R RRRRH M R ZITIODU H. APADADADADADRLRLA (151110 50 L LELELEL L OAOAL HIOET1C E1 on rue FLOOR E s t 1 e a o 9 ULUTUTUTULULFTFTU PRDPle 1 TL GAGACAGAGAGAINING x1CTAC11 S4 NCNRNRNRNCNCNONON E1N10MC9 P1 ATAOAUAUAIATUZUZA K0C1 1X51. ”8 TT‘erF}erT1LI.I.:lT .5.!0|.11T nu. CRCRCRCRCRCRNRNRC L‘11011N111 EEEEEEEEEEEEOOOOE LCO‘100UOH9 RVRPRPRPRVRVNHNHR 1PlH‘lZOlR1 0 1H1UYT‘C118 0. OEDNARR10CZ .0 ITGTRCEIZP. 9..60. O9 011 1H T)DL 011111/ 1.1 T. TMHO‘Hq '00 9.1 19 21.... 11 N618 1108111 0 HNSNHCXOOEI 001.cl1K O. 181 .6 112H 3(1JJJ1 10 10 1 1 10CT/ 00 . .3113K 1EEBEE 1 1F. 9 5158 1 85811111- 01111112M HO ..OONNNK1NUU1PU55TUJ13U311171AIMHH1 LSOSOOOIVNC: 00.. (1 N‘NNBYNTT N 8 NJ BJ 8L ITTJ NINIIIPAO A0..DHZTSZTLIICTIE5014101 O‘TOTCODODC LETETT‘X1HATaDHSSbNLbéETTDITTTTTSDTTATDYTDNTSHLD AHRHHRCE1HTATRRCC UU SSNNA‘NI.1 N A N AA A: sssG ElOlACHYbOADTSSDDOOOOPPOOEFORROOOEOOOOEROENOSHLI RDNDmfl“MhCONNSSTTDCCDSSCCRICHHGCDRGCDGRTGRNGSHLS 1.. 20 9 2 4 1 5 67 8 63 5 5 15815 T T YR1HPLYN1NCLASTJ11ND1NDAY D O E 1 RAY A 1 TR AINC ENPT1501HTJ11HDTHTJ11LDTH‘J11TPUSTJ11TNUHTJ11NCLAS‘J1 ATE NTRAY N EAS 1111: 9155 6 H ' e E NCLASTI} NCLASTZ) NCLASta) NCLASI.) NCLAS(5) NCLAS¢6I NCLAStT) NCLAS(8) NCLAS(9) c.1111 c.1111 c1.... c1.... c1111. c1111. c1111. c1111. E11... 1.... c1111. C11... C11... c.1111 c1111. c.1111 5.1... 11.11 1.111 .111. c.1111 APPENDIX A A5 J C 1 N A 1 R J F 1 N H e . A \l R J H Y . A 1 R J T 1 | H 1. V. . J A 1 l. R J o H T . T Z 1 ”I o O I 0 . o 0 1 S 1 .I. 1 I. t J N | A | I A 4 0 | E 1 0 1 N . 1 I S % H R E 1| E ll 0 ‘ 0 D I H N 1 6 H \l R I! I 1 1 I t J 1 J o 1 1 1 1| 0 I 1 0 J E C H 1 3 1 H | P . 0 . P 6 . m V. I. .L H 1 l t c N 1 . ST 1 . B Y 1 3 Y L Y 1 T1 Y 8 H L D 1 1 1 I L 8 A . D1 1 1 A 9 . P C 1 Y Y 1 P u R a N2 Y Y R . 1 N N 1 J EA A E N H . T 9 U|E EA A T I J . X N 1 PR R P Y . 1 N . 1HP . PR R N 1 E1 R § N H YT T Y L R J 1 I RCV T YT T 1 . P0 Y 1 1 I TN N T P Y T 1 1 E T A TN N 1 1 YO R J J D 11 1 1 H R 0 s . H+1 A 11 1 a 1 T1 0 1 1 L 11 1 1 . D 0 J 1 R 15 I 11 1 J 1 TH H 1 1 H 1 t 1. s 1 R H 1 1 + 111T A 1a a 1 J 1. . P P C J 6 SJ J U V Y . N 1 1 1 1E00 ‘ TJ J 1 | 11 1 x 1 1 s 111 6 41 1 1 A R 1 . J J 1J TPQN . ‘1 1 J R TJ J E | N E 1JJ 1 '1 1 O D 0 J 1 1| 1| J O TV. 9” l 1 1 '1 1 1| E 1‘ '1 K D N u s [I 9 9 0T 5J J 8 N Y“ Y| YJ RY R '11 s CTOt 5 I 1 TJ J RYN Y1T T 1 c 1 RSEV,011 .P 61 | 1 1 A. AT A1 EAE A11 A P156 t T 1 0| 1 EAX ATH N JPN JN ’EMA C|| +N 1T T 1 1 R1 RH RT HRH R|D E H116 U c151 1T T NR1 R11 | 1XX 1C CHRR H00 0E 6H H 8 7 TJ T| TH XTX TDC N E111 D P1P112H H RT. T1: 3 1E1 13 s TR/T XCC 20 11 | 1 5 N1. N N1 11N1. NCN N T|45 SA N|H|11| | |N1 N41 1 TKa1|1 AIS/UN zHN At 11 1 1 1 1T 1.. 1.. 1 1: 1HX 1 1H 1 . TB EHUFT 11 1 1 1J 1ZJ J1 °=1JQJ E+ = US 1 1.51. o o 2.9 8 5 6 1H 11 11 511 1x = 1 9CD 0U TR 101‘. 8 5|. 1 I. 1. O E1J|E 1 NS1R .— 11J .. .. 14EE2869E2E553|EsJEOEaJana JP... 31E 8 8 5 IZN ..E++§DE18393831E351 ‘IEXJ £Y1ENAIS1: 4 11 3=U01141U|U|UJ=UJ1UZUJ1U21J1UJ1JU 1111|14U1UCUUP°|11111JPUJ1P 2PUE11AAPU E1:1JT1JJ 11NN 8 8N N N 1N IN N 1N 8 IN J|N.. +83 1 :XNTRSVE 3 8 8 1N ‘1 1NK1‘LL1N2H111 T111 JJTTOTOTTUTOISJI6110171101411311100.0111010U‘155 010101311001 0‘1 TEC ‘1 NC1|1N01C ((TTTOTOTTTTTSTTZOTTTZOTTDkOTZlDTa=OlaOITSTDST==.LLTOTDTO§OT1TO TDTLKTNLOTS P153=CDH RNNN A AN N N NN CN N CN A CN CCNCU. 1A1 P APNCU LL A A CN C1 CNLPV=LCNE=HCP THCI OEUOOEOEOOOOOOEOOHOOOUHODEOHOOHMOTRUOPEHOHUBHOTRUAADEOEDEOHOOOH OHOAXANAHOHIEHMOTVHV PDCCGRGRCGCGCDDCDXCGCDXCGRDXCDXCCSSSDTRRGUGUUCSSSCCGRGRGRDXCDGXUGXCCEXNCCCRITRUDNACA 943 Z 56 8 6 57 6 5 7 6 £0 3 0 1 Z 1 7 2 33 5 TA 0 2 44 l S 55 2 2 2 1 42 2 4 A 4 1 Q 1 41 1 12 1 A APPENDIY A A5 I 11 CHIJ11CHCH(J11AV $01N1J19H01H1J11L01H1J11PUR1 ‘. J ’6 m H V. A ’ ) J A H C M” C Q 1. 0 1" Q J 1 1 1 D 9 1 H E 1 I "J 1 C 1 1 1 Q 1 1 1 H 1 1 C E1 1 1 X 1 C H .P. A 1 ' | M Q 11 E C 1 A Q E J1 M H J E E . 1D S Q 1 H . 11cc E E 1 S 1 J1MM 1 NN N 1 D '1111 ’VA 1 1N N J C 1111C1A 1 1 1 1 1 1 Mn 1JCJMP11 1 61 1 1 v 1 1M iXI/J S 3J J 1C A S1X1111 1 D. 1.1 1 1H 9 pp1p/0111 H 4 AN N JX 1 H1/11C1PJ 1 1 U 6 3:... E 1 J U111 M11111“ K 1 1 10 D 1/ 1 101D1V11CJ 1 1 1 1 4 1 1 11 1 OCICIAFUDM 1 K s N 31 1 1 D1 1 0M1M1+MCR1P 1 c N F. 1J J J C1 01 1XCCC oQMVp1 5 nu H1 1 P 41 1 1 H1 CJ H+M+H1ECA11 C 1. H61 0 J Y. 35 S S XC M1 o 1 RoQoU1-111D D 1 R16 o 1 T 10 U A 1»... CC 0 J 11E1E/111DC 1 1 .7 1 K 1 1 1 A 1 4p 9 l. .0 1H 1 O 11.1.1JJJCM1J1J 1 S 1 1:1 11 .1 C 1 3T T C 1E 1O\ + 1 1/1/1J 1 1MVJ1J1 K F. N 1K: AA 1 1 1 1 1 1 1 N 1.1 JV 1 D. 11J1J 11RCA1C1C 1 1 N N 1 1K TT 0 N N 3 41 1 1 ,1J 1A N 1 oCJ 1J 11PPC. .HHRN 1N1 3 R 1 11 11 AA V. N N 3 3J J 1 1J 1 1 1 1 S N 1 OP 11 11P11M11CHCR KNK 1. I L 0CK113 DD 1 V 1 1 1 11 1 J J 1 J111 A 1 D .0M1P1P111CJJHVHV 111112 1 E 0P1K11 RR N A S 5 JA 3 4H NH 1 '11111JUJ E .1 C01Ep1p11nuD 1 1 OCACA CE$135 K S oOMCl‘SS // A1A+ L1 A 3 3U U N 110JJH1C1 H N H0¥T1111DCC111. . . . DSC11 1 1 POlEDECC DH T9710 U11E 1: 1 1N N E 1DC11CRHR N1U x11 11D1DCMMJPP11116¥pDSS1 6C SO¥T1SDD RR AXA .1 UIILH 11 2 61 T D DALMHRMCXC 1+0 .. #110CDCMVX111JJJJ 1S+CC3 15 .. 11111.11 SS CPU... 1C11N 1J 3 31 1 1 1CMXCCXM1M6 1AC 1111CHCMVA1R1111111K =1DD1 11b1¥11O1DH ASS NYR‘ J: F1 10 1. 1 1O 1 1». 3M.X _. HM .. XZC 1 T .. A1C7MXMCA12CDUHHRR 11K+ +1 T 1K11009$S T11 1+// 11.1.U1 E1 2 .091 9 9 9X11XX1:9 11 2A1 T1M8X1C1: :9MCCCCCC:CK1UH. :R1 11111QZLL A11 1YYU Suifltri. +YPE3E3 1J5 15 1E 1: :J: :J1 1.. . DN AHQ 1.. .. z = 11 1XMMMMMH .U VCRRSE Q..NIC 1 1 1DDEOURRO: HMYOO AnIOrQI A1U1U1513S35U511 1111JSJKOINN10RE51111JJS 1XXXXXXK:HISSSAJKCJKNIIM‘SL:STTUljn‘x..wxi ogflUUV o o L1V_C 1L1N N .a.lU 1 1N1JJ1JJC111 : :11N _. ..1JJJJ1111: : : __ : z 1N :SSE N. : 1HAU111: : H1 : 3.\.O r) )AOO CS )U 01“ 1r .... GUEU. C1E11111u;LC...K311AT111OOE1111C. YrLJ 111111 9K1): .. M 1.3141 .RF. FFLCLJHLJA : : ..1: : : : : NLLL.) : LLTTTTTITTTTTTHRDNR RMTNLQKIJTA : FOUTHRHRM MI. T11Z345641ILK l n 113K OE. _. : TTT, .r)rlr|ro JAY 0V. iUh UH : ULL 1Lu.. N N 1.3 1 1N1. LCC L.LV.KT.M- 1 A U1X111C LCC HRIC 111111 5310.. K1..- 1 S 1,-..111L n... 3.: .M M YYTT. NUAAUPAVUUUCR 1URURURM.” M. MLAVKXUPLUO UPEHQRHMMMVVRM»LC.L.L.LCU LP»U .3...» C. ULUD HOP R< l L. U.. )-L JUMLUVVSCJ NLCCDICALLULGR1AUHGHCNXXrLLC AH 1UrJUHrL1YREHXXCCAAHHUUUUUUU U..\.() 431...! 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No.- hh.- No.«— Neouu «Moda w~oau O¢.- mood— Doon— oo.o~ utaw dqm_wmu> n~0~ N 733 ohoan om.- uoowa Noo~ neonu anon —O.nu OncN o~o¢~ to.- Amoeu ¢0o~ moo!“ Noun oh.«~ Phoo o—on ~0.o ”com umoo (wtww warn nwhda Nsoao onooo nm.mm nmomm amoun cocoa ONown moouo ooooo kaoao 1x OOoON 21w! 00.0m Omnufi omo~n 00o~n 000‘s Goa—n 00.0N omoON onon~ fiNMIU‘ON'Do unxwh wiwt 11(58 AGPFNDF<1\ A6 TOTAL NUMBER OF OBSERVATIONS 36 MEAN MOISTURE CONTENT. DRY BASISa 1.273 HET BASIS= 0.560 ¥féhi°§6§53p°33u£82§§“R555‘°“ 0:2: 19:23; 3:23;: 3:29; COEFFICIENT 0F DETERMINATION. DRY BASISa 0.997 HET BASIS! 0.998 TOTAL ERROR OF ESTIMATION. DRY BASIS= 0.031 NET BASIS 0.005 NUMBER OF DRYING EXPERIMENTSa 6 ERROR OF ESTIMATED FINAL MOISTURE USING AVERAGE DAILY CONDITIONS. 0.8.- 0.033 2m 0” OQQOU’UNI—f’fi ,0 MD OF 0. 5. FINA COULS 0. 4. 0. 0. 0. 1. 0. 0. 1. 0.000 0.000 0.012 0.000 0.000 0.057 0.000 0.033 0.000 0.000 0.000 0.010 0.000 0.000 0.067 SEAVD 0.000 0.027 0.000 0.000 0.000 0.033 0.000 0.000 0.038 0.000 0.034 0.000 0.000 0.000 0.002 0.000 0.000 0.046 ‘*"‘ NORMAL TERMINATION “"O SECH 0.000 0.004 0.000 0.000 0.000 0.006 0.000 0.000 0.00? L MOISTURE VALUES FOR EACH FLCD FEAVU FECH 0.000 0.005 0.000 0.000 0.000 0.007 0.000 0.000 0.006 169 SEAVH 0.000 0.004 0.000 0.000 0.000 0.015 0.000 0.000 0.006 CLASS FEAVH 0.000 0.005 0.000 0.000 0.000 0.001 0.000 0.000 0.006 SECR 0.000 0.016 0.000 0.000 0.000 0.023 0.000 0.000 0.026 FECR 0.000 0.016 0.000 0.000 0.000 0.021 0.000 0.000 0.021 SEAVR 0.000 0.014 0.000 0.000 0.000 0.065 0.000 0.000 0.017 FEAVR 0.000 0.016 0.000 0.000 0.000 0.008 0.000 0.000 0.021 APP"N DIX A C‘**t¢ PROGRAM TQISAHULATE NATURAL DRYING 0F CASSAVA USING 51 5v 1: S C‘**‘4 DRYING Cttttt Cttttt Cttttt R 3r)...” ERR... - \I‘ A \\ r. (LURE I“?! s.“ RQD L”... - .v AAIIJUU r o. 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ICE _ EZUEII E!MlTleTINT=TTuI.l ”a“. 5.1 .aiNllIlIllD ION IAUODEKUcLuRnPrRlAuRl8?LUc UPCHHDICHHIHNGHNCHUI 1 (5,84) JUE IT 05 HF IT 05 2. 3 5 h \ 0 ‘DEH‘leID InorIt‘nh’ 6811 I. 11 1 .31:OSV1LLL:PanhLa-LH H MIPM‘LLLflrrbrLIILerILU EOEaHEHAAAHAMRAIAHRAL .TU‘IUTRLCcssLDCHCCUCN O 10 IUH'loZ lHr-‘U’?+lo OOHRU.1000 T ‘ O H13Hl*3.5 H3'*.5 RU“. kUl 5U . 6 1 2 3 A12 APPENDIX A g I\..\ 1’1 .k. ..\ H .1... .A I C r... afl. F S g N 0 U .A u»... I C D S x I. #5 T 7 F l P N 1 O 0 I E I II I: 1.. 1 l - I S ’ D C c I E 0 c F. H x .I II C F E A. T. R D I H E T I c E C D A O I 3 S P H G T C I o I 0 X I. C x 8 u R I s S VI 6 F P I, . I VI I I 15 0 R U Y. I X I c 2 0 S I. R l. C) R CO I .I I T. I a. .910 T MEN 2 I. .1 I I I X a... 0.1.: H H q x x x9 H E50 $ C N 4 8 Q I C 9P I L. S .k I I #3 14 L )ID 4 i S - x]. .U 0 1 C O’C 1 ) 2 I 5" cs A 20” o I H H I p/3 P’ D IZX - III C A x H. 0. MM E Alt ’ 9 ,3 S T 5 ””2 E! T CSC o 3.9. I L 3 I A flTX C MPH .0 T/ H S I 9'05ng 9 r: SHAH 1 II I. an.) I. 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Aswan lem. .n.u .n.o HWo a a co .p.u .p.u Hue a u oo .Howm mxwm Hm : mm a anon H¢Jm mama Hm 5 mm a anon H H 217 tuvnasz puma maowpwcaoo Hdpauaouw>cm 33AMPQH . mm Ev .uopaaz puma uaoHpHunoo HupaoaouH>nm Amwma . ma .35 mmdad> pcopuoo ouspmwoz owuno>< copaasuado can Hdpqvamuomxm APPENDIX Bl .mm has no paoawuomxo no nowadaawpnoo c: 0.85%. woman 5 co>ww and «gonads anon on» «o unawvdomnwvaucH t ommuomm mumdm aw nu>wm who muogasc 9mm» 039 no maowuuowapnocH t mmo.o uouuo m.Hm mo.H m.H> m.~m no»: o»o.o gouge m.mm mo.H m.o~ H.mm .o>< .m>< can: Hmm.H HmH.H m.H mo.H m.m~ o.mm OH omm.H mmH.H p.mH Hm.w m.mm o.~m m om:.H omm.H m.mm Hm.m m.mm m.mw m mam.H ~m:.a >.mm m:.H o.Hm m.om p mow.H «mm.H m.Hm m».o ~.Hm 0.0m m mom.o 42m.o mm~.H mm>.H H.mH oo.m m.m» m.:m o.Hm Hm.o :.mm m.om m mmm.o mmm.o mam.H 0mm.H m.mm m:.H m.mw o.wm m.: mw.o :.mw m.mm : :o~.o m:>.o Hmm.H mam.H m.H: No.0 H:.mm m.om m.mm mm.o o.m» o.»m m ~w~.o :Hw.o >>m.a ohm.H m.m: mm.o m.mw m.mm o.mH p~.o H.mm m.mm m Hmw.o mmm.o mmo.m ~mo.m m.mH mm.o :.mm o.mw ., m.mH mm.o w.mm m.mm H wwm.o www.o m»o.m w»o.m nNao omm unNEo com .p.u .p.o Hue .JM. a no .n.u .p.c Hug a u no Huwm mxwm Hm : mm a .Hamm mxwm Hm : mm a “so: H thunadz pave unawpwcnoo prqu80hw>nm thoaasz puma unowpwvnoo Hdpnusonw>qm s.Am»mH .om hazy AmpmH .mm hazy moaad> unopnoo cuspmwo: owduo>< vopddzoado can Hdpcoawuomxm 218 APPENDIX Bl 9H 0C3.“ no pgmfihmmxfl MO “Owflpddpd—Huvgou ** ommuomm mvwam aw qmznm mud muogasa pump on» no maowpdowwwpnvcH ammuomm mmman cw am>wm mud mumnadn pump may no mnowpdowm«pcovH * taAMPmH .N mushy AmpmH .H cushy omo.o noun» ~.HH mm.H ».Hm :.mm any: «no.0 gouge o.mm mm.H m.mm m.om cam: . 0>< . ”>4 pmm.o m:m.o mwm.o mmw.o I--- mm.m m.om 0.0m m «.0 mm.m m.~m o.mw m Hmm.o mam.o mmo.H mam.o u--- mm.m m.mm m.Hm w m.m mo.m H.mm m.om m omm.o m»m.o HmH.H mHH.H m.mm 0H.m m.mm m.Hm P m.mm mm.H m.»m m.Hm r mmm.o omm.o pmm.H mmN.H m.mm ::.H m.>m o.Hm m o.mm m~.o m.mm m.Hm w omm.o m»m.o ~::.H FHH.H :.om :m.a m.om o.Hm m m.»: mH.H m.pm m.mm m mm:.o mm:.o pwm.H mmm.a o.mm mo.H m.mm o.Hm : n.4m mH.H o.mm m.Hm H P3.0 mm:.o :mm.H wwm.H 0.:w »~.o o.Hm o.mm m m.mm mH.H m.om m.om m mmm.o mmm.o mm>.H mom.a m.:: Hw.o m.ww m.mm m m.mm mo.H m.~m o.mm m oom.o :om.o mom.H owm.H o.mH Hm.o >.Hw m.mm H ».mm mm.H m.:~ m.~m H mmw.o mmo.o mom.H mmm.H Aswan 0mm swab com .p.c .p.c Hug a a no .p.c .p.u Huo .nmfl a co .Haoz .mxoz Hm : mm a usom .Huuz .nxoz Hm : mm a anon H mvsad> paupnoo oudumwoz omduo>< copdasoado can adpnuawuomxm 219 APPENDIX B2 Physical Characteristics For Each Test Number Drying Date Test Particle Initial Number System' Geometric Load ** (Ks/m2) Aug. 31, 1972 l 2 1x1x5 cm 20 5 2 1x1x5 cm 20 2 2 1x1x5 mm 20 h 2 1x1x5 cm 20 3 9 1x1x5 cm 20 Sept. 1, 1972 l 2 1x115 cm 20 5 2 1x115 cm 20 2 2 1x115 cm 20 h 2 1x1x5 cm 20 3 9 1x1x5 cm 20 Sept. 2, 1972 l 2 lxle cm 20 5 2 1x115 cm 20 2 2 1x1x5 cm 20 h 2 1x1x5 cm 20 3 9 1x1x5 cm 20 Sept. 1h, 1972 2 2 1x175 cm 8 6 2 1x1x5 cm 8 Sept. 21, 1972 2 2 1x1x5 cm 8 1 9 1x1x5 cm 8 Sept. 29, 1972 l 2 1x1x5 cm 8 2 2 1x1x5 cm 12 Oct. 5, 1972 2 2 11:le cm 8 5 2 1x1x5 cm 12 6 2 1x1x5 cm 16 Oct. 17, 1972 1 2 1x1x5 cm 8 2 7 large chips 8 3 2 1x1x5 cm 12 5 7 large chips 12 Oct. 27, 1972 l 2 1x1x5 cm 8 5 2 1x1x5 cm 12 6 2 lxle cm 16 7 7 large chips 12 8 7 large chips 16 h 8 small chips 12 9 8 small chips 16 March 7, 1973 23 l l.2xl.2x5 cm. 16 25 1 l.2xl.2x7 cm 16 2h 1 1x1x5 cm 16 32 1 lxlx? cm 16 ' Drying systems are described after this table. *' This is the initial load f6r the first drying day. is considered as a proportional value of the dry matter through the analysis. 220 The initial load APPENDIX B2 Physical Characteristics For Each Test Number Test Drying Particle Initial Date Number System’ Geometric Load 9* (Ks/m2) March 7, 1973 35 2 1x1x5 cm 16 (Continued) 3!. 2 1.2x1.2x7 cm 16 29 2 13:12:? cm 16 33 2 l.2xl.2x5 cm 16 6 2 lxlxl cm 16 March 8, 1973 23 1 l.2xl.2x5 cm 16 2S 1 l.2xl.2x7 cm 16 2h 1 1x1x5 cm 16 32 1 lxlx? cm 16 35 2 1x1x5 cm 16 3h 2 l.2xl.2x7 cm 16 29 2 lxlx? cm 16 33 2 1.2x1.2x5 cm 16 6 2 lxlxl cm 16 March 10, 1973 27 1 lxlxl cm 20 21 1 1x1x9 cm 20 31 1 1x1x5 cm 20 22 l O.8x0.8xl cm 20 99 2 lxlxl cm 20 23 2 O.8x0.8x5.0 cm 20 30 2 1x1x5 cm 20 2 2 lxlx9 cm 20 31 2 0.8x0.8x9 cm 20 March 11, 1973 27 1 lxlxl cm 20 21 1 lxlx9 cm 20 31 1 1x115 cm 20 22 1 0.8x0.8x1 cm 20 99 2 lxlxl cm 20 23 2 0.8x0.8x5.0 cm 20 3O 2 1x115 cm 20 2 2 lxlx9 cm 20 31 2 0.8x0.8x9 cm 20 March 1h, 1973 35 1 1x115 cm 28 36 l lxlxl cm 20 33 l 1x1x5 cm 28 31 1 1x1x5 cm 2h 21 l IXIXB cm 20 3h 1 lxle cm 20 ' Drying Systems are described after this table. ** This is the initial load for the first drying day. The initial load is considered as a proportional value of the dry matter through the analysis. 221 ‘J‘m 11541:... __ ., - II— Physical Characteristics For Each Test Number APPENDIX B2 Test Drying Particle Initial Date Number System Geometric Load '* @121. March 1h, 1973 23 2 1x1x5 cm 20 (Continued) 32 2 1x1x5 cm 20 March 15, 1973 3S 1 1x1x5 cm 28 36 l lxlxl cm 20 33 l 1x1x5 cm 28 31 1 1x1x5 cm 2h 21 1 1x1x3 cm 20 3h 1 1x1x5 cm 20 23 2 1x1x5 cm 20 32 2 lxle cm. 20 March 21, 1973 33 1 12:12:? cm 20 3h 1 lxlxl cm 20 31 1 1x1x5 cm 20 27 1 11¢le cm 16 36 l lxlx3 cm 20 32 1 1x1x5 cm. 2h 30 2 1x1x5 cm 20 29 h disc bars 20 35 h disc bars 20 March 229 1973 33 l lxlx7 cm 20 3h 1 lxlxl cm 20 31 1 1x1x5 cm 20 30 2 lxlx5 cm 20 29 h disc bars 20 35 h disc bars 20 March 2h, 1973 3h 1 1x1x5 cm 2% 31 l lxlxl cm 2h 36 l lxlx3 cm 2h 27 l 1x1x5 cm. 28 32 1 lxlx3 cm 28 33 l lxlxl cm 28 March 25, 1973 3h 1 1x1x5 cm 2h 31 1 lxlxl cm 2h 36 1 lxlx3 cm 2h 27 l 1x1x5 cm 28 32 l lxlx3 cm 28 33 1 lxlxl cm 28 23 2 1x1x5 cm 2h * Drying systems are described after this table ** This is the initial load for the first drying day. The initial load is considered as a proportional value of the dry matter through the analysis. 222 APPENDIX B2 Physical Charasteristics For Each Test Number Test Drying Particle Initial Date Number System‘ Geometric Load“ Kg/m2 March 28, 1973 31 1 1x1x5 cm 20 33 1 lxlx8 cm 2h 36 1 lxlx8 cm 2h 3h 1 1x1x8 cm 28 27 1 1x1x5 cm 21‘ 2h 1 lxlx5 cm 16 32 2 1x1x5 cm 16 22 2 1x1x5 cm 2h . 23 2 1x1x5 cm 20 2 March 29, 1973 31 1 lxlr'j cm 20 g 33 1 1x118 cm 2h f 36 l 1x1x8 cm 2h 3J1 3h 1 1x1x8 cm 28 'g 27 1 1x1x5 cm 2h 2h 1 1x1x5 cm 16 22 2 1x1x5 cm 2h 23 2 1x1x5 cm 20 March 31, 1973 36 3 disc bars 2h 33 1 1x1x2 cm 20 3h 1 lxlxl cm 2% 31 3 disc bars 20 27 1 1x1x2 cm 2h 2% 1 lxlxl cm 20 32 2 lxlx2 cm, 16 22 2 lxlxl cm 16 April 1, 1973 36 3 disc bars 2h 33 1 1x1x2 cm 20 3h 1 lxlxl cm 2h 31 3 disc bars 20 27 1 1x1x2 cm 2h 2h 1 lxlxl cm 20 32 2 lxlx2 cm 16 22 2 lxlxl cm 16 * Drying systems are described after this table. '* This is the initial load for the first drying day. The initial load is considered as a proportional value of the dry matter throught the analysis. 223 APPENDIX B2 Physical Characteristics For Each Test Number Test Drying Particle Initial Date Number System' Geometric Load ** (Kg/m2) April A, 1973 3h 3 disc bars 2h 33 1 1x1x5 cm 20 27 3 disc bars 28 31 l 1.211.2x5 cm 20 2h 3 disc bars 16 36 3 disc bars 20 32 2 1.2x1.2x5 cm 20 22 2 1x1x5 cm , 20 April 5, 1973 3h 3 disc bars 2h 33 1 1x1x5 cm 20 27 3 disc bars 28 5 31 1 1.2x1.2x5 cm 20 a 2h 3 disc bars 16 F j ‘ 36 3 disc bars 20 L) 32 2 1.2x1.2x5 cm 20 ' 22 2 11115 cm 20 April 7, 1973 2h 1 1x1x5 cm. 20 31 1 1.2x1.2x5 cm 20 33 3 disc bars 20 36 3 disc bars 2h 27 3 disc bars 16 3h 3 disc bars 28 29 2 1.2x1.2x5 cm 20 7 h disc bars 20 32 2 1x1x5 cm 20 April 8, 1973 2h 1 1x1x5 cm 20 31 1 1.2x1.2x5 cm 20 33 3 disc bars 20 36 3 disc bars 2h 27 3 disc bars 16 3h 3 disc bars 28 29 2 1.2xl.2x5 cm 20 7 h disc bars 20 32 2 11115 cm 20 April 11, 1973 3k 1 1.2xl.2x§ cm 20 33 3 disc bars 20 2h 1 1x1x5 cm 20 ‘ Drying systems are described after this table. *' This is the initial load for the first drying day. The initial load is considered as a prOportional value of the dry matter through the analysis. 224 APPENDIX B2 Physical Characteristics For Each Test Number Test Drying Particle Initial Date Number System Geometric Load ** (Kaine) April 11, 1973 27 3 disc bars 2h (Continued) 31 3 disc bars 28 36 3 disc bars 16 32 2 1x1x5 cm 20 29 2 1.2xl.2x5 cm 20 7 h disc bars 20 April 12, 1973 3k 1 1.2x1.2x5 cm 20 33 3 disc bars 20 2h 1 lxle cm 20 27 3 disc bars 2h 31 3 disc bars 28 36 3 disc bars 16 32 2 lxlx5 cm 20 29 2 1.2x1.2x5 cm 20 7 h disc bars 20 April 1h, 1973 2h 1 1x1x5 cm 2h 33 1 l.2xl.2x5 cm 20 36 3 disc bars 20 3h 1 1.2x1.2x5 cm 2h 31 1 1.2x1.2x5 cm 28 27 1 1x1x5 cm 20 32 h disc bars 20 7 2 1.2xl.2x5 cm 20 29 2 1x1x5 cm 20 April 15, 1973 2h 1 1x1x5 cm 2h 33 1 1.2x1.2x5 cm 20 36 3 disc bars 20 3h 1 1.2x1.2x5 cm, 2h 31 l 1.2x1.2x5 cm, 28 27 1 1x1x5 cm 20 32 h disc bars 20 7 2 1.2x1.2x5 cm 20 29 2 1x1x5 cm 20 April 17, 1973 27 1 1.2x1.2x5 cm 2h 3h 1 1.2x1.2x5 cm. 20 26 1 l.2xl.2x5 cm 16 2h 3 disc bars 16 ‘ Drying systems are described after this table. '* This is the initial load for the first drying day. The initial load is considered as a proportional value of the dry matter through the analysis. 225 APPENDIX B2 Physical Characteristics For Each Test Number Test Drying Particle Initial Date Number System. Geometric Load " (Kaine) April 17, 1973 33 3 disc bars 2h (Continued) 31 3 disc bars 20 April 17, 1973 27 1 1.2x1.2x5 cm 2% (Night) 3h 1 1.2xl.2x5 cm 20 36 l l.2xl.2x5 cm 16 2h 3 disc bars 16 33 3 disc bars 2h 31 3 disc bars 20 2h 2 1.2xl.2x5 cm 20 7 h disc bars 20 May h, 1973 l 5 disc bars 2h.5 May S, 1973 1 5 disc bars 2h.5 May 9, 1973 1 5 disc bars 27.6 May 1%, 1973 l 5 disc bars 2h.5 May 15, 1973 1 5 disc bars 2h.5 May 21, 1973 l 6 disc bars 25.6 May 22, 1973 l 6 disc bars 25.6 May 25, 1973 1 6 disc bars 25.3 May 26, 1973 1 6 disc bars 25.3 May 29, 1973 l 6 disc bars 2h.8 may 30, 1973 1 6 disc bars 2h.8 June 1, 1973 1 6 disc bars 26.h June 2, 197A 1 6 disc bars 26.h * Drying systems are described after this table. ** This is the initial load for the'first drying day. The initial load is considered as a proportional value of the dry matter through the analysis. 226 APPENDIX B3 Drying System Nomenclature Drying System Description Number 1 Vertical trays loaded with cassava rectangular bars. 2 Horizontal trays elevated 30 cm.from the floor. Loaded with cassava rectangular bars. 3 Vertical trays loaded with cassava " disc bars ". h Horizontal trays elevated 30 cm from the floor. Loaded with cassava " disc bars ". 5 Vertical drier loaded with cassava disc bars. 6 Vertical drier modified with wings. Loaded with cassava disc bars. 7 Horizontal trays elevated 30 cm from the floor. Loaded with cassava large chips. 8 Horizontal trays elevated 30 cm from the floor. Loaded with cassava small chips. 9 Tray on the floor. Loaded with cassava rectangular bars. 227 BIBLIOGRAPHY BIB LIOG RAPHY Aderinkhing, P.G. (1952). Ob uteplenii pochv putem izmeneniia ikh tsveta. Met. i. Gidrologiia. 8:28.Quoted by Geiger, 1971. Anon. {1962). Wealth of India. Raw Materials 6(L-M):293-297. Coun. Sci. ind. Res. ,New Delhi. Quoted by Ingram and Humphries, 1972. Aoki, M. (1971). Introduction to Optimization Techniques. Macmillan Co. ,New York, N.Y. Bakker-Arkema, F.W. and Brooker, D.B. (1970). Proceeding of the Institute for Simulation of Cooling and Drying Beds of Agricul- tural Products, Agricultural Engineering Department, Michigan State University, East Lansing, Michigan. Bakker-Arkema,F.W.,Patterson, R.J. and De Boer, S.F. (1971). Drying 'of Red Kidney bean see.d.American Society of Agri- cultural Engineers. ASAE paper No. 71-350. Bakker—Arkema, F.W. , Lerew, L. E. , De Boer, S.F. and Roth, M.G. (1974). Grain Dryer Simulation. Research Report No. 224, Farm Science, Technical Information. Agricultural Experi- ment Station, Michigan State University, East Lansing, Michigan. Beck, J.V. (1972). Parameter Estimation in Engineering and Science. Preliminary Edition, Department of Mechanical Engineering East Lansing,Michigan. ~ 3 Brooker, D.B. (1970). Modeling of the psychrometric chart. In ' Proceedings of the Institute for Simulation of cooling and Drying Beds of Agricultural Products, Agricultural Engineering Department, Michigan State University, East Lansing, Michigan. Buelow, F.H. (1956). The Effect of Various Parameters on the Design of Solar Energy Air Heaters. 'Unpublihed Ph. D. thesis. Michigan State University. East Lansing, Michigan. 228 229 Carnahan, B. Luther,H.A. and Wilkes, J. (1969). Applied Numerical Methods. Wiley and Sons, Inc. ,New York, N. Y. Chirife, J. (1971). Diffusional process in the drying of tapioca root. Journal of Food Science. 36: 327-330. Chirife, J. and Cachero,R.A. (1970). Through—circulation drying of tapio‘ca root, Journal of Food Science. 35;364-368. CIAT (1973a) . Annual Report, 1972. Centro Internacional de Agricultura Tropical. Cali, Colombia. CIAT (1973b). Cassava Program. Centro Internacional de Agricultura Tropical, Cali, Colombia. Cock,J. (1973) Personal communication. Coursey, D.G. and Haynes, F.H. (1970). Root crops and their potential as food in the tropics. World Crops. 22(5) :261-265. Crank, J.(l956). The mathematics of Diffusion. Clarendon Press. Oxford, England. de Vries, C.A. , Ferwerda, J.D. and Flach,M.(1967). Choice of food crops in relation to actual and potential production in the tropics. Neth. J. Agric. Sci. 15:241 - 248. Draper, N.R. and Smith,H. (1966). Applied Regression Analysis. John Wiley 8: Sons, Inc. ,New York, N.Y. Dye, J. L. and Nicely.V.A. (1971). A general curve fitting program ’ for class and research use. Journal of Chemical Education 48:443 - 448. FAO (1971) Productions Yearbook, 1970. Rome. Farmer, D.M. and Bakker—Arkema, F.W. (1971). Sensitivity studies of optimal controls for minimum cost-high quality stationary bed corn drying.American Society of Agricultural Engineers. ASAE paper No. 71-818. Gebhart, B. (1973). Natural convection flows and stability.In Advances in Heat Transfer.Vol.9 Academic Press. New York,N.Y. _ Gebhart, B. and Pera, L. (1971). The nature of vertical natural convecti- on iflows resulting from the combined buoyancy effects of thermal and mass diffusion. Int. J.Heat Mass Transfer. 14:2025-2050. Geiger, R.(l971). The Climate Near the Ground. Harvard University Press, Cambridge, Massachusetts. ~ . films-9.3 r 230 Gill,Kisham Sing (1972). Drying regimes for artificial heat drying of tapioca chips.Project paper. Faculty of Agriculture, University of Malaya, Pantai Valley, Malaysia. . Gill,W.N. , Del Casal, B.and Zeh, D.W. (1965). Binary diffusion and heat transfer in laminar free convection boundary layers on a vertical plate. Int. J. Heat Mass Transfer. 8:1135-1151. Crace,M.(l971). Processing of Cassava, Agricultural Services Bulletin No. 8. FAO,Rome. Hachero, L. E.(1951). A cottage cassava slicer. Philippine Agricultural Engineering Journal, 2. Manila, Phillippines. Hall,C.W. (1957). Drying Fram Crops. Edwards Brothers, Inc., Ann Arbor, Michigan. . 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