OVERDUE FINES ARE 25¢ PER DAY PER ITEM Return to book drop to rembve this checkougufrom your record. 4,;\ ' . ' f ~nn—.vi. q - r [7#4_?I jquTTEVEEEEIF Mi 0 vefiru m .M” . 9 ' 11 1 (DEN DRYING WITH SOLAR HEATED AIR By Edison Wamara Rugumayo A DI SSERTATICN Sutmitted to Michigan State University in partial fulfillment of the requirements for the degree of IDCI’OR OF Plum Agricultural Engineering Department 1979 ABSTRACT (DEN DRYING WITH SOLAR HEATED AIR by Edison Wanara Rugumayo The supply of the two principal grain drying fuels (LP gas and natural gas) is diminishing throughout the world. As a result there is increased competition for than from non agricultural users. Deannd for these fuels is outstripping supply, creating a need for development of alternative energy sources for grain drying. Solar energy is one alter- native fuel for grain drying. Previous research has shown that the diffuse nature of solar energy precludes its use in high temperature dryers. A low temperature fixed bed drying system is therefore the most technically and economically feasible approach. The objectives of this thesis were to develop and test equations for thin-layer corn drying and moisture adsorption at low tameratures encountered in solar drying and to evaluate the perfornance of a solar air-heater in conjunction with a fixed bed corn drying system. Experi- mental tests included a) Thin—layer corn drying and moisture adsorption using drying air between 4.4% and 21.1% and 30% and 60% (for drying) and 85% to 90% (for revvetting) relative humidity. Edison Wamara Rugunayo b) Drying of a bin of corn with a flat-plate solar air heater (0.46 m. wide by 4.88 m. long) to test the thin—layer corn drying and rewetting models, and for evaluating the effi— ciency of the solar collector. A new heat transfer coefficient equation for an asymmetrically heat— ed air duct was developed and was used to develop models for calculating the collector efficiency, heated air temperature rise and the operating cost of a solar air heating collector. Between 10:00 A.M. and 2:00 P.M. the efficiency of the experimental collector was calculated as 57%. The average experimental and simulated temerature rises were found to be 700 and 5°C respectively. A thin-layer drying equation and a thin layer moisture adsorption equation were developed by non—linear parameter estimation which simu— late the corn drying and moisture adsorption processes more accurately than the thin-layer equations for low temperature drying and adsorption presently available in the literature. The equations were tested in conjunction with the Michigan State University fixed bed drying model and agreed well with the experimentally determined corn moisture contents in the corn bin. The simulated average final corn moisture content was 2% higher than the measured average final corn moisture content. Also, the corn dry matter loss was calculated to be less than 0.5% so that grain market quality was not adversely affected by solar drying process. I/. ',/' . ‘ '/ I" / /.‘ / ,/ . " / /// ~/, " - , '_ c mfg/.4. _,. ‘E: 1143.5; Approved , .9, _ e . Major Professor /.:;‘/‘ ,_ ~ / 7/ ‘1 I App... Mm" Department Chairman ACIQ‘IOWLEIIEMENTS The author expresses deep appreciation to Dr. F. W. Bakker-Arkena for his guidance and encouragement during the cource of this investiga- tion, and for serving as major professor. Sincere thanks is expressed to Dr. D. Penner (crop and Soil Sci- ences), Dr. L. J. Segerlind (Agricultural Engineering), Dr. M. C. Smith (Mechanical Engineering), and Dr. R. Spence (Physics) for serving as guidance committee members. Their advice along with that of Dr. J. V. Beck (Mechanical Engineering) is greatly appreciated. A special note of thanks to the entire community of Agricultural Engineering Department for making the author's stay at Michigan State University a joyous one. The partial financial support provided by Makerere University, Uganda through the Rockefeller Fbundation and Michigan State University is much appreciated by the author. Special thanks to Mrs. Sarah N. Rugumayo for her encouragement and support during the course of the study. ii TABLE OF CONTENTS Page IJSE'OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . v LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . viii LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . xi Chapter 1. INTRODUCTION 1 1.1 Solar energy collectors 2 1.2 Fixed bed dryer . 5 1.3 Nature of the problem. 6 2. LITERATURE REVIEW . 7 2.1 Cbrn thin-layer drying . . 7 2.2 Cornmoistureadsorption............. 10 2.3 Research in solar energy . . . . . . . . . . . . . 11 2.3.1 Nature and availability of solar energy . . 11 2.3.2 Flat-plate solar energy collector . . . . . 15 2.3.3 Transparent covers . . . . . . . . . . . . 16 2.3.4 Absorber plate . . . . . . . . . . . . . . 17 2.3.5 Heat losses . . . . . . . . . . . . . . . . 20 2.3.6 Heated air duct . . . . . . . . . . . . . . 24 2.4 In-bin solar drying . . . . . . . . . . . . . . . . 31 3. 'THEORETICAL ANALYSIS . . . . . . . . . . . . . . . . . . 34 3.1 Thin-layer corn drying and rewetting equations . . 34 3.2 Derivation of solar collector efficiency . . . . . 41 3.2.1 Step 1: Calculation of beamnand.diffuse radiation components of solar radiation incident on an in- clined collector surface . . . . 41 3.2.2 Step 2: Calculation of radiation absorbed. 44 iii Chapter NM pw 9’?’ °3°° ~10) min Step 3: calculation of heat loss fromnthe absorbing surface to the atmosphere Thermal model . . . . Step 4: Calculation of useful heat removed from the solar air heater Preparation of in-bin solar drying equations In—put data .......... . . . . . . 3.3 Economic analysis . 4. EXPERIMENTAL INVESTIGATIONS . . 4.1 LOW'temperature thin-layer corn drying/rewetting operation . .............. 4. 2 Solar energy collection and in—bin corn drying 5. RESUETS . 5.1 Introduction . 5.1.1 5.1.2 5.2.1 5.2.2 5.3.1 5.3.2 5.4.1 5.4.2 £1 CIRKIUSIONS. Thin-layer corn drying results. Discussion of corn thin-layer drying results Thin-layer corn rewetting results. Discussion of corn thin-layer rewetting results Fixed bed in—bin solar corn drying results. Discussion of in-bin solar cron drying results Solar collector test results . Discussion of the solar collector results . 7. SUGGESTIONS FOR FUTURE WORK 8. APPENDICES . Appendix A Appendix B Appendix C Appendix D Appendix E 9. REFERENCES . iv Page 47 49 61 75 78 78 81 81 85 91 91 91 115 116 130 134 145 148 156 158 159 160 167 178 195 257 274 Table 2-1 2—3 2-4 2—5 4-1 5—1a 5—1b 5—lc 5-1d 5-1e 5—1f IJST‘OF TABLES Guide to selection of number of transparent cover plates Values of ReGrit for rectangular ducts . Factor Mf/fO for the duct with a flat galvanized steel sheet absorber plate, (Malik, 1967) . . . . Factor 3710 for the duct with a corrugated steel sheet absorber plate, (Malik, 1967) . . . . . . . Thin-layer corn drying and rewetting conditions Experimental thin-layer corn drying test one results for drying air temperature of 21.00C and air relative humidityof60% Experimental thin-layer corn drying test two results for drying air temperature of 21.00C and air relative humidity of 50% Experimental thin-layer corn drying Best three results for drying air temperature of 21.0 C and air relative humidityof40% Experimental thin-layer corn drying test four results for drying air terperature of 15.5 C and air relative humidity of 50% Experimental thin-layer corn drying test five results for drying air temperature of 10.0% and air relative humidityof40% Experimental thin-layer corn drying test six results for drying air temperature of 4.4°C and air relative humidity of 30% Experimental and simulated corn thin—layer moisture content and drying parameter, K of test one for drying air temerature of 21.0 C and air relative humidity of 60% Page 18 25 30 3O 95 97 98 100 101 102 Table 5-1h 5-11 5—1j 5-1k 5—12 5—2a 5-2b 5—20 5—2d 5-2e 5-2f Experimental and simulated corn thin-layer moisture content and drying parameter, g of test two for drying air temperature of 21.0 C and air relative humidityof50% Experimental and simulated corn thin-layer moisture content and drying parameter, § of test three for drying air terperature of 21.0 C and air relative humidityof40% Ebcperimental and simulated corn thin-layer moisture content and drying parameter, K of test four for drying air temperature of 15.5% and air relative humidityof50% Experimental and simulated corn thin-layer moisture content and drying parameter, l; of test five for drying air temperature of 10.0 C and air relative humidity of 40% . Ekperimental and simulated corn thin-layer moisture content and drying parameter, K of test six for drying air terperature of 4.4% and air relative humidity of 30% Experimental thin—layer corn rewetting test oneO results for rewetting air terperature of 21.0 C and air relative humidity of 90% . . . . Experimental thin-layer corn rewetting test two results for rewetting air temperature of 21.0 C and air relative humidity of 90% . Experimental thin-layer corn rewetting test three results for rewetting air temperature of 21.0 C ' and air relative humidity of 90% . . . Experimental thin-layer corn rewetting test four results for rewetting air terperature of 15.5 C and air relative humidity of 85% . . Experimental and simulated corn thin-layer moisture content and rewetting parameter, K of test one for rewetting air temperature of 21.0 C and air relative humidity of 90% Experimental and simulated corn thin-layer moisture content and rewetting parameter, K of test two for rewetting air temperature of 21.0% and air relative humidity of 90% Page 104 105 106 107 108 118 119 120 121 122 123 Table Page 5—2g Experimental and simulated corn thin-layer moisture content and rewetting parameter, K of test three for rewetting air temperature of 21.00C and air relative hmnidityof90%................... 124 5-2h Experimental and simulated corn thin-layer moisture content and rewetting parameter, K of test four for rewetting air temperature of 15. 5 OC and air relative humidityof85%................... 125 5—3 Experimental and simulated corn moisture content, dry basis, from in-bin drying of shelled corn with solar heated air . . . . . . . . . . . . . . . . . . . . . . 132 5—4 Some of the in—put parameters to the computer program "SOLARUG"............. . 151 C—1 Experimental corn temperature, drying air terperature and absolute humidity, and all other "FIXED" bed in— put data . . . . . . . . . . . . . . . . . . 179 C—2 Simulated hourly corn moisture content and dry matter loss . . . . . . . . . . . . . . . . . . . . . . . . . 189 D—l In-put variables of the program "SOLARUG" used to evaluate the flat—plate solar collector air heater . . 213 D—2 Detailed list of hourly variables from the output of the computer program "SOLARUG" of Appendix E . . . . . 230 D—3 Output variables from the program "SOLARUG" used to evaluate the flat-plate solar collector . . . . . . . 231 Figure l—l 1—2 3—2 3—3a 3-3b 3-4 3-5 4-1 4-2 4-3 5—la LIST OF FIGURES Page Description of sun—earth orientation angles . . . . . . 4 Definition of solar-hour angle HS (CND), solar declination 68(VOD), and latitude L (POC) . . . . . . 4 Electromagneticspectrum................ 12 Electromagnetic spectra of solar and terrestrial radiation . . . . . . . . . . . . . . . . . . . . . . 14 The equation of time, ET, in minutes, as a function of timeofyear..................... 42 Flat—plate collector design sketch . . . . . . . . . . . 48 Cross-section of the flat-plate solar collector . . . . 50 Thermal network of collector heat loss . . . . . . . . . 51 Fully developed turbulent flow in an unsymmetrically heated parallel plate channel . . . . . . 63 A stationary control volume for applying the conserva- tion-of-energy principle . . . . . . . . . . . . . . . 66 Shear stress distribution for fully developed flow in a rectangularduct................... 68 Schematic diagram of the experimental low-temperature, thin-layer corn drying equipment . . . . . . . . 83 Schematic diagram of the experimental solar collector bindryerequipment................. 89 Perforated false floor system for bin drying of corn with air heated in a flat plate solar collector . . . 90 Experimental and simulated corn thin-layer moisture content for drying air temperature of 21. 0 OC and relative humidity of 60% for test one . . . . . . . . 109 viii Figure 5—1b 5-1c 5—1d 5-le 5—lf 5-2a 5—2b 5—2c 5—2d 5-3a 5-3b 5-3c 5-3d 5—3e Experimental and simulated corn thin-layer moisture content for drying air terperature of 21.0 C and relative humidity of 50% for test two . . Experimental and simulated corn thin—layer moisture content for drying air temperature of 21. O0 C and relative humidity of 40% for test three . Experimental and simulated corn thin-layer moisture content for drying air temperature of 15. 50 C and relative humidity of 50% for test four . . Experimental and simulated corn thin-layer moisture content for drying air temperature of 10. O0 C and relative humidity of 40% for test five . . Experimental and simulated corn thin—layer moisture content for drying air terperature of 4. 40 C and relative humidity of 30% for test six Experimental and simulated corn thin—layer moisture content for rewetting air temperature of 21. 00 C and relative humidity of 90% for test one Experimental and simulated corn thin-layer moisture content for rewetting air temperature of 21. 00 C and relative humidity of 90% for test two Experimental and simulated corn thin-layer moisture content for rewetting air temperature of 21. 00 C and relative humidity of 90% for test three Experimental and simulated corn thin-layer moisture content for rewetting air temperature of 15. 50 C and relative humidity of 85% for test four . Experimental and simulated corn moisture content for a bin depth of 0.00 meters . . Experimental and simulated corn moisture content for a bin depth of 0.30 meters . Experimental and simulated corn moisture content for a bin depth of 0.61 meters . Experimental and simulated corn moisture content for a bin depth of 0.92 meters . Experimental and simulated corn moisture content for a bin depth of 1.22 meters . Page 110 111 112 113 114 126 127 128 129 136 137 138 139 140 Figure 5-3f 5—3g 5-3h 5—31 5—4a 5—4b 5-4c 5-4d A—4 A-6 Experimental and simulated corn moisture content for a bin depth of 1.52 meters . . Experimental and simulated average corn moisture content Simulated average hourly corn moisture content . Simulated average hourly corn dry matter loss Temperature distribution in the flat-plate solar collector air heater, during the deep bin solar drying test Heat transfer coefficient, h and air flow variation with time in the flat-plate solar collector air heater components of solar radiation incident on an inclined flat-plate solar collector and the collector efficiency . Annual useful solar heat from the flat-plate solar collector air heater and the cost of obtaining the heat energy Corn drying and moisture absorption coefficient, K for drying air temperature of 21.00C and relative humidity of 60%, and rewetting air temperature of 21.00C and relative humidity of 90% for test one . . . Corn drying and moisture absorption coefficient, K for drying air temperature of 21.00C and relative humidity of 50%, and rewetting air temperature of 21.00C and relative humidity of 90% for test two . . . Corn drying and moisture absorption coefficient, K for drying air temperature of 21. 00 C and relative Ohumidity of 40%, and rewetting air temperature of 21. 00 C and relative humidity of 90% for test three . . Corn drying and moisture absorption coefficient, K for drying air temperature of 15. 50 C and relative humidity of 50%, and rewetting air terperature of 15. 50C and relative humidity of 85% for test four . . . . Corn drying coefficient, K for drying air temperature of 100°C and relative humidity of 40% for test five Corn drying coefficient, K for drying air temperature of 4. 4 OC and relative humidity of 30% for test six Page 141 142 143 144 152 153 154 155 161 162 163 164 165 166 so so E3 eF’ m5” ‘D K WC‘ 11> 0 5e». 000C) LIST OF SYMHDLS constant duct depth, m area, m2 area of collector size a, m2 area of collector size b, m2 rewetting parameter, l/hr area of solar collector, m2 perimeter area of solar collector, m2 apparent standard time, h duct width, In collector width, m coefficient 8f free convection heat transfer in a tilted collec— tor, w/(m2 - €1.25) constant mass concentration coefficient, kg/m3 specific heat, kJ/kgaOC speed of light in any medium, cm/sec cloud cover, dimensionless cloud cover , dimensionless annual additional cost, $/year total additional investment , $ air flow rate, ma/min xi DEL DELT DPK DMISRA DMS DRUG DY speed of light in a vacuum, cm/sec capital recovery factor, $/$/year solar energy cost , $/mW diameter of tube, m diffusion coefficient, cmz/sec dirt loss factor, dimensionless moisture content by delGuidice thin-layer equation, decimal d.b. time increment total bed depth, m drying parameter, l/hr duct hydraulic diameter, m dry matter loss by Misra thin—layer equations, percent dry matter loss by Sabbah and delGuidice thin—layer equations, percent dry matter loss by Rugumayo thin-layer equations, percent day of the month spectral emissive power, 1y/min—u equation of time, min experimental corn moisture content, decimal d.b. emissivity factor, dimensionless outer collector cover to non-outer cover heat transfer resistance ratio mass transfer rate, kg/cmn2 sec mean friction coefficient, N/cm2 acceleration due to gravity, m/sec2 dry weight, kg/m mass flow rate per unit area, kg/h—m2 xii gravitational acceleration 9.8 m/sec2 convective heat transfer coefficient, w/ (mZ—OC) latent heat of vaporazation of water in a product, kJ/kg equivalent radiative coefficient. w/ (mZ-OC) convective coefficient, w/ (mz—OC) wind coefficient of heat transfer, w/(mZ—OC) absolute humidity of air, kg/kg inlet air absolute humidity, kg/kg time, hrs solar hour angle, degree angle of incidence, degree internal energy, kJ/kg annual discount or interest rate, S/S/year net energy absorbed, w/m2 insolation, w/m2 bean radiation, w/m2 diffuse solar energy, w/m2 total incident solar energy, w/m2 number of nodes between prints parameter, l/h thermal conductivity, w/m—OC coupling coefficient phenomenological coefficient thiclmess, m subscript or superscript extinction coefficient , l/cm latitude angle, degree xiii L length, m 131‘ local standard time m constant M moisture content, decimal, d.b. MISRA moisture content by Misra thin-layer equations, decimal d.b. MR moisture ratio, decimal n number of days since the beginning of year n number of glass covers n refractive index NED equation type NLPF number of layers per meter Nu Nusselt heat transfer number, dimensionless pressure , N / can2 "0 PP pumping power, w or kg-mz/sec3 Pr Prandtl fluid number, dimensionless PS saturated vapor pressure. Pa PSDB vapor press, Pa q heat energy, w/m2 q heat flow rate kJ/h—m2 Q heat flow rate kJ/h r angle of refraction, degree r radius, cm rh air relative humidity, decimal R radius, cm R resistance to heat flow, (mZ-OC)/w Re Reynold's fluid flow number, dimensionless RH air relative humidity, decimal xiv RUG SMC St TA TAI R TBTPR THIN TIN moisture content by Rugumayo thin-layer equations, decimal d.b. sun of squares function, scalar shading factor, dimensionless moisture content by Sabbah equation, decimal , d.b. moisture content by Sabbah and delGuidice equations. decimal d.b. recorded insolation, w/m2 Stanton heat transfer number, dimensionless time, h thickness, an expected solar collector life time, years terperature, OC ambient air terperature, OC bulk terperature, OC collector terperature, OC mixed mean fluid temperature, C plate terperature, OC air temperature, 0C transpose ambient air terperature, OK drying or rewetting air temperature, 0K time between output , h recorded heated air temperature , OK glass temperature, C)K grain terperature, OK inlet or initial grain terperature, OC inlet or initial air terperature, OC time of day, h absorber plate terperature, OK Tedlar cover temperature, 0K total time, h heat loss coefficient, w/(mZ—OC) GGESE fully developed fluid flow rate, m/h constant, dimensionless overall heat transfer coefficient, w/(mz-OC) ‘5‘? wind velocity, m/sec < wind velocity, m/sec <1 fluid velocity in duct, m/sec VA wind speed, m/sec W weight , gms W width, m x distance , m x x—coordinate XME equilibrium moisture content, decimal, d.b. XII) inlet or initial moisture content, decimal d.b. y y-coordinate y distance , m 37+ constant , dimensionless symbols used as subscripts a air b back b black body b,coll beam on inclined collector surface c collector crit critical 'U‘CS'U '1 downward diameter equilibrium fluid glass hydraulic hydraulic heat inlet lamdnar long loss initial outlet smooth perimeter plate product radiative solar sky surface time total useful upward vapor xvii Greek H} 4} re [-6- X water symbols altitude angle, degree absorptance, dimensionless constant collector tilt, degree finite difference solar declination, degree constant difference emittance, dimensionless error vector efficiency, decimal grain temperature, 0C or 0K wavelength, um dynamic viscosity, kg/(m—hr) density, kg/m3 reflectance of beam radiation from one surface, decimal constant variance of observation errors Stefan-Boltzman constant, 5.67x10‘8 w/(mz—OK“) shear stress, N/m2 transmittance, dimensionless frequency, cycles/min kineratic viscosity, mz/hr solar azimuth, degree diagonal matrix fraction of long-wave radiation absorbed covariance matrix of observation errors xviii CHAPTERCNE INTRCDUCI‘IQ‘I A diminishing supply of petroleum and natural gas coupled with in- creased competition for these products has made the conservation of energy important in regard to cost and management factors in grain drying. Several universities and other research institutions have been searching for a viable system of drying crops using air heated with solar energy as an alternative to liquid propane (LP) and natural gas. Solar energy as an energy source has the following desirable char- acteristics: a) it is clean and silent; b) it is abundant and widely available all over the world; c) it is dependable statistically; d) it is inexhaustible; e) its transportation cost to the point of use is free; f) it is estimated that the sales of solar industry today, in the United States alone, are worth about two hundred twenty-five million dollars per year. The solar crop drying units reported in use fall into two major categories; they are the covered and the bare plate collectors (Stove, 1977). Within these two categories a variety of designs have been made. Sane of these are: 1) large steel bins with the outside wall surfaces painted black (Haley,1974); 2) steel bins with the outside wall surface painted black, to act as the absorbing surface, and a wall of clear fiber glass around the portion of the bin which the sun rays strike; 3) the 44 cm space between a building's steel roof and its ceiling has fans installed to draw air through the space and up to an elevated center duct in the roof; 4) a suspended plate collector where air is moved along both sides of the suspended absorber plate. Most of these units have back-up energy systems SUCh as electric or gas air heaters. Either alone or in combination with other energy systems solar crop drying units have worked with some success even though they appear to be proof-of—concept designs and can therefore be improved upon. 1.1 Solar energy collectors Heating air with solar energy is accerplished by first absorbing the solar energy and then transferring the energy to the air. The absorber may be heated either by focusing the sun's rays on it with a parabolic mirror or by allowing the rays to fall on it directly. The former systems are used to increase the flux density of incoming solar energy and are exployed where high terperatures are desired, as in metal lurgi- cal and aerospace industries. Without optical concentration, the flux of incident radiation is, at best, about 1100 w/mz (349 BTU/hr-ftz) and is variable. 3 The wavelength ranges from 0.3 to 3.0 mm which is considerably srorter than that of the emitted radiation from most energy absorbing surfaces. Thus flat-plate solar collectors are for applications requir- ing energy at moderate terperatures, up to perhaps 1000C (212°F) above ambient temperatures. They have the advantages of using both beam and diffuse solar radiation, not requiring orientation toward the sun, re— quiring little maintenance and are simple in mechanical design. The important parts of a typical flat-plate solar collector are: l) the "black" solar energy-absorbing surface, with a means for transferring the absorbed energy to a fluid; 2) the envelop(s) which is transparent to solar radiation and is placed above the solar absorber surface to reduce convection and radiation heat losses to the atmosphere; 3) the back and side insulation to reduce heat conduction losses. Basically, then solar drying units with flat-plate solar collectors are low terperature systems. Well designed units are those that have been engineered based upon consideration of the heat and mass transfer between the crop and the low-terperature drying air and of the ”optimum" solar collector design. The word "optimum" does not imply use of optimi- zation techniques in designing the collector. It, rather, refers to designing the solar collector for drying grain to moisture contents which are safe for grain storage. Particular consideration sl’ould be given to the flat-plate efficiency and terperature rise. Both are affected by: a) solar declination; b) local solar time; c) time of day and year; d) latitude; e) collector inclination; f) upward heat loss coefficient; a) wind speed; h) intensity of solar radiation. The angles in parts (a), (d) and (e) are illustrated in Figures 1-1 and 1-2. ch = solar azimuth B = collector tilt .5 Figure 1-2 Definition of solar-hour angle HS (CND), solar declination 5s (V03), and latitude L (Pm). 5 Once the relationships of these parameters have been established and programmed for evaluation with a high speed computer the design of solar energy air heaters for grain drying will be greatly simplified. 1.2 Fixed bed dryer The investigation of corn drying with solar heated air would not be complete without considering the heat and mass transfer relationships in the fixed bed dryer where the grain is dried. In a fixed bed dryer model, energy and mass balances can be written on a differential volure at an arbitrary location within the grain bed. In these equations, there are four unknowns, (a) corn moisture content, (b) drying air humidity ratio, (c) drying air terperature, and grain terperature. Therefore, four equa— tions must be set up. However, without loss of generality the air terp- erature, T, can be taken equal to the grain teiperature, 0. This assurp— tion leads to an establishment of (a) two equations obtained from the conservation of moisture, with no free water accounted for, (b) one energy equation obtained from a combination of the drying air and the drying grain equations. The grain equation can only be obtained from an erpirical thin—layer equation. In the Michigan State University drying model, one thin-layer low temperature model is used. No suitable adsorp- tion equation is available yet . The moisture adsorption equation which is currently being used in the Michigan State University model to pre- dict moisture adsorption in corn is inaccurate. The developrent of an appropriate low—terperature rewetting equation for corn is imperative . Hence, a better knowledge of both the drying and rewetting parameters in a shallow bed of corn should permit improved understanding of the deep— 6 bed solar grain drying. The moisture adsorption equation is developed from the mathematical theory of diffusion. 1.3 Nature of the problem The problem studied in this thesis can be divided into three major parts: 1. development of mode1(s) for thin-layer corn drying and moisture adsorption at low terperatures; 2. design of an optirmmn efficiency flat-plate solar air heater for low terperature in—bin solar corn drying; 3. evaluation of the performance of the solar air-heater in con— junction with a fixed bed corn drying system. CHAPTER TWO LITERATURE REVIEW 2.1 Corn thin-layer drying A survey of the literature on physical mechanisms of the drying of thin layers of grain has been made. Several empirical drying equations have been developed for shelled corn for both high and low temperature operations. The most commonly used empirical thin—layer corn drying equations (Brooker et 31., 1974; and Pfost et a1., 1976) are modified versions of Thompson et 31. (1968) equation. These are valid for air temperatures ranging from 26.7OC to 148.9OC. Due to the wide working temperature range these equations have worked rather unsatisfactorily in predicting drying grain.moisture contents. Narrow temperature range models appear to be more desirable. Flood gt El! (1969), Troeger and.Hukill (1970) and.Muh (1974) de- veloped.empirical drying equations for corn in temperature ranges of (a) 2.2°c to 21.1%, (b) 32.2°c to 71.100, and (c) 26.7OC to 104.4°c, respectively. Flood et a1. (1969): MR = exp(-k to-eeu) (2-1) where M-% NE{_'E%:::]%3 k = exp (-x ty) x = (6.0142 + 1.453 x 10‘” (rh)2)0.5 _ — 2 o — (1.86 + 32) (0.3352 x 10 3 + 3.00 x 10 8 (rh) )0 5 y = 0.1245 — 2.197 x 10'3 (rh) — (1.80 + 32) (2.30 x 10"5 (rh) + 0.58 x 10'”) Troeger and Hukill (1970): — . ‘ C1 ‘ ‘ -55 p1(M - me) 1 - p1(MO - Me)QI, for M0 3 M 3 Mxl (2-2) I;__ _ , Q2 _ _ , Q2 , 60 p2(M Me ) p2(MX1 Me ) + txl, for MX1 > M 3 MX2 1;— : ' _, '1 q3 _ __ q3 , . , 60 p3(M Me) p3(MX2 Me) + txz’ for sz > M 3. Me where M = 0.40 (M — M ) + M X1 0 e e M = 0.12 (M - M ) + M X2 0 e e = , _ . Q1 _ , _ . Q1 x1 [p1(MX1 Me) p1(Mb Me) ]/60 = _ Q2 _ , _ Q2 tx2 [p2(MX2 Me) p2(Mx1 Me) ]/60 + txl p1 = exp(-2.45 - 6.42 M01'25 - 3.15(rh) + 9.62 Mb(rh)0°5 + 0.0549'- 0.036 Va + .96 exp[2.82 + 7.49(rh + 0.01)°°67 - 0.03220 - .5728 DZ 9 p3 = [0.12010 - Menml ‘ ‘13)(p2q2/q9 q} = -3.468 + 2.87 M.O - [0.019/(rh + 0.015)] + 0.02886 q2 = -exp(0.810 — 3.11 rh) q3 = —l.0 Muh (1974): t=AlnMR+B[1nMR]2 where M - Me MR=M -M o e A = -3.28700 — 0.10440 B = —3.34114 + 0.12860 (26.7OC _<_ 0 5 37.7OC) A = -13.71244 + 0.171590 B 3.69212 - 0.057580 (37.700 < 0_<_ 60°C) A -8.20750 + 0.079830 B 0.44881 - 0.004170 (60.0°C < 0: 82.2 C) A = -4.69252 + 0.037060 10 B = -7.75868 + 0.023150 (82.20C < 0 : 104.000) Obviously, only the Flood et 31. (1969) (called the Sabbah equa- tion in this thesis) and possibly the Muh (1974) equations would apppear of interest for use at the solar heated air temperatures. Hewever, these equations are erpirical and complicated to use. An equally ac- curate, if not better but simple and.less empirical equation would be more desirable. Hence, an attempt will be made to develop such an equation from mathematical diffusion theory (and non-linear parameter estimation techniques) similar to the model presented by Chu.and Hustrulid (1968). 2.2 Corn moisture adsorption For proper evaluation of in-bin solar grain drying it is necessary to account for grain moisture adsorption, especially at night and on rainy days. Mbreover, proper understanding of the adsorption kinetics will provide useful information on grain quality and a guide for grain conditioning, storing, processing and fumigating. In grain rewetting studies, del Guidice (1959) developed an equation of the form: 118 = exp[—4.309(PS)0'“65rh(rh)3nt] (2-4) where M - M t e MR.= -———————- Mt_l — Me 11 The data used in developing the above relationship included dry bulb terperature in the range of 15.600 to 40.6OC, relative humidity in the range of 60% to 100% and air velocities of 3 mpm and 12.2 mpm. The del Guidice equation does not perform satisfactorily at air velo- cities and temperatures outside these ranges. Suc-Won—Park _e_t_ a_1_. (1974) developed a semi-expirical moisture adsorption equation for yellow (Pioneer 3306) in which the constants are dependent on the initial corn moisture content. The develoment of an appropriate low- temperature rewetting equation based on mathematical diffusion theory, as in the case of the drying equation was considered imperative. A better knowledge of both the drying and rewetting parameters in a shallow bed of grain should permit improved understanding of the deep- bed solar grain drying operation. 2.3 Research in solar energy 2.3.1 Nature and availability of solar energy The nature and availability of solar energy are important factors for consideration in the design of flat-plate solar heat collectors. Since collectors of this type can utilize both the direct and diffuse components of solar radiation, and in many localities substantial quantities of solar energy can be collected on partly cloudy days, flat- plate collectors should not be operated on perfectly clear days only. Solar energy is a form of electromagnetic radiation emitted by the \ sun because of its terperature. It is propagated at the speed of light C, which can be expressed in terms of wavelength A, and frequency v, c such that c = 52 = Av (2—5) 12 where, Co = speed of light in a vacuum, ft/sec or cm/sec n = refractive index 0 = speed of light, 9.8 x 108 ft/sec (3 x 1010 cm/sec) A = wavelength (in cm or micrometers, mm = 10’6 m) v = frequency, cycles per unit time Figure 2-1 shows a portion of the spectrum of electromagnetic radiation. In the thermal radiation range of 0.1 to 100 mm the wavelengths of im- portance in solar energy and its applications are in the ultraviolet to near-infrared range, that is from 0.20 to about 25 mm. This includes a) the visible spectrum range of 0.35 to 0.75 mm; b) solar radiation outside of the earth’s atmosphere which has most of its energy in the range of 0.20 to 4.0 mm; c) solar energy which is received at the ground and is substantially in the range of 0.29 to 3.0 mm. 'I'hermal.._.__> radiation will log A,m 1 3 2 1 0 -1 -2 -3 —4 -5 -6 -7 —8 —9 -10 -11 -12 L 1 l J l 1 l l l L, L 1 l l L L | «<— n—-x rays ————pl radio 1 ‘— infrared—fl ultra waves violet . Y rays visible v] Figure 2—1. Electromagnetic spectrum 13 The energy distribution in the electromagnetic spectrum is called the spectral emissive power, Eb, A' The adjective ”spectral” denotes that the radiation depends on the wavelength spectrum. If the total radiation spectrum.is divided into small wavelength bands of width AA, the quantity Eb, A AA dentoes the amount of radiation emitted in the waveband AA. Figure 2—2 shows the variation of the spectral emnssive power at a given temperature as a function of A for black bodies at solar and building temperatures (Kreider and Kreith, 1975). Figure 2-2 clearly illustrates the factor that as solar radiation penetrates the atmosphere of the earth it is partly absorbed and partly scattered by the various constituents of the atmosphere such as clouds, molecules of air, water vapor, ozone, carbon dioxide and suspended particulate matters. Both direct or beamland diffuse solar radiation available at the surface of the earth are functions of these variables. Beam radia— tion is that solar radiation received frcmxthe sun without change of direction. Diffuse radiation, on the other hand, is that solar radia— tion received frcmxthe sun after its direction has been changed by re- flection and scattering by the atmosphere. In addition to spectral variation, therefore, the amount of solar radiation incident on a surface depends on its location, orientation, the time of the year, and time of the day. Johnson (1954) has deter- .mined that the rate at which solar energy falls on a surface normal to the rays of the sun at the earth's surface without losing any energy to the atmosphere is 1393 w m‘2 or 2.0 1y min"1 or 2.0 cal min"1 arm-2 at the mean distance of the earth from the sun. This value is generally referred to as the "solar constant", and its spectral variation is shown in Figure 2-2 as extraterrestrial solar radiation. 14 The solar radiation actually incident on a horizontal surface is called "insolation (1)". Seasonal variation of insolation has been considered by previous investigators ( Buelow, 1967 and miguiayo, 1974). The former used spherical geometry to develop an expression with many unknowns and its evaluation requires use of both tables and graphs. The latter investigator, on the other hand, used a statistical tech- nique to develop an expression for insolation in a tropical region. 5 O | T T V l I r I .- ‘ .Ultroviolet—qwsuble A named \ ,’ \\ Black-body radiation at 6,000°K (2.3ly 2,0 . \’ mm") \ Extruterrestnol solar radiation '0 ._ (ZOly mm“) .. '2 a 3. l E O 5 ' I, "‘ E I E " Durecf-beom (normal-mmdence) 5 l solar rOdlCHOn at the edrtns < 0.2 " surface (L3ty mm") ‘ 53. T O-l . -1 .1 Block-body radiation at 300°K I -I .5 0.05 _ I. (0.6ly mun ) . E ' Estumared mfrured > \v“ ._ a emussmn to space 1 u from the earth's ,5 o o? . DIfoSe '. surface (0 IO ‘ “1 solar “ I m‘ -| " ' ‘ \ y ‘n ) v, I rOOIatlon at| 5 0 Cl -Oxyqen the earth's . .5 one ozone surface(0.l4 ubaulyiluu ‘y ”1H1", 0.005 - ‘— ' - Absorption bands of water vapor 0.002 ' and carbon '1 dioxide . I J 1 0.00.0. 0.2 0.5 1.0 2.0 5.0 no 20 so :00 Wavelength A, [1. Figure 2-2. Electromagnetic spectra of solar and terrestrial radia- tion. The black-body radiation at 6000°K is reduced by the square of the ratio of the sun's radius to the aver- age distance between the sun and the earth to give the flux that would be incident on the top of the atmosphere. 15 .Buelow's and Rugumayo's relationships do not distinguish between direct and diffuse solar radiation. The mathematical relationships for diffuse and direct solar radias tion as affected by seasonal variation have been presented Duffie et a1. (1974), and Kreider and.Kreith (1975). These are considered suitable for use in this thesis because, in addition to distinguishing direct from diffuse solar radiation, they can easily be programmed for use on high speed computers to give hourly values of temperature rise, useful energy and efficiency. 2.3.2 Flat—plate solar energy collector Flat-plate solar heat collectors have potential for application in air and water heating systems due to their simple construction. Litera- ture reviews (Whillier, 1963) show that it is possible to produce tem— peratures up to the boiling point of water. Care in the selection of materials of construction and methods of fabrication is essential if costs are to be kept at a level low enough to make solar heating attrac- tive. A typical flat-plate solar heating collector consists of a radiation-absorbing flat plate beneath oneior more transparent covers. The radiation-absorbing plate is a flat memal.plate blackened on the side exposed to the sun. The air to be heated.passes across the front and/or back surface of the blackened plate. The back side of the ab— sorber place is usually insulated to reduce heat losses. If air passes behind the plate, as it is the case in the present study, the insular tion forms one side of the air passage. The tranSparent cover(s) may 16 be glass plate(s); the glass plate(s) may also be replaced by thin plastic cover(s). To make glass and/or plastic coverings effective, air spaces between the coverings and between the bottom covering and the blackened metal surface is necessary. The number of covers is de— termined by the temperature difference required and by the economy of using additional layers of cover materials. 2.3.3 Transparent covers The optical properties of transparent cover materials (usually glass, or thin plastic films) that are of most importance in solar col— lectors have been extensively studied and reviewed. Whillier (1963) studied the transmittance of solar radiation by a 0.01016 cm thick poly- vinylfluoride film comronly known as Tedlar (a Dupont product) and com— pared it to that of a low—iron sheet of glass (0.3176 mm thick) in the temperature range of 00C to 2000C. His conclusions were: 1) the transmittance of Tedlar to solar (short wave) radiation at normal incidence is 92 percent. (This is better than any glass, unless the glass is surface treated to reduce reflec- tion losses); 2) the transmittance of glass for long wave radiation in solar absorbers is, for all practical purposes, zero; 3) the transmittance of Tedlar for long wave radiation is constant at about 30 percent, for radiation emitted by surfaces at tem- peratures anywhere between 0 and 200°C. This is not neces- sarily true for all plastics. It is valid for Tedlar because this material is completely opaque to radiation between l7 wavelengths of 6.9 to 13 microns, and about 45 percent of the radiation emitted by surfaces in the temperature range 0 to 2000C lies in this wavelength region; 4) the solar transmittance of multiple cover collectors is con- siderably improved by the replacement of the inner glass covers with Tedlar. The protection afforted to the inner Tedlar sheets by the outer glass cover should prolong the Tedlar life considerably (five years, beyond the freely ex- posed life of five to seven years claimed by the manufactures); 5) Tedlar is cheaper than glass. The number of transparent cover plates that should be used in a solar collector depends on many factors. Whillier (1964) noted that the addition of an extra glass cover increases the cost of the solar heater by about 15 percent and an extra Tedlar layer the corresponding percentage is about 5 percent. He, however, considered the most im— portant factor to be the terperature at which it is desired to collect the heat, compared to the ambient texperature. As a guide for choosing the number of transparent glass covers to be used in a flat-plate solar collector, Whillier (1963) presented Table 2—1. In cases where plastic covers are incorporated into flat plate solar collectors the numbers may vary from those proposed in Table 2—1 . 2. 3.4 Absorber plate The purpose of the absorber plate is to absorb the incoming solar energy and transfer the heat to the air or water passing over the 18 Table 2—1. Guide to selection of nurber of transparent cover plates (Whillier, 1963). Collect ion terpera— Typical applications Nurber of cover plates ture above ambient Black-painted Selective terperature absorber absorber (t -t),°C c=.90r.95 c=.2 c a -10 to +10 Heat source for heat pump none none Air heating for drying 10 to 60 Sumer water heating Air heating for drying Solar distillation l 1 Space heating in non-freezing climates 60 to 100 Winter water heating 2 1 Winter space heating 100 to 150 Summer air conditioning Steam production in summer 3 2 Refrigeration Cooking by boiling surface of the plate. The hourly temperature values at any point of the absorber plate is assured constant. This requires that the thermal conductivity of the plate be high enough so that any amount of addi- tional heat is conducted through the plate to a surface where it is reroved by convection. The desired heat absorbing properties of the surface exposed to the sun can most easily be obtained by coating the surface of the plate with a good solar energy absorbant. Therefore, 19 the plate can be thin and strong enough to require support based only on the strength of the glass cover. A glass covering requires support at spacing greater than 0.457’mlto withstand.moderate stresses without breakage. The plate surfaces should have good coating holding Char- acteristics. Copper sheet metal meets all of these requirerents, is easy to handle, (though more expensive than aluminum) and, therefore, seems to be the best metal. The optimum.coating for an absorber plate has characteristics that formla.ccmbination of high absorptance a, for solar radiation and low emdttance, E, for long wave radiation. This combination of properties is possible to achieve because there is little overlap in wavelength ranges between inccmdng solar energy (outside the atmosphere of the earth is 98% at wavelengths less than 3.0 mmo and emitted long wavelength radiation (less than T% at wavelengths less than 3.0 mm) for a black surface at 127°C. Research by 16f and Tybout (1972) on selective surfaces has produced selective surfaces that have sufficient durability and have low cost to warrant use flateplate solar collectors. Essentially, such selective surfaces consist of a very thin upper layer which is highly absorbent to short wave solar radia- tion but relatively transparent to long wave thermal radiation. The substrate has a high reflectance p, and a low emittance c, for long wave radiation. Presently, the only camercially available selective surface that has been extensively field tested is the selective black surface mar- keted under the trade name 'Mircmit". Electrolytically coated galvan— ized sheet steel is used as the plate material for solar water heaters in Israel. It has a solar absorptance of 0.92 and a long wave emnttance of 0.1. Nun—selective, black paint such as lamp-black (which is 20 camercially known as Nextel) has been in general use for both air and water heating. The use of new and cheaper selective paints on solar collector plates for air heating would certainly be necessary improverents. (be such paint in commercial production is Krylon No. 1602 ultra flat-black enamel, manufactured by Borden, Inc. , at Columbus, Ohio. It has an ab— sorptance of 0.95 and an enittance of 0.2. 2 . 3 . 5 Heat losses Thermal losses occur in solar collectors by the usual three modes of heat transfer (convection, radiation and conduction) because the blackened absorbing plate in the collector is hotter than the surround- ing ambient conditions. The heat transfer losses include: a) upward radiation and convection through the transparent cover plates. A semi- erpirical expression for the upward thermal losses qup (for negligible bottom and side losses) was developed by Butz (1973) Tf - Ta 0 (T; - Tg) qu=$+(n/C) +£+2n+f-l-n (2—6) a” Vuf — Ta)/(n + f) 6p 68 where T. + T = 1 o 2_7 Tf ————2 ( ) T. T = collector fluid inlet and outlet terperatures, 1’ 0 respectively Tf = average collector fluid temperature T = ambient air temperature 21 0 = Stefan-Boltzman constant (that is, 5.67 x 10‘8 w/m2 °K") f = outer collector cover to non-outer cover heat transfer resistance ratio h = coefficient of heat transfer from the ouhrost collector cover. w/(m2 °C) C = factor to account for collector tilt in the expression for coefficient of free convection heat transfer on glass collector covers, w/(m2 °c1°25) 8p = non-selective collector surface enittance cg = glass cover enittance n = nurber of glass covers and hw = 5.7 + 3.3V (2—8) 0 = 1.08 - 0.0044 8 (2—9) B = surface tilt angle from horizontal cp = 0.95 (2—10) cg = 0.90 (2—11) f = 0.76 x 10-° °1“V, for v 5 3.1 (2—12) f = 0.36 x 10'°'°°°(V‘°), for 3.1 < v 5 6.6 (2-13) f = 0.24 x 10'°°°°“(V"’), for v > 6.6 (2—14) where v is the wind speed in m/s. The upward heat coefficient, U up’ of the collector with covers is obtained from the relation, qup = Ufip (tp - ta) (2-15) Equatims have been derived by Whillier (1964) for calculating U up for various combinations of glass and plastic covers. ’lhese are given as equaticn (2-16) . Equation 2-16. Equations for computing collector heat loss coefficient, U . . up Transparent cover A ta. ta Plastic Uup = 1 Collector , (‘1 ° t3) 1 h + t h -— 18 h + ‘1: w 1 r“ t --ta cl El 1 ‘ t c t-t U -nh (c S)+ ‘ up crcs tc-ta 1 , -t 0' hcl+Eclhr hwfllhr 149 cl 1 r— l a l 2 h .5 h +h .8 h c2 :2 rd 21 21 :21 t Plastic . 2 , -t a Plastic U _z in (c 5;), 1 t3 Collector up 1'x c x.cs tc.t 1': £1 h on IE h + ‘ T c2+ c2 82 21' 21c21 hw"1hr1'(‘l's) ‘1": Glass ts / Plastic / Plastic ta Collector tl ° ts hw + ‘lhrls (t -t ) l a N 3 5.7 + 3.8 V, ('Jind coeff.) 1/4 I"my ' C “x - ‘y) ' , (convection cocfl.) tilt angle 0 30 60 90. C 1.58 1.38 1.18 0.99 4 4 h ' l -t l - rxy °(x y)/(x (y) (equivalent radiative coeli.) l Exy - l ‘ ‘ - , emissivity factor (x Cy ‘ . emissivity. t collector , 0.95 (black paint) .2 (selective) I 0. 63 I 0.88 ‘ plastic t - t ‘ Glass x-‘a' h + l cl__l____ l l h *8 h 9 v- “ ‘3 rc3 h32’532"r32 h21421".-21 t. = equivalent black bony temperature 0! the sky t3 = ambient air temperature tc = collector - plate average temperature t1, ta, ta, =- temperature of transparent covers 7 - transmittance of plastic {or long-wave radiation (0. 3 for Tedlar) x - traction of long-wave radiationttnt is completely absorbed at first plastic ( x - O. 45 tor Tedlar) 23 When plastic films are used to cover solar collectors, the upward heat losses are greater than with glass because the plastics transnit more long wave radiation. However, when 0.004-inch think Tedlar is used to cover an absorber plate coated with selective paint the higher heat losses are more than compensated for. b) Downward heat losses through the rear insulation are by conduc— tion in the bottcxn insulation, and by convection and radiation from the exposed bottom surface to the environment. With sufficient insulation, 7.62 an to 15.24 cm thick of mineral wool, the downward heat loss coef- ficient is about one—tenth the upward heat loss coefficient. c) Edge heat losses are by the same heat transfer modes as those for the downward heat losses. Based on the outer exposed edge area, the edge heat loss coefficient is given by the relation, q i = ”edge (up) up — ta) (2-17) where D is the depth of the collector box, and P is the perimenter. Use of sufficient edge insulation usually makes q l e negligible. The collector heat loss coefficient, UL’ embodies all the above losses, and is calculated as follows: A = _E _ UL Uup + Urear + Uedge Ac (2 18) where A0 = area of the absorbing plate {‘9 ll perimeter of the collector. 2.3.6 Heated air duct The shape of a collector and the air passage(is) influences the ef— ficiency with which the air passing through the collector is heated. The shape of the air duct also determines the pressure drop of the heating air as it passes through the collector. The velocity of the air and the width of the duct influence the convection and radiative heat transfer coefficients for heat transfer frcm the absorber plate to the air and hence the heat losses already discussed. The highest heat transfer rate is obtained from a duct having a rectangular cross-sect ion as compared to ducts with either square or circular cross—sections with the same pressure drop per unit length and the same wetted area. The duct having circular cross-sect ion has the lowest heat transfer rate. The maxinmm pressure drop that can be tolerated in the collector is governed by the following: a) the fan pressure drop or power, and b) the pressure drop necessary to move the air through the grain and through the ducts. The use of separate small fans and mixing of cold and solar heated air streams is recarmended instead of using one large fan which tends to overheat. The fans usually used in grain drying have a maximum static pressure head of about 10 cm of water. Most of this pressure is re— quired to move the air through the grain and through the ducts. There- fore, a collector can only use a small portion of the total pressure drop of the system. The coefficient ’of heat transfer by convection, hc’ should be a maximan because the higher it is the lower will be the temperature of 25 the absorbing plate. A low absorbing plate temperature is desirable because radiant heat transfer from the absorbing plate to the top covers will be less and, therefore, the overall heat loss from the col— lector will be less. The Reynolds number, which combines the depth of the air duct, the rate of airflow and the air properties is defined as: = _VDD ReD p (2-19) Eckert _e_t 21; (1960) suggested use of an equivalent hydraulic diameter, Dh’ instead of the tube diameter D in equation (2-19) for all heat- transfer applications in which the bulk of the heat transfer is in the boundary layers close to the wall. This eliminates the cases of low Prandtl numbers or those in which the secondary flow effects may be ex— cessive. The hydraulic diameter for a duct with rectangular cross- section of depth a and width b is 2ab/ (a + b). A survey of the lit- erature on the critical Reynolds number (i.e. a number at which a fluid velocity, V in a duct changes fran streamline to turbulent flow) was made by Malik (1967); a summary of the critical Reynolds number for rectangular ducts is presented in Table 2-3. Table 2—3. Values of Beer t for rectangular ducts. i Investigator Ratio of b/ a Re . crit Nikuradse (1930) 3.50 2800 Washington and Marks (1937) 2.0 and 40.0 2800 Schiller (1923) , 3 . 52 1600 26 Table 2—3. con't. Davis and White (1928) 40.0 2800 Eckert and Irvine (1957) 3.0 5000 Cornish (1928) 2.92 2800 The aspect ratio (width divided by depth) of the duct used in this investigation is 3. Hence, the critical Reynolds number for the duct, according to some of the figures in Table 2-3, falls in the turbulent flow range. Barrow and lee (1967) observed that about 20 hydraulic diameters are required for flow to develop thermally for a Reynolds number of 70,000. Since the Reynolds number used in this investigation is much less than the one cited above, a duct length of 16 ft (4.87 m) was considered reasonable for flow to be fully developed both thermally and hydraulically. A Reynolds number (Re) of less than 2100 is generally accepted for laminar flow with a uniform velocity profile in pipes and ducts (Kays, 1966 and Bennett _e_t_ _a_._l_. 1962). Above this Reynolds number the flow be— comes unstable to smell disturbances, and a transition to turbulent type of flow will generally occur. The hydrodynamic and thermal boundary layers start simultaneously at the entrance of a duct . The thermal boundary layer develops only on one side as the duct is heated only at the top. Based on the equivalent hydraulic diameter and Reynolds number Kays recamends use of the following expressions for the mean friction coef- ficient, fm in non-circular ducts for laminar flow: 27 f = 2:6— m Re (2—20) For turbulent flow the following equations hold, rm = 0.046 32"”, for 30,000 < Re < 106 (2-21) rm = 0.079 Re-°°25, for 5,000 < Re < 30,000 (2—22) Equation (2—22) is consistent with the l/7-power velocity distribution. Irvine recommends use of equation (2-22) in a wider range of Reynolds numbers (Reor < Re < 50,000) for non-circular ducts. it Using equations (2-20) through (2—22) and the normal D'Arcy form- ula an expression for pressure drop in the heated air duct can be formulated; = 2 . - Ap 4 fm L v /2 Dh g (2 23) If pumping power (P.P) is of more interest to the solar air heater de- signer than the pressure drop, this is given by the relationship, P.P = m A p (2-24) The heat transfer relationships for forced convective heat transfer within the duct are reasonably well represented by an equation com- prising at least two of the following four dimensionless numbers: Reynolds, Prandtl, Nusselt, and Stanton. For laminar flow, Sieder and Tate (1936) proposed the following expression. 1/3 1 2 Nu = 1.86 (Re Pr) %/ (fi—w-l“ (2-25) s The fluid viscosity 0, is evaluated at average bulk temperature. The term p/us is an empirical correction for the distortion of the velocity 28 profile which results from the effect of high temperature on viscosity. Equation (2—25) applies when the pipe—wall temperature in uniform. This equation obviously cannot be used for extremely long ducts since it would yield a zero heat-transfer coefficient. It is observed by Buelow (1956) that equation (2-25) is valid for air when, D Re Pr 3 > 10 (2—26) The problem of heat transfer with turbulent flow in rectangular ducts has not yet been completely solved. Experimental work reported in the literature shows that forced convective heat transfer within a duct is reasonably well represented by the following relation: Nu = 0 Ram pr” (2-27) The Constants C, m, and n have been evaluated under various types of heating conditions (Siegel and Sparrow, 1960). Both constant axial heat flux and constant axial temperature conditions have been employed. The solar—air heater falls into neither of these simple categories, but may be approximated by the former (Tan and Charters, 1970). The first such equation was recommended by Dittus and Boelter (1930) for flow in smooth tubes. The equation is of the form, Nu = 0.023 (Re)°'8 (Pr)°'“ (2—28) for heat flow from the wall to the fluid, and Nu = 0.023 (Re)0'8 (Pr)°‘3 (2-29) for heat flow from the fluid to the wall. Review of work by various investigators has led McAdams (1954) to conclude that an acceptable 29 correlation for heating and cooling of various fluids with turbulent flow in horizontal tubes is given by equation (2—29) . The equation is valid for the following conditions: (1) the Reynolds number is in the range of 10,000 to 12,000; (2) the Prandtl number is between 0.7 and 120; (3) the pipe length divided by its diameter is greater than 60; and (4) the physical properties of the fluid are evaluated at the bulk temperature. For asymmetrically heated rectangular ducts, Charters (1970) recommended use of the Dittus-Boelter equation with one modifi- cation. The modified equation is of the form, Nu = 0.0182 (Re)0°8 (Pr)0"* (2—30) Another well-known equation is that of Colan (1933), 11 Va 0 Cp (Pr)2/3 = 0.023 (Re)‘°°2 (2-31) The fluid properties are evaluated at the arithmetic mean of the wall and bulk fluid temperatures. Malik (1967) after experimenting with both rough and smooth, asym— metrically heated parallel plate channels with an aspect ratio of 4 and L 5 = 120, recommended use of the Dittus-Boelter equation in the fol- lowing form, Nu = 0.023 (Re)0‘8 (Pr)0°‘* /f/f0 (2-32) The values of the relative roughness, @713: for different Reynolds numbers and two different types of absorber plates (one was a flat galvanized steel sheet and another was a corrugated steel sheet) are given in Tables 2—4 and 2—5. The value of the friction coefficient, f0 for a smooth duct was given by the Blasium equation, 30 Table 2-4. Factor ./f/fo for the duct with a flat galvanized steel sheet absorber plate, (Malik, 1967). Reynolds Number Factor ff—fi: 10,000 1.18 15,000 1.218 20,000 1.245 25,000 1.280 30,000 1.305 40,000 1.355 50,000 1.390 Table 2—5. Factor ,5 710 for the duct with a corrugated steel sheet absorber plate, (Malik, 1967 ). Reynolds Number Factor Jf7f—O 10,000 1.435 15,000 1.438 20,000 1.461 25,000 1.509 30,000 1.542 40,000 1.601 50,000 1.656 31 f = 0.316 Re-0'25 (2-33) Equation (2—33) was found to be in good agreement with a simplified re lationship for an asymmetrically heated air duct. The relationship is of the form, _ 0.0192 Re-l/“A St ' 1 + 1.22 Re4T7B*(pr — 2) (2-34) This equation takes into account only the laminar and turbulent sub- layers of the three-layer velocity profile, Kays (1966). The buffer or transition velocity zone is not considered. For gases and liquids the foregoing relationships are valid for long ducts. When turbulent flow is observed in short ducts the fol- lowing relationships can be used (McAdams, 1954), h _E£._ 120.7 - h — l + (L) (2 35) c L forZEB :20, and h cL- 2 _ EE—-— 1 + 6 L (2 36 for 20 < 11% 5 60. In both of the above equations, h 0L unit convective heat transfer for the duct of finite length L.and hc is is the average the convective heat transfer for an infinitely long duct. 2.4 In-bin solar drying In the United States, Buelow and.Boyd (1957) were the first to in— vestigate in-bin solar grain drying. This and other recent studies (Foster and Peart, 1976; Shove, 1977; BakkerbArkema et 31., 1977; and 32 Thompson and Pierce, 1977) have shown that in-bin solar corn drying is feasible. The drying process of a solar fixed bed grain dryer has been simulated by Bakker—Arkema e_t 3;. (1977). By making energy and mass balances on a differential volume (S dx) located at an artibrary loca- tion in the stationary bed a set of three differential equations is obtained. The model equations are (Bakker-Arkema e_t £1. , 1977): a) for the enthalpy of the air and product, 8T 3T op (0p + MCW) a—t +Ga(Ca + HCV) 3— 8H __ Ga [(CW - CV) (100 - T) + hfg] 5; — 0 (2-37) b) for the humidity of the air, 8M 8H __ _ ppat+Ga 8x 0 (2 38) and c) for the moisture content, Op 3% = an appropriate thin layer equation (2-39) Equation (2-37) and (2—38) along with an empirical thin—layer equation consitute the Michigan State University (IiBU) solar grain drying model. The auxiliary equations for the grain and bed properties, and the psychrometric relationships (including condensation) required for the solar drying model, have been discussed by Abkker-Arkema (1974). An analytical solution of the system of these equations is impossible. Therefore, numerical techniques have to be used. It should be noted 33 that the MSU solar drying model does not contain an equation for de— scribing corn rewetting (frcmihigh humidity air on a cloudy day or at night) so as to accurately model condensation. CHAPTERTHREE THEORETICAL ANALYSIS 3. l Thin-layer corn drying and rewetting equations The mathematical theory of diffusion, first formulated by Fick (1855) and later considered in detail by Crank (1956) and others is the the basis for development of the thin—layer equations. According to this theory, in an isotropic medium, the rate of transfer of the diffusing substance through a unit area of the section is proportional to the concentration gradient measured normal to the section. The rate equation is of the form: _ _3_<_3 _ F--Dax (31) where F is the rate of transfer per unit area of section, C is the concentration (mass per unit volume), and x the space coordinate measured normal to the section. D, a constant of proportionality, is defined as the coefficient of diffusion and has dimensions (length)2 (time)-1. The negative sign in the equation arises because diffusion occurs in the direction of decreasing concentration. The fundamental differential equation of diffusion, with constant diffusion coefficient, is derived from equation (3-1) and reduces to ac 320 ’51? = D ”5552‘ (3’2) Equations (3-1) and (3—2) are known as Rick's first and second laws of diffusion, respectively. Luikov (1966) and his co—workers in the Soviet Union developed the mathematical relationships describing the drying of capillary porous products based on the following assumptions: (1) liquid movement is due to surface forces (capillary flow); (2) liquid movement is due to moisture concentration differences (liquid diffusion); (3) liquid movement is due to diffusion of moisture on the pore surfaces (surface diffusion); (4) vapor movement is due to moisture concentration differences (vapor diffusion); (5) vapor movement is due to temperature differences (thermal diffusion); (6) water and vapor movement are due to total pressure differences (hydrodynamic flow). The system of differential equations are of the following form: %%=V2K11M+V2 K120+V2K13P %%=V2K21M+V2K229+V2K23P 3P 5E=V2 K31M+V2 K320+V2 K33p (3'3) 36 where K11, K22 and K33 are phenomenological coefficients. The other K values are coupling coefficients. Neglecting the pressure and tempera- ture gradients in a corn kernel during the drying and rewetting processes leads to a simplication of Luikov's equations. The ultimate result is 8M 5%- = V2 K11 M (34) The transfer coefficient K11 is called the diffusion coefficient, D. Researchers have used a number of solutions of equation (3—4) for pre- dicting the drying behavior of cereal grains. For a constant value of D, equation (3—4) can be written as: _ 32M -D——-2-+ Gr (3-5) 30°21 HIO 3|? where C is zero for planar symmetry, unity for a cylindrical body and 2 for a sphere. A number of solutions to equation (3-5) for various solid shapes have been used as drying equations for grains. The following initial boundary conditions are often assumed in solving equation (3—5): Mao) = MO (3—6) Must) = Me (3-7) The analytical solutions of equation (3—5) for the average moisture content of various regularly shaped bodies can be obtained directly by integration (Crank, 1957). Thus, for an infinite plane: .. 8 °° __1__ _ 2 2 2 MR " if? E (2n+1)2 eXp[ (21‘H'1) H X 1 (3'8) n-o for a sphere co _ 6 1 112112 2 W-fi‘z—Egz'em-l 9 X] (3-9) ml 37 and for an infinite cylinder: 8 12 X2 n MR = exp[— 4 ] (3—10) 11 u M oil '8 l where An are the roots of the Bessel function of zero order (Perry, 1963). In the above equations the average moisture content and the time are expressed as dimensionless quantities, MR and X, respectively. M - Me 0 e and X = 9,; (Dt)1/2 (3-12) where A represents the surface area and V the volume of the body. For the plane V/A = half thickness; for the sphere V/A = (radius) / 3; for the cylinder V/A = (radius)/2. Chu and Hustrulid (1968) found equations (3-8) through (3—12) describe the drying rate of a solid satisfactorily M - M in the moisture ratio, MR range of m—TM—e- _>_ 0.4. o e Chu and Hustrulid (1968) studied diffusion of moisture in corn kernels assuming that the kernel could be represented by a sphere of equivalent radius, R. Previously published results of several thin- layer drying studies were used in the analysis. The specific temperature, relative humidity and moisture content ranges included: (1) relative humidity 10 - 70%, (2) air temperature 4900 - 71°C, and ( 3) corn moisture content 5 - 35% dry basis. For a moisture content dependent diffusivity the following equa- tion was recommended: 38 M - M 2 6 :1: e = 112' exPE‘IIDEE‘ D 13] (3'13) Mo - Me The concentration dependent diffusivity, D, the pseudo initial moisture a: content MO, and the equivalent radius, R were found to be: _ 2513 D — 1.513 exp[(0.045 T - 5.485)M - ] (3-14) abs T abs where Tabs is the absolute air temperature, in degrees K; M: = 1.0655 Mb — 0.0108 (3—15) R 31““ (3—16) =mm+m+m) where L, W, K are the length, width and thickness of the average kernel, respectively. Equations (3-13) through (3-16) worked satisfactorily under the test conditions used. This may not be true for other condi- tions. In order to improve the effectiveness of the Chu and Hustrulid equation several of its coefficients will be determined for lower air and corn temperatures and mean equivalent radius. The value of the mean equivalent radius (4 = 0.32 cm) is obtained from data of 0111 and Hustrulid (1968). The pseudo moisture content which is important when grain tempering is part of the drying process is replaced with corn initial moisture content. Hence, the resulting semi-theoretical diffusion equation considered for analysis in this thesis is of the form: M - Me 0 e where, mzn 2 K — Ez— — C1 + Cth_1 + C3lcg(Mt_l) + 0,01:le eXp(I‘h3c) (3-18) The parameters K and C1 have units of hr"l , C2 and C3 are dimensionless, and C. has units of OK" 1. The diffusion coefficient, D has units of cmz-hr- 1. The values of the parameters C1, C2, C3 and C1. can be estimated to any desirable accuracy by multiresponse sequential procedures that minimize the sum of squares function. Various sequential methods are discussed in detail by Beck and Arnold (1975). The use of any sequen- tial method depends on the type of information known about the model and the parameters to be estimated. In case the model is non-linear, as in equation (3-18), and the number of measurements at a given time m, is less than the number of parameters p; the measurements are also dependent. A dependent vari- able is linear in a parameter if (a) the differential equation and the associated bormdary and initial equations are linear, and (b) the para- meter enters in a non-homogeneous term in a linear manner. In other cases the variable is non-linear since both conditions must be satisfied. For a linear differential equation and associated conditions, the dependent variable may be linear with respect to some parameters and non-linear with respect to several others, then the problem is a non— linear one. In any non-linear parameter estimation problem, invariably some search is required to find the "best" value by minimizing the sum of squares ftmction, S. Usually this search involves an iterative procedure that reduces S from step to step. Such a procedure naturally 40 leads to continually updating the parameter estimates as new observations are added. Considering equation (3-18), the sum of squares function to be minimized, in vector form is as follows: 3 = (K - K)T W“ (K — K) (3-19) 00 — — —- — where w” 1 = o‘ 2 o’ 1 is the weighting factor. If nothing is known re- garding the weighting factors before analyzing the data, then all the i?— 1 can be set equal to unity. The parameter K is estimated from equation (3—19) by differentiat— ing 800 with respect to 5, setting the result equal to zero, and solving for the estimate, _12 and hence the values of C1, C2, C3 and Ct, are obtained. A modified computer program "NLINA" developed in Beck and Arnold (1975) can be used to estimate the parameters C1, C2, C3 and C... The program which estimates up to six parameters has two subroutines. (he is called "NDDEL" for handling the models to be used and the other "SENS" for incorporating the model sensitivity coefficients. The sensitivity coefficients are derivatives of the dependent variable _I_{_ with respect to tie parameters C1, C2, C3 and C... It is assumed that the observations have additive, zero mean errors that are normal and independent. The independent variables, (at, Mt— 1and rht) are error- less and no prior information is known regarding the parameters C1, C2, C3 and C... The assumption allows for use of a unit weight fimction. In order to make the off-diagonal weighting functions zero, large values of the covariance matrice are chosen. The use of this program is described in Beck and Arnold (1975). 41 3.2 Derivation of solar collector efficiency, n The efficiency of a flat-plate collector is defined as the ratio of delivered heat to the insolation. In equation form this is given as n = qu/qT (3—20) where qT is the total incident solar heat flux and q u is the useful energy gained by a heat transfer fluid. A specific number of steps is used in obtaining the collector efficiency. 3.2.1 Step 1: Calculation of beam and diffuse components of solar radiation incident on an inclined collector surface. This is necessary because of the seasonal variation of insolation which is a function of the following: a) Solar Declination, (SS. This can be obtained from the relationship given in Duffie and Beckman ( 1974). The relationship is of the form, (SS = (23.45) sin[--5- (284 + n)] (3—21) 360 36 where n is the number of days since the beginning of the year. b) Local Solar Time (131‘), HS. The value of IS'I‘ is given in Kreider and Kreith (1975) as the local solar-hour angle measured west from solar noon. H8 is equal to 15 times the number of hours from local solar noon. As an example, 10:00 a.m. local solar time corresponds to a local-hour angle of 30°. In mathematical relation terms: 42 HS = (15) absolute value of (12 - AST) (3—22) where AST is the apparent standard time. AST = IST + ET - 4 times the number of degrees of 181‘ west of the meridian; (3-23) The letters ET, in equation (3—23) stand for the equation of time, in minutes. Its value for any day of the year can be obtained from Figure 3-1 and may be considered constant for the day. ,5 A .s' \ E no a." ° m r. 3 j \ \ a 5 \ - I 5 .. ‘7 ,_ - < \ / 8 -1: V N J F M A M J J A S O N 0 MONTH Figure 3—1. The equation of time, ET, in minutes, as a function of time of year. In the present study solar radiation data were collected during the month of November only. Hence, instead of finding the value of ET from Figure 3—1, an equation obtained by linear regession analysis of data given by Threlkeld (1962) is recom— mended. The equation is of the form: RT = 16.79 - (0.11) times day in November (3-24) d) 43 Equation (3—24) has a 92 percent correlation coefficient and a 0.498 standard deviation. The angle of solar altitude above the true horizon, ca. For horizontal surfaces, the amount of solar radiation incident at the outer edge of the atmosphere depends, in addition to time of the year and the time of the day, on location, expressed by the latitude, L. The angle of solar altitude above the true horizon can be obtained from the following equation in Kreider and Kreith (1975) srnoa=81n (SS srnL+coscSS cochosHS (3—25) The diffuse component, I is given by the relationship: hd Ih,d = 2.46 + 3.37 01a + 19.45 cc (3—26) where cc is cloud cover, 0 _<_ cc _<_ 10. The beam component at a horizontal surface would then be given by the equation: Ih,b = In - Ih,d (3—27) where Ih is solar radiation in w/m2 recorded by a solarimeter on a horizontal surface. Angle of Incidence, i. For a collector surface inclined at an angle, 8 from the horizontal of the latitude in question the angle of incidence to the collector surface is given by the equation: cosi=sin<$ssin(L—B)+cosc§scos(L—B)cosHS (3—28) 44 The beam component, Ib-coll meldent on the inclined collector surface is given by the following equation: I _ Ih,b Cos 1 b,coll _ sin a (3—29) a 3.2.2 Step 2: Calculation of radiation absorbed, 10011 Although glass is still considered the most reliable material available for solar collector covers its cost is higher than the cost of plastic covers. However, in multicover designs the high cost of glass covers can be greatly reduced by using a glass cover together with plastic cover such as Tedlar. Not all types of glass are appropriate for collector use. Some types will transmit more solar radiation than others. The transmittance depends directly on the refractice index of the glass. Glass with a low refractive index has a low percentage of iron oxide content, low reflectance and absorptance losses and a high trans- mittance of normal incident radiation. Because Tedlar has a lower refractive index (1.45) than glass (1.5 to 1.526) its light transmit- tance is high (greater than 90%). The reflectance of a cover plate (glass or Tedlar) also varies with the incidence angle, 1. An expression (the Fresnel equation) to calcu- late the reflection of beam radiation from one surface of a transparent solid, is given in standard optic texts as b1 _ 1 sin2(l - ra) tan2(l - ra) sin2(l + ra) tan2(l + ra) 45 where ra is the angle of refraction, and sin r = 5m 1 (3-31) lc where nlc is the refractive index of the collector cover. If the inci— dence angle is exactly 00, the special form of the Fresnel equation is used 2 = (n1C 1) 2 (n1C + 1) Bbl (3’32) The reflectance of several covers with the same material is given by (3-33) where n is the number of similar collector covers (polarization ignored). The transmittance of each cover plate is given by an emperical re- lationship (mffie and Beckman, 1974) t=€m<1-%pul+%p (as) where K is the extinction coefficient for each cover. Both the glass and Tedlar have the same extinction coefficient of 0.508 cum—1. The letter L represents the distance in a particular cover traversed by the energy rays. L has units of centimeters in this case and it is obtained by the relationship L = t/cos ra (3-35) where t is the cover thickness. The thickness of the glass used in this experiment was 0.3175 cm while that of the Tedlar was 0.01016 cm (4 mil). For a system of two covers Duffie and Beckman (1974) give an emperical relationship for the transmittance 1: = (1.006)T r (3—36) 192 1 2 where T1 and T2 are the transmittance factors for the individual covers and each is obtained from equation (3-34). The fraction, FC of emery absorbed by a black painted absorber of absorptivity coefficient a is given by an experical relationship of Duffie and Beckman (1974) F = (1.012)T T a (3-37) 0 1 2 The effective transmissivity-absorptivity coefficient to = Fe is given by Whillier (1967) e—K2 L2 = _ -K1L1 _ Fe FC + a1 (1 e ) + a2":l (l ) (3—38) where a1 and a2 are constants dependent on the number of cover plates. For a system of two covers a1 = 0.1 and a2 = 0.44. The subscripts l and 2 on the extinction coefficient K stand for the first and second cover plates starting from the tppermost cover plate. The distances traversed by energy rays in the first and second cover—plates are repre- sented by L; and L2, respectively; and T1 is the transmittance of the first cover plate. The net energy, Icoll absorbed by the collector is obtained from the relationship given by Whillier (1967) 10011 = 0.98 [Fe(1—D)(1—S)]i I’IUI‘ = f 1,101. (3-39) 47 where , H II .101. total incident solar radiation (it is the sum of direct solar radiation, I and the diffuse solar radia- b,coll tion from the Sky’Ih,d); dirt loss factor which is usually taken as 0.98; ( l-D) (l-S) shading correction factor. Hottel (1950) made plots of (l—S) versus time of the year for collectors having various combinations of latitude, L and collector tilt, B from horizontal and facing toward the Equator. These plots are for collectors having length, width and depth in the ratios of 10:10:l. The collector used in this research has length, width and depth ratios of 256:2411. Hence, the (l—S) factor shall be taken as unity. 3.2.3 Step 3: Calculation of heat loss from the absorbing surface to the atmosphere The heat loss depends on the following variables: a) terperature of the absorbing surface, Tp; b) temperatures of the ambient air Ta’ and of the sky, Ts' Several relationships for clear skies have been proposed to relate TS to the other measured meteorological variables. Brunt (1932) and Bliss (1961) related the effective sky tempera- ture to water vapor content of the air and/or air temperature. Swinbank (1963) related the sky temperature to the local air terperature as follows 1- 5 TS = 0.00552 Ta (3—40) .93 330538 5 venomous one magma—0H 05 H2. "cuoz .fiucxm sawmoe 55558 33983 .mlm 0.5mm 96 season: . we as 3de nodded someones. amass educate J88 some 5 was Canoe. is a J. on .850 233985 own 3. am. Hotpou sea mom." 49 Where TS and Ta are both in degree Kelvin Whillier (1967) used even simpler expressions for the sky temperature 1) TS = Ta - 6 (3-41) which is good for fairly most environments. 2) T8 = Ta - 10 (3—42) which is good for dry temperate climates. Equation (3—41) was used in this thesis because the ambient air relative humidity for the time the experiment was performed was above 70%); c) number of top covers and their spacing; d) tilt of the covers from the horizontal; e) wind heat transfer coefficient, hW over the topmost cover and which, according to Whillier ( 1967) is given by the relation- ship: hW = 5.7 + 3.8 V (3—43) where V is the wind speed in m/sec and hw is in w/m2 OC. The solar collector cross-section and the thermal network of heat loss from the collector are shown in Figures 3-3a and 3-3b, respectively. 3.2.4 Thermal model A flat—plate collector consists essentially of a metal absorber plate mounted in an insulated housing fitted with one or more glass and/or plastic covers. In this thesis the discussion is restricted to one glass cover and one plastic cover (Tedlar) , depicted in cross-section 50 . 99 9855380 5 @0589: one mfimdca cap H2 "coo: .sooocHHou smfiom cumfim-ucfiw cap mo :cwuocm-mmouo .wm-m ensued IS'9I --—-> 99 SS-—*- sz'ts' o u.eflc odendOinn a .cummd sophombm ucpocflficu // a . .u.pwm w A . “0.7.; A' A. E“ \O o e .nc>co nuance m Why. .wvuw l WH [IV a) o .cumHa no>co mmeH H\\. H—gs SS 51 Figure 3—3b. Thermal network of collector heat loss. NOde l m Upper half of glass cover NOde 2 - Lower half of glass cover Node 3 - Upper half of Tedlar cover Node 4 — lower half of Tedlar cover NOde 5 Black coated upper half of absorber plate NCde 8 - Surroundings R1 = Radiation resistance to surroundings R2 = Convection resistance, glass-to surroundings R3 = Conduction resistance through glass R. = Radiation resistance, Tedlar-to—glass R3 = Conduction-natural convection resistance, Tedlar-to-glass R3 = Conduction resistance through Tedlar R7 = Radiation resiStance, absorber—to-Tedlar R3 = Conduction-natural convection resistance, absorber plate-to-Tedlar' R3 = Conduction resistance through the bottom insulation 52 in Figure 3—3a. The approach taken in analyzing the thermal performance of such a collector is essentially that of Hottel and Woertz (1942), as modified by Hottel and Whillier (1955), Bliss (1959) and Eaton and Blun (1975) . The principal assurptions made are: a) b) C) d) The hourly heat transfer is steady—state and one dimensional, i.e. losses through the sides of the collector housing are negligible. This assumption is reasonable because within one hour weather changes are negligible and the lateral area of the collector housing is small (0.1858 m2) compared to the area of the absorber plate (2.2297 m2). The loss from the copper plate to the Tedlar is by both radia- tion and convection. The same quantity of heat is transferred through the Tedlar to the glass plate covers. No radiant heat is transmitted through glass since it is opaque to long wavelength radiation from sources at only a few hundred degree Kelvin (Hottel and Woertz, 1942). Since air is diathermic, the loss of heat by natural convection from a plate to an air space equals the loss by natural convec— tion from the air space to the next higher cover. Hottel and Woertz (1942) calculated the natural convection heat loss from the absorber plate of the collector using the equation q = C(Ts - Tm“ (344) PSI. 1 CW5 - Tu)”1+ Using R3 = (3—45) quz. = (Ts -' TU/Re (3-46) 53 where C is a constant dependent on the collector tilt. Assum- ing negligible thermal mass of plates, the total rate of heat loss per unit area from the collector plate to the first cover plate is given by qa=Cds—nf“+odi-mV%;+i-1> (2%) Using h5., = C(Ts — T.)1/‘* = %— (3—48) 6 _ 1 1 Es. - 1/(E- + “— " 1) (3'49) 5 8» hrs“ = (KT: - TZ)/(T5 - Tu) (3'50) R7 = 1/851, 11 (3—51) r51, give (151. = (hsm + E51. hrs“) (T5 '- Tu) (3‘52) Using Rsu = 1/(h5u + ESL. hr ) (3'53) 5:. Equation (3-52) becomes Clsu = (Ts - TU/Rsu (3’54) Since thermal mass of plates is negligible both R and R are zero. The total rate of heat loss per unit area from Tedlar to the next cover, glass is, “(T3 " T3) S/lo C15,+ +C1T Tglm = 1 1 + C(T3 - T2) (3—55) <~+—-n 82 83 54a Equation (3-55) can also be expressed as follows: qs, +dT tgrm = (T3 - T2)/R32 (3—56) where, Raz = l/(hsz + E32 hr32) (3'57) haz = C(T. - T2)“ = 1/Rs (3—58) R, = 1/E32 hr32 (3-59) E3. = 1/(21-3- + 31:; - 1) (360) hm = on“; - Tau/(T3 - 1‘.) (3—61) Using q32 = qst, +dT thm (3'62) makes equation (3—56) become: Q32 = (T3 - T2)/Raz (3'63) The energy loss from the glass cover is that due to wind at tempera- ture Ta’ and that due to radiation exchange between the cover and the sky at terperature Ts‘ An energy balance at the glass plate gives q , m . c: _ 0 T“ T" , T T su T TgITUl‘ g TT TgITUI‘ 61 ( 1 s) hw ( 1 a) (3'64) Using qie = qsn. + (0.1. 'rg + cg TT Igflm (3-65) 54b and (T'i - 1;) hr1s = W (3'66) T1 - TS (he = (53v + 81 hrs alt-111: (T1 - Ta) (3'67) Putting equation (3—67) into equation (3—63) gives T1 - Ta Q13 = T (3—68) where R - 1 (3—69) 18 T1 _ T 81 h S 1i» rls T1 - Ta _ 1 R1 — (3—70) T1 - T 81 I‘ S S 1 T1 _ Ta w ITOT: is solar flux incident on the inclined collector surface (w/mz). qsn: is heat loss from collector plate. 0: is Stefan—Boltzman constant. T; = T2: terperature of glass. T3 =1 T1,: terperature of Tedlar. T5 = T3: terperature of collector plate. 01g, dT: absorption of glass plate and Tedlar, respectively. Ta’ TS: ambient and sky terperatures , respectively. T g’ 1.1.: solar transmission of glass plate and Tedlar, respectively . 55 61, 62, e3, 6., es, 852 emissivity of surfaces 1, 2, 3, 4, 5 and 6. hw: is wind coefficient . Equations (3-54), (3—56) and (3—67) have three unknowns, T1, T3 and C15». The procedure for solution of these equations is substitute for q3., of equation (3—47) into equations (3-55) and (3—63) and setting the resulting two equations into a form that lends itself to use by the Newton-Raphson method. The Newton-Raphson method is iterative and converges more rapidly than other methods. The method is described in Barrcdale _e_t_al. (1971) and Carnahan _e_t__a_l_. (1969). In this thesis only a summary of the method is given and it is as follows: 1) In order to find a root or solution of general equations of the form f(Xk) which may be linear or non—linear, set each equal to zero. 2) Choose a starting vector Xk = X0 = [X10, X20, ,XN]. where X0 is hopefully near a solution a. 3) Solve the system of the equations ¢1 <3—76) are evaluated by a subroutine named CALCN. The system of equations obtained from equations (3—55) and (3—63) is solved by calling on the function SIMUL. These equations are = 1+_ 1+ _ _ + f1(T1) €10(T TS) + hw(T1 Ta) [(01.13g OthTTg)ITUr + E35 (Ti - T‘s) + C(Ts - Ta)5/"] (3—77) 3f1(T1) = 3 ————3T1 4 elo’I‘l + biv (3—78) 57 3131(T1) 3 5 1/1+ T = 4 OE35T3 + Z C(Ts - T3) (3-79) 1 E35 = 1 1 (3—80) ——-+ —— — 1 83 65 f2(T3) = 0E13(T‘§- Ti) + co. - T1)5/‘* -IaTrgI.m + cEaso‘: - 1‘3) + C(Ts - 1355“] (3—81) 8f2(T3) 3 5 l/u T = -[40‘E13T1 + 4 C(Ts - T1) 1 (3-82) 3f1(T1) 5C T = 40(E13 + E35113 + 4—[(T3 - T01“ + (T5 - Ta)1/“] (3-83) _ 1 E - 1 1 (3-84) _ + ._ _ 1 81 £3 The increrents AT1 and AT3 in T1 and T3 are determined by 3f1(T1) 3f1(T3) T ATI + T AT3 = -f1(T1) (3‘85) 3f2(T3) 3f2(T3) T ATI + T ATa = -f2(T3) (3'86) or, writing the determinant D of the coefficient matrix (the Jacobian), 3f1(T1) 3f2(T3) 3f1(T3) 3f2(T3) 8f1(Ta) 3f2(T3) them no.) [—33:71 - f1(T1) [T] AT; = (3—88) D 3f2(T3) 3f1(T1) f1(T1) [w] - f2(T3)['—5'TT1-"‘] AT3 = (3-89) 58 The upward heat loss coefficient, U up shown in Figure 3—3a is calculated from the resistances R1, R2, R1,, R5, R7 and R3 shown in Figure 3—3b. Whillier (1963) solved a system of such equations for U 11D where , His result is of the form, U = 1 (3—90) up 1 + 1 Tl-TS 1 +8 h —-—- h + hw 1 1‘18(T1-Ta) TT‘Epg mg 1 1 + hpT+ErYPhrpT th+Ethng hW = 5.7 + 3.8V, (wind coefficient, w/m2 OC, and V is wind speed, m/s) hxy = C(TX - Ty)1/", (convective coefficient) Tilt Angle 0 30 60 90 C 1.58 1.38 1.18 0.99 hrxy = (T;‘ — T;)/(Tx - Ty), equivalent radiative coefficient 1 . . . E = ermrssrvrt factor a L+L_1 y e e X Y e = emissivity. ecollector = 0.95 (black paint) = 0.20 (selective) cplastic = 0.63 eglass = 0.88 UP] “qt-3 gut-3 (Dr-3 equivalent black body temperature of the sky ambient air temperature terperature of glass and Tedlar, respectively collector-plate terperature 59 = transmittance of plastic for long wave radiation (0.3 for'Tedlar) The collector heat loss coefficient, UL is a function of, in addi- tion to Uup’ downward heat loss coefficient, U and edge heat loss d, coefficient, Uedge' The relation for calculating U , is as follows, in UL=Uup+Ud+Uedge (Ac) (3-91) where Ac is the area of the absorbing plate and A p is the perimeter area of the collector. According to ASHRAE (1960) U (1 can be determined from the following relationships (3—92) and (3—93) where X is insulation thickness in cm; hb— f is the convective heat transfer between the insulation and heat transfer fluid; kb is the thermo—conductivity coefficient of the insulation; and hWb—s is wind coefficient. The edge insulation loss coefficient may be obtained from the relation , qL-edge = 0.08 (D) (P) (tp - ta) (3—94) where D is the depth of the collector box and P its perimeter. From equation (3—94) it is obvious that the edge loss coefficient is, U edge = 0.08 (D) (p) (3-95) 60 Edge losses are important in stall solar collectors where the perimeter to collector area ratio is large. This is not the case in the present design where the ratio (Ap/Ac ) is small (0.18). The recom— mended thickness of edge insulation is 2.54 em and generally, it is at least half the thickness of the rear insulation depending upon the degree of exposure of the edges. Both the rear and edge loss coeffici— ents with insulation of 7.6 on to 12.7 cm, (as in the present design) thick of mineral wool will result in negligible heat loss through the transparent covers (Whillier, 1964). Hence, in this thesis UL will be calculated from the relation: UL: 1.1 Uup (3-96) 3.2.5 Step 4: Calculation of useful heat removed from the solar air heater An equation for useful heat removed by a fluid being heated can be obtained by considering an element of thickness dx at a distance x from the air inlet end, as shown in Figure 3-2. Whillier ( 1964) made three heat balances (one for the absorber plate, the second for the air stream being heated, and the third for the rear plate with no bottom heat loss) on such element. In order to solve these balances for the useful heat removed the following boundary conditions were used Oandt a) x t at the air inlet end of the collector; b) x L and t t at the air exit end of the air heater. The relationship is of the form - -U /GC _ Qu __ l 1 - e O p qu ‘ Ii" “ ( ULX 00/ch )[f Iror ’ UL “‘1 ' ta“ 1 + E“ (3—97) where , 61 h is the effective coefficient of heat transfer between the absorbing plate and air stream and it is given by, _ 1 h-hc+1/(B— + her: hrc : G = W/BL: Band L: 1 E b er rc ); (3-98) is convective heat transfer coefficient between the absorber plate and flowing air stream; is heat coefficient between rear plate and air stream; is equivalent radiative coefficient, and it is given by, = lo _ 1. _ . hrc 0(Tp Tr)/(Tp Tr), (3-99) is the emissivity factor given by the relation, E = 1/(1— + 1— - 1); (3-100) 8p 6r is overall heat transfer coefficient from air inside heater to ambient and it is given by the relation, _ 1 1 . UO — mg; + 3), (3-101) is the mass flow rate of air per unit collector area (A = BL); is specific heat of air; are width and length of the collector, respectively; is the effective transnissivity—absorptivity product of the collector cover system (f is the fraction of incident solar energy that is transmitted by the cover plate and absorbed by the absorbing plate); are the absorber plate and rear plate terperatures, respectively. From equation (3-97) the term, 62 -Uo/GCp F = (1 - e )/(U0/GCp) (3-102) is lmown as the "flow factor". Equation (3-97) can be used in equation (3-20) to calculate the collector efficiency at a given total solar radiation rate, ITOT from the known ambient terperature t a’ inlet fluid teiperature ti’ fluid flow rate W, and heat transfer properties of the solar air heater. Among the heat transfer coefficients used in equation (3-98) mo sufficiently accurate relationship for finding the convective heat transfer he has been formulated. This will be derived from the Navier- Stokes equation with some simplifying assumptions for a three- dimensional flow. The derivation of the heat transfer coefficient, h c’ is made by finding a correlation for either Nusselt or Stanton nurbers for fully developed heat transfer between two parallel plates. The plates are stown in Figure 3—4; the lower plate is insulated and the upper one is exposed to a constant heat flux. The velocity profile is assumed to be parabolic. [ 7////// f/l/ / ///////////// $0 Figure 3—4. Fully developed turbulent flow in an unsymmetrically heated parallel plate channel. Restricting the problem to constant properties, zero mass diffusion, zero chemical reaction, zero axial conduction and negligible pressure in the x—direction, for gases the following relations can be developed from the Navier—Stokes and conservation of energy equations (Kays, 1966) 31 = a at _ where the enthalpy change, 31, is given by ai = C dt (3—104) Substituting equation (3-104) into equation (3—103) gives QE.=._§ .21 - UOCP ax ay ( 3y (3 105) 64 According to Kays (1966) when turbulent heat transfer is present the thermal conductivity, k, in equation (55-105) is assumed "turbulent conductivity". Altlough the "turbulent conductivity" arises from velocity fluctuations and the flow in reality is not steady, the assumption does in effect lump all effects of the fluctuations in this term and then treats the flow as steady. From Fourier's law of heat conduction, with k replaced by (EH + a), the following equation can be written: 62/11 = pc (:1, + a) g—f, (3406) Then equation (3—106) becomes _<_1_i;_ _8_ at . Upc dx -pC 3y [(e:H + 01) a—y—] (3—107) Restricting consideration to constant values for p and C yields a at dt ' __ + _ = _ ay [(EH 0‘) 3y U dx (3—108) For fully developed constant heat rate at d we (a... and hence, 3 at d 5;[(€H+a)fi]=Uaxt-’m (3-110) The boundary conditions for terperature are 65 The expression for the velocity U in equation (3—110) is obtained from the Navier-Stokes equations. It is of the form — = — — = constant (3-111) and has boundary conditions: 1) U=0aty=0 2) U=0aty=2a Integrating equation (3-111) twice and applying the boundary condition gives 1 (Zay - yz) (3-112) C} II Mo” E5% [. At y = a. the velocity is maximum and it is of the form, v = (ac/2m2 [- $1 <3-113) 66 Theiexpression for-gfim»is obtained by application of the conservation of energy principle to a srall volume of the fluid being heated. As shown in Figure 3-5, the rate of creation of energy is zero. 1 — . g (35 dx 2a (2apr) C tm —>g z—v (ZabVO) C (tm + dx ) /// / // / / / x7772'7ti71/ / / /////7/r7 Figure 3—5. A stationary control volume for applying the conservation- of-energy principle. The conservation-of—energy principle gives, (1" = 2a WC 3;?“ (3-114) When equations (3-112), (3-113) and (3-114) are substituted into equation (3-110), integration and application of the boundary conditions to this equation will yield the following expression for the fluid temperature t: n 3 t 415-33,: {y {I {-9.37% --§]/<€H+n)} dy (3.115) If y+ is used as an independent variable and d is replaced by v/Pr, equation (3-115) becomes 67 y 1 X 3 4 .. + [- - -< > - —1 t - tp = q fy a 3 a 3 dy+ (3-116) 29C "gov" 0 EH 1 v—+ (m) where y+ = y 'gcTo; p and positive q" is defined as heat transfer from v the fluid. The shear stress T c at the wall surface is evaluated from the gradient of the velocity profile at the wall. Considering the expression, (3-117) for U = 37—2— (2ay - yz), the apparent turbulent shear stress is given by a the equation, _ Y - T _ To (1 - E) (3 118) The apparent shear stress varies linearly frorm a positive maximum at one wall surface to zero at the duct centerline and then to a negative maxi- mum at another wall surface (see Figure 3-6). 2a i<: / //7//7///‘ 7///O/7/1f/ / I/f///77f///// Figure 3—6. Shear stress distribution for fully developed flow in a rectangular duct. When momentum is considered to be transferred by both molecular and turbulent processes the total apparent shear stress is described by the equation (Kays, 1966). g T . . . + U Introducrng the dlmenSlonless constant U = —— “8:070 into equation (3-119) and substituting equation (3-118) into (3-119) followed by solving for the eddy diffusivity yields: 6 = 1 - (2,) .. 1 (3-120) C| + 69 A three-layer scheme (laminar sublayer, buffer layer and turbulent core), most commonly known as the "universal velocity profile" (Kays, 1966), can be applied as follows 1. for the laminar sublayer, o < y+ < 5, so that, U+ = y+, du+ _ _: .. 1, dy 1 —-X 2‘1, a 8M EH and therefore, T = 0 = 'v— t = tp " 300 l 73CT0/0 . + . usrng y = 5 gives _ 10 q" Pr p 30C Vgcto7o an d by analogy, + ’ n + [y — g-Pr dy+ = ‘4q Pr 3* , and ° 60C v’gCIO/o (3—121) 2. for the buffer layer, 5 < y+ < 30 so that, 0+ = + IUI &% + ‘< + - 3.05 + 5 1n y+ 7O l—X—l a e: + 6 i=1._ =1 0 5 1 v and by analogy, H + 4 + 61 y -_3'dy t—t = f . 1n t_t=10;1 (5Pr+1); ( 3—122) + 3. for the turbulent core, y > 30 so that, 0+ = 5.5 + 2.5 1n y+, ()1 911-2 dy + <2]. .1. 511.. +(1- 1) v —y _____a 2.5 By neglecting -1 and (51,1), (Kays, 1966) e: H +(1_X) T: y ____a 2.5 and " y+ i (l — X) 2.5 dy+ t - t = q {o 3 a b + 3 20C V80T07o y (1 - E) _ -5 <1“ 1n (37939 t'tb——3 ’ ET /0 CO At the center of the duct, y=a +_ VgcTO/p y -a —— \) and M [(21 V'8C."fO/o)/30 V] , chTO/p -i i"_ t. - tc-s pc @123) where tC is the temperature of the fluid at the center of the duct. Equations (3—121) through (3—123) constitute the complete terperature profile. It generally is preferred to use the mixed mean fluid tempera- ture tm, and the absorber plate terperature tp in finding the convective heat transfer h c’ relationship. The fluid mean terperature tm is given by the relationship, t = —1— f U t dA (3-124) m A V c c A c where U is obtained through application of the 1/7th power law: U+ = 8.7 (y+)1/7 (3—125) 72 Using U+ = ——U— in equation (3-117) yields, gc TO/o U _ y 1/7 E- — (a) , (3-126) C and t - t 1 7 t____P_ = (x) / (3427) C - tp a The fluid mean velocity V is given by the equation, 1 V = A— f U dA (3—128) Substituting A c = Zab and dAC = 2bdy in equation (3-128) and integrating the resulting expression between the limits of o and a gives: (DIR) (3—129) Oc2|2 acmpcoo mpsumfioz u «mmHz Chasswsm an acmucoo wASHmfioz n max :wnnwm an pcmucoo mpspmfios u m¢m pamacoo manumflos amusmmms n osxm 685 and“ .8,“ §v Ho 3323 m>3§mm can vooém mo .oHmeKBMfim mgpgwefie .HQ ”SHE new pamucou 95382 .537559 ECU 832m 98 Hmycghwg w&,————-u--n.QFEH.—. OPP: .F\CI T-ua;h la-\pN 112 950: 2H mt: r LZ'O 8.9.. SJ,” 8. on” 21% 8. pa 8. m: 8. a. 8% 8...". "m 950 ... 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L ? , f 1...... . nu » r ’ 0» o o 0 0 o “a 5.2.. .1 ‘ ‘ J N t0H" Vnu . am II. nu N. 25 ... ...-II! .mB 2:. a 03 E w I. 3. ON" '0 1 7w t0 3. .J aw n1. m .u [at P o mpmHz an Hcopcoo wHSHmHOE n 9 pcwucoo mpsumHoz u 4mm pcmacoo wHSHwHoz ampswamz u uzxm ..HsoH Hmwp .HOHH». mm Ho 332-5 @935me can 0 o.m 2 Ho gugwge .HH< mcHuHmamm .HOH 28:00 magic: .HEEHIGHE. FHOU HumpaHauHm Him HdpcmEHquxm .Umnm magma 130 5.3.1. Fixed bed in-bin solar 00m drying results Hourly experimental values of corn terperature, drying air terpera- ture and absolute humidity together with the input variables (XMO=O.32, THIN=8 . 9°C, CMM=2. 84988CMM/M2 ,DEPH=1.9812M,IM)PR=1,NIPF—-6,'IT=313.0, TBTPR=1.0,DEIH=1.0 and NEQ=1,2,or 3) for the fixed bed drying conputer program are listed in Table C-1 of Appendix C. The absolute humidity was calculated from recorded wet-bulb and dry bulb temperatures of the drying/or rewetting air using the psychrometric chart equations presented by Brooker gt _a_l_ . ( 1974) . The equations were converted into the inter- national system (SI) of units. The hourly corn terperature values listed in Table C-1 of Appendix C is for comparison with the listed air tempera- ture values since the program assumes the air and grain temperatures to be the same. The tables show that this is almost true for most of the time. Differences exist when the grain is starting to warm up. The air terperature changes faster with changes in solar radiation than does grain terperature . The thin-layer drying equations (2-1), (5-2) and (5—3); and the re- wetting equations (2—4), (5—4) and (5—5) combined with the deep bed solar drying equations (Bakker—Arkema _e_t 53:1; ,1976) and the DeBoer equi— librium moisture content equations presented by Brooker _e_t_ _a_1_ . (1974) were used to calculate simulated oorn moisture content from non-constant hourly experimental values of drying air temperature and absolute hunid— ity. Appendix C—l lists the computer program "FIXED" used to simulate the corn moisture content in the fixed bed during drying with solar heated air. hiring the experiment, corn samples were taken from the 131 grain bin at selected time intervals and their grain moisture content determined the air oven method. The experimental and simulated corn moisture contents at various time intervals and bin depths are presented in Table 5—3. The moisture content values are plotted in Figures 5—3a through 5—3g. Simulated average values for the hourly corn moisture content and dry matter loss obtained using the Steele gt El. (1969) and Thompson (1972) equations are presented in Table CLZ of Appendix C. Figures 5—3h and 5—3i are plots of the simulated corn moisture content and dry matter loss, respectively. 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Discussion of in-bin 'solar corn drying results As in thin—layer corn drying and rewetting results, the in-bin corn drying results show that, in general , the thin-layer models developed in this study simulate the moisture content of corn at different times and bin depths with only slightly better accuracy than the combined Sabbah g §_l_. (1968) and delGuidice (1959) model (SUC). Few cases (as at a bin depth 0.3 meters after 48 and 72 drying tours; and at a bin depth of 0.92 meters after 96 and 120 drying hours) exist where this is not true due to bad corn samples. The combined Sabbah _et al_. (1968) and delGuidice (1959) equations over—predict the final measured moisture content by 10%. The equations developed in this thesis have only 2% over-prediction of the final aver- age moisture content . The thin—layer equations developed in this thesis give better over— all moisture content prediction than the Misra (1978) models. Up to one hundred and twenty hours of drying the Misra (1978) models give moisture content prediction comparable either the combined Sabbah _e_t_ fl- (1968) and delGuidice ( 1959) models or the models developed in this thesis (RUG). The Misra (1978) models over predict the final measured moisture content by 43%. These results give further support to the reasons discussed in Sections 5—1 and 5-2 for selecting the thin-layer equations developed in this thesis for use in low temperature corn drying and rewetting studies. Simulated average hourly corn dry matter loss results show that none of the models used predicted corn moisture content resulting in dry corn with more than 1% dry matter loss. According to Steele _e_t 2.1. 135 (1969), a dry matter loss of less than 0.5% due to fungi respiration does not affect the market grade of the corn. Desirable properties of high market quality grain are (Brooker e_t_ a_l_. (1974): l. Appropriately low and uniform moisture content. 2. Low susceptibility to breakage. 3. low percentage of broken and damaged kernels. 4. High test weight. 5. Low mold count. The moisture content predicted by the cambined Sabbah gt _a_l. (1968) and delGuidice equations is accompanied by the least amount of dry matter loss. This is due to the fact these models predict less corn over drying at the bottom of the bin than the measured moisture content as shown in Table 5—3. Figure 5—31 illustrates that the moisture con- tent predicted by the Misra (1978) equations is associated with the largest dry matter loss (DMISRA) due to high moisture content predicted in the corn. The moisture content predicted by the models deve10ped in this thesis is such that some corn over drying takes place at the bottom of the bin while at the top of the bin the corn is almost undried. Both corn over drying and high moisture content lead to a high dry matter loss. This problem can be eliminated by using a. batch in-bin drying method. This method is characterized by use of large floor areas, limited grain depths and medium drying terperatures and air flows. Most of these characteristics easily lend themselves to solar grain drying. 136 mxzo: z~ uzuh 29‘0 3.8.. 3.3.» 3.3» 3.0% 3.3% 8.8% 8.3.“ 3.3— 8.3 8.». 8.? . r 03 O “a N g: ....uW W7 [T a 98 - a 1 n no '03 ‘. 3 am I. can... 3 ON 3|. 2 90 3 3 I H U .I 0 8 t '0 0’ cowowsoflcc cam nanomm an pampcoo manumwoz n 02m omaezwsm an ucmacoo opzwwwoz n man came: an uncacoo cuspmfios n 9 acopcoo opsumwoz n 9 acoucoo manumfioz u 02m o>w83wsm an acopcoo whzuwfloz n max “am“: an pampaoo mushmfioz u 9 usmpcoo musumfios u 02m czasswsm an unmuaoo mpsuwwoz u cam upmflz >n ucmpcou waspmfioz u < Bugs—Em US». Haucgnngm .wmnm $.3th 143 manor z~ wzmh 8.3m 8.»... 8......“ 8.3.. 8...». 8...... 8...» 8.9» 8...u w to m L 8.. - ...u 8» . ..Iii 1 n Cflaut .’.Ia /. 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HVI< 95th 165 manor z 9:» oo.a~ 88.5“ oo.mw, aawmw ao.wu noun onus noun P x: 88 8:8 .95 83 .85 How 50 3.68:: 855mm 98 voodH Ho 83535.5. .5. 8&5 .88 x .823th 55 Eco oo-d° I 01'0 0235 3.4303 NOISflJJIU ‘0 I as 3131 0730 UH/I NI 1N V 09'0 . ml¢ 8.5mHm 166 manor 2“ m: m ._. 8.8% 8.8 8.8 8.8." 8.£ 8.: 8;. 8.» P h P 5.88 2.28 .x8 88H .HOH «Sm Ho .SHUHEE m>HHHHmm new vov.v Ho waspagmgewe gH< wcHHpa pom x .pcmHoHHHmoo waHmpa choc ca. 001? or‘o Ell-VI NI lNBI I 09‘0 .mn¢ mnstm APPENDIX B (Listing of program "NLINA" used to determine the unknown constants in the thin—layer corn drying and rewetting equations) 167 ImamfimIB KB - ! fl h o o & Q 2 .. O D- u 0 H 4 > ' t o H a 0 0 cos x u «0 0 I m ~D '- " I- a: *0 0 < . d” A ' X em u U) o O a o D U . '4 ma 0 m o r '0 z 4 " ‘ N 0 A L) a. A MD 0- d d‘ 00) 2 Ln “1 CD CD wen u 0- ¥ 1» can. > 1' Q o- a O '02 X t- 4 X ~~WH < w 4 o osDO.> I D H o' o u 0- L9 C) " M>N4 H 2 H I “<00 ht H m . NWWO h 2% O m m ‘9sz Z Hx w m - H a u a H mm W m mAHN m mu u s r aocw a H! O < - A “H H '4. D F X 900.0) 0- t—Z V) U 0 ca" 9 o- .- QQ v-I n>d> a o- D u r ~22: '- O HX Z 00 t ~>H3¢ H on do . o>m .- 0 .J 0 U... N =~~~m d 0; Oh: v QQA’ O CO. ZQO m b.0md 0 Z Nwh I 30"0. a t of LL: 0 0°) “W fi X " ”UH x a ~mmma X (X 1mm- 9 Q vamu < 2D Ah mm H 2 Dr- . 04 1: p- . a: u z .. .. '0 Q “Q.- c-O H! a ozm< u t «H '4 2-0 I,” O 02 .OO r1 “Q n M H0~Z~ ~N ht 0H Oh" fiaH . ”OUOH h- 2. dkthH van A N .30.... a. 29 «x IL N U i OV‘HND H (VOMW 0° m¢~avxm . me:. M ZWGHm § 2 it 900—) u-fi a... .: a Hmooehad hZH achafi QHV X'OJfi N J 'NNJMO DO“ ZIZfiHoIHmHOX“flL H zzma-wuo 12° hdHHNO h'ddo'kOOOQODW OWQh-DUJGUZ uam d\£¥h\|l hz 0M\HU\\D\ o o o O can] ZHG OOSHHODn Um-VhOH: ~-:~'eoaoah3 4W 00.122 0:32 v-IHZ #04thsz h. O-O-Il H II II "0.2 mz~AOOfiHHh ~Hhh<¢<<° Q h<~h<<~~*~-OH uuwmttnwthZbZZtothmHDzzmzrzwncmlo OIVDXCWVJZ(<'ZHHMXMQ Lu (Hm ”Hum-vvvw vvz mHmooodn6hmmcmmo:oouomwmommoommmmmuo momooomwommnommmfiuuHondkndmummmmmHo H a N o H n «a d :m N a o fi fi J: H N N n n o ’ ouo Appendix B Continued 169 X v Q \D a. A " i n d 0: V A X m N o- O‘ O o)( 0- § Ho n ' U Q. A x ha a N § A x 0 ON C- ‘ X 3 J. on Q3 v N .v a v 1 t— A D m at J o- O '4 u 0 x . “X VD O‘ a '50 LL 0 x w o- m . N ... . A O ‘ A a G. ' '40 N X A X D . O H \Dfi \D M up 4 I— I- .i- O. m alt 2 X2 g. g '5 u o. H a . . vx H Va x X (\D II NH o N I: o. )— ‘F‘ a a 0‘ X «Hg 9 9 HA a o 0- a 0 Wm A ‘7“ 0. W 1‘ O b— u..— x H 9'5 ¥ 0! .- C XH o X 9 N i ODI— 3 ”.5 H an O .1 " C: "" G. 0.0. X a .- OFH— 3 22 k 1 X U a 0" o a a a «a u "n- - x «a o a. a ma W m nu < a; '5 .— u'fi a .. 0.0- K '— >5 " .JX'GN Q 0‘ XX 0 U +J N mfiNGQ A‘ he M t h o 0 D “U I“. 0.4-u AA A 0' '0 X3 H MHNm xm at a o x 0' m own; a! ¥¥ x o 0 0+— . AC Olga q-q o a a a n 0 § 5 0‘ OLLflO-5 “$0 an “A l C. Q ‘- H oufid- 9 av HH mm m QQH O W tx * ox~~~ mung gnaw“ 0. 2m zzv O ¢ “O Z> ofl>ow 22°. 092W” 03 *4 00m n u x- o-oca-HH «one Xh-Ql ddhfiHD «HE A x ataHXomMXHW HH~" MXd’v 903"“. nu" h J n\atn~HoH-\nmwuum-w \mu.-wcwddooumdaw2m \ dUMAfiJ aucvanammxnamvommm3~~2HnnaH¥¢3HDN~ bun Hflfih hfiZZonxz hQHH ZhhH aaz xzmz h h<fi~u ~zzzNthNHuhz:aothzt HHHththhzz Huh” <4~mHmuzz 'Hszx «Hzmmo v-z szZHm m°$ #0141me KOHO Doom-coma OONMOODZOMOODO*OKOQ° Q“. 00 DMDHU- QLLWQDDQQ Q00.“- BDMQDLLKUOQQUDDQOHQQIL dN M 0 n 3 3 on N m ommv o a N h H a HH H9 fl d o n o n § 0 Appendix B Continued N0 )- A V) o a O a- n0 2 H a Q cu m N (D A 0 Q H H <1 " " A A9) I- X m < A\ _J N A X DO U a V) A x a '5 D an O m H v < -n \ > a > - N '5 mm a. m m H N o w my 0 q "’ Q Q A O. [A 1» a (I) H .1 1 A0 A > (D " (I) " 1: A 0'5 CD V) at O. \ x D < '5~' H H a o O U m g “N ~— w x o m m + v m+ < and N A 2 «H n «a QQN ova qa- zzu - - hm mma H2 22+ 2+0 hZ+ --~ ‘ O f“ U! 22.) U a a on oAfi “J A HF!) A H II —I U D O to” NH HHQ v40" I '10 II II (I) 3 Hm H ”UAW HHN C) II D II n '1 ll “L? m u H >>fi “m N+< H ZDHH un+mufio m<<~uo~omomvmmmm In: DXID wo-vmaxgx m'fic Dfi¥<=fiN II DI HmaH"): oz 2:! 99 m2)"- :3 ll ":2 uz «bAZa HZ VIZ 9H ath-a n>oaoWH<¢~oHOOaHomUHHa~HH~HH ov- || #- " MQHHJJDW ll NN n t-o—N-sop-mmqo—Jo'fihvmcm—J:-h XZOXZX HZ >2 NO1|<°cll<~DOODDMO"WODOVODWUDHOHOOOWD ~0HZOZ?WDHQQKWWDDWODD 0 1' V) C "’ (“D HH Q A O O a: DJ m ‘l" D Q A 9‘0 ~' )2") O )5 d ¥ > a h H G H U) H O A d a 3‘ J‘ 4“ c Q 3 D H H ofida‘ ° " 0 AA W m A H H A m NQZQ H G. H '1 Q0- 0. Nth O. H to O '- flow?! a 0.2 QQU" m '3¥N"' do '5 3 Q, >> D d “.102 o .7 Zn zz~ . ..cm I: v m 2 HH H h DJ<¢ o 9) ham 0‘ mat/)0 mm N O. 0. av Lu 0 x0 (1 HH HH¢ 3 XHQDamd>w3m>>H-mum uzmAu>daAm2m~w\mOHo> momma-ZmZHz > Hzmz th x\o NNHAHQHmHnumgmaQOHHH.HnmnuHmHAHq A<>m < mmummXAfithn HQHthahmHmDhHhZhZ mtmm UszcOCHIIvaZZZv-iz t HZ~ZHZMD<~uv ooaoououommmmdmumoao-oo>o~omomODZAmmu QDWDOHQHQlQmmKMHQQmUQQDHomoHQQDKwWHWH m m :m A N n o cow. n 3 c mm m m m a a 1+ 9 ‘ n A d O Q 0 C44 Appendix B Continued A n A W m a a H A H O. H ' W d H ' > Q a a N m m m x 0 m + d H A A H XD U) m Q Q - QZ \ U) H H M “H D 3 A “A 5' “Av-1 i’ '0 U) Qa Q QW QWW W‘WOH XE H ZW - 26) 2mm QWQWHA <12 m ,m X 0H oHH zmHmu-m.-c : " z (' fiH N «v H'* ~0~~< «1 r4 uJW W) a W0 oWWm &Qum~mm Kt H 40H mm NId DH Nmmn HiJWIDJN“ H MAM HDMHHF‘UHAM \H H Alt-l H'CDLLJCDOZH\v-OUJNLU H DH+U "DNvND WDGMJ «m3: MADQHHMUHDHDG o-Q: CA2 h ZNQZoo>z fithzoo JUhh'QHMHZHZQ HJWQZ O'CdOOODWOQZdOV/‘WDZ ll own < szomomcn-ou O DDQQQWOQQQOOQDQQUHWDDQQ HHQQQOQUWDHQMWQ m o N : a O n J tom N a d H o H d H H H$H d H N N «I H r1 1'! M H; r! H U *GAL‘CBCIBS)~BSS(IBS)) 172 ‘NP‘,5X,‘INDEX*.8X,*IP‘) ZgngCI),ETA,RISD,Z(IP)9SYP9DELB,SIGZCI) Appendix B Continued 173 m a H X M M 1' H I! Q o >- A .. W m 9 § " ¢ 0: N o- X a x N " 4' o x H \D N o I '1 ‘ Ln 0 3: H a y I.“ A a I ..r x II v N 0. N '4 > t (f) o- t X o N X H N Q " O o A a V) N w H N h. 5 A Q. I " A )- I! x Z W —J N m o. ‘1 v" H >- 0 O A .0 V) . 5 L9 V) a —J A A ‘ U) U 'J N D .J m an“ 4 V z < a In t N 0 L9 A o (f) l A \D.‘ Z c- m K O " CL C"): a: i’ 91 A O H O X 2 0.40 H X DJ O. H d” O N o fi‘N U Q Q 2 " '4 “>9“ *1 F1 ‘Hdb m z a u w «mm . u on» v + m a O “O OJ * H .flm 1 u I N H NHQq A o N 'U I K m H " viva-0 H a UHQ + h H u. 0 HO‘W‘ v H 1"»- Q_- ... u, a ° '°" N “ ' on ZZ QOH H d O‘NHJX . “‘2 N ‘.w 9m 0.x ... A (IN-v.4") A O O " .JZ\ 0 HH >-< . CD x mHHu~ X‘QH . <30 N uv WZO v Lu CAN no HOAHH N OW: 1- ZW O? “H " D N a>.cz OHOUfiWO o IXJNOD mm «Iowmdm Z nutWOOH O\~N ZOMOM>M24 h hOhGW z ZHQQ u.zn~zz hd h “OOHW*JOHJHHZHHh<“~HmHH QHOO>QQ¢OOQOHOOQQOOD¥QHOQHOQUOOQOWQOQE HIOQWHHQQ «Lu. *QDQQDDQWHIQQIQDQQQQQO QLLQQ m H H \D N HU‘O H o o Hoo a H H HHH a N Dr! H F4 N ”H H N M HH N N H H mm H H «N a 1002 1003 MmambiB thMmm TM w 0 Ln .4 D Q. t H 0"! V) CL H a '5 't (I) X CL $4 H of v P- A V) Z < A U) Q. 0 I: of Q. 0 H as A H H O P. 0. z I: r o X <1 2 O 4 H V) V) L.) '- H -' H CL. 0- H H fi- fi- H H J‘ Q H. J' 4 0: H ‘I' H H "7 H a A «O H Q a - N D 2.: Lu NU) ~ It O x H O " Q: m\ A A ll Lu '- Q 0 .N H + Q. A Z O D x 0 mm H u H Q H “ V) o- f mH a D 3 x a a <1 Q. A * “H“ s Q. o O- '- 0. H ~22 CLH N XQH'K Q. 2H XQ-QCL Q. 2 O NM 2" 0 m2 OQH 2. out MZZH z . '4 .2 H; m uaHa-v -M HII a..- on x H m< HU H QHHAQ H» “H OHHW HQ 4 X HX H a O Illell H h (0‘!) INNO- IIHO Z LU w! QN OMHuKHA mm mm Nfimlu av. :* 0 mx HQM\M\HHuNwHowHHMN\H¥HwHQOMHH zm ”DOW ND'H" can: MD fiDH' 0.3 [I n DMHNHD hm p 2b FQQHHZN zmmz h@¢¥Zo~AZ 02 < bahH OH i ON * fi 2 Q “A Q0: A A H xmA d A o > 4 DR < N O 0- Mt— 0- (D " M .J ZuJVIH O!- H V 0 PH” #2 v N D «Lao,— ZQ #- H a ( 00 V) O m N 23 HP 2: fih ~ Q OQZOJ DO 04 a H HQHOUJ HO DUJ O V) ’— >—IO .— .10 O o a.m.Jd‘ (LU (1’ M >- “11.00 A «I t A v - OhXAA Oh AA > < m M. m M. " " UJ QWVN D C ”N A m DIUWJ (3 Wk 0 a «mm. d m‘ “ °- NJQ+A U4 +a 9 " C WALD a math 0 In 60 DWDN 0‘ DWZN a. M Q WHN .- “ “H 0— ho 9H "‘ 'O O. WXZH" W)! 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MAA WC¥NJDJOO ZDQAQ ICC/lat} ZZZ flutZLUU-J Dunn-loo th 44: OHWNHD OMWND DW'ZZwDOZAJ mo 244mm¢22 OZAOOJODHNMZ'HOHNMD'HHM «moztmtzho>muvhho>4n~h: DIVIZD"ZDUOI~*OBZ w MDQODDHHQ U0 L90 MM 0 a a a 5090 ooét a H¢++ NQ$V a ¢a+ n++ H 19' ¢¢& 000 000 177 ozm zmahmm mazahzoo OOH ..~...m.~.».axu...~...~.H.h.¢.n.H.p:hnmon.:.~ ..~.H.».OHwon~H>Hhmmzum .-.:o maszzoo aw an“ o» co ..N...m.H.h.ax“...~»..~.a.h...n.H.h;h4mau.:.~ ..~.H.».ofluon<+h4mon.n.~ .~.H.»+hnmou.~.~ bnmou.«.N mm< Juno: bmmmm u:» «on 6:.N oh.fi.~ .mpzmHonumou >~H>Hb~mzmm o‘..u . mazahzoo afi aw oh on .~.cu.nooz.mH an ab ow .a.om.4ooz.ua ma.m zoamaowmm mmmuwm az.>zH>.4aoz.Non.>.<.m.a.ma.z~>..m.mma ..o a.m..o_<..o.~..o.c..oon.~uHm..oom.>..o.oan.h..o.o.ma onmzuxHo mzmm mzapaoxmam 823:8 m $.23 AIPENDIX C (Listings of in-bin solar dried corn data and the computer program "FIXED" for simulating corn moisture content and dry matter loss) 178 179 Table C—I . Experimental Corn Temperature, Drying Air Tmperature and Absolute Humidity, and all other "FIXED" Bed In-put Data. XMO = Inlet or initial Moisture Content 'IT = Total Time THIN = Inlet or initial Grain Temperature DELT = Time Increment (MM = Airflow Rate NED = Equation Number DEPTH = Total Bed Depth HIN Inlet Humidity INIPR - Number of Nodes between prints NL‘PF = Number of layers per Meter in x—direct ion TBTPR = Time between mtputs TIN = Inlet Air Temperature TIME TIgIN TgN HIN Hr C C Decmlal 0.0 8.90 11.39 .00354 1.0 8.92 11.06 .00411 2.0 9.99 13.45 .00480 3.0 9.50 14.95 .00565 4.0 10.29 15.72 .00498 5.0 10.68 15.83 .00444 6.0 10.75 10.56 .00325 7.0 10.60 9.61 .00324 8.0 10.86 7.56 .00371 9.0 11.14 10.33 .00374 10.0 11.04 9.72 .00387 11.0 10.70 10.22 .00366 12.0 10.24 10.CB .00377 13.0 9.79 9.89 .00382 14.0 9.28 9.83 .00355 15.0 8.83 9.56 .00382 16.0 8.57 9.50 .00371 17.0 8.40 8.43 .00381 18.0 8.07 8.28 .00347 19.0 7.96 8.(B .00343 20.0 7.76 7.78 .00342 21.0 7.79 8.45 .00300 22.0 8.04 9.78 .00283 23.0 7.65 9.61 .00330 24.0 7.58 10% .0G311 25.0 7.53 10.50 .00307 Table C—l. Continued COM .059 we“: <3 <3 <3 E> E> c: c> c> E> c> c> C) E: E> c: c: E: E> c> c> c: c> C) &> &> E> c> E> c: c: c> C) E) 01 05°. 7.50 7.47 .76 .78 aaaaasaaaaasxaa .25 .21 .3 sb .3 .5 .3 sh «> a: «J c» 01.3 <3 c: c> c: c: C) c> c> c> c> c> c> c: c> c> c> c> c> C) C) C) c> c> c> C) c: c: c> c> c> c> c> c> 91.0 6.51 6.40 9‘ £3888 .61 .61 .70 .72 .72 88888 .50 .88 q .82 8.49 9.07 9.49 9.83 9.92 9.75 9.70 9.45 9.14 8.76 8.57 8.45 8.10 181 9.50 9.45 9.61 9.72 9.83 9.89 10.56 10.78 10.89 11.06 11.17 12.61 12.95 13.45 15.06 16.50 17.39 18.00 18.89 20.17 19.22 19.06 18.11 17.50 17.11 17.00 16.83 16.39 15.83 15.28 14.61 14.17 13.89 .00202 .00198 .00196 .00279 .00216 .00232 .00243 .00246 .00252 .00254 .00250 .00241 .00246 .00204 .00240 .00267 .00266 .00424 .00402 .00464 .00496 .00431 .00444 .00450 .00438 .00407 .00369 .00351 .00330 .00301 .00303 .00316 .00308 Table C—l. Continued E; g; E; g; P4 k1 P4 F1 P1 P1 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 88888883388988 OOOOOOOOOOOOOOOOOOOOOOOOOOOOOObOO 58338 3888388 883868 8 «Jflggqpopopopooooozqq-«Jqq-«Jqqq g t—J o 95» 88252 6.33 6.14 5.83 5.71 5.68 5.78 5.65 5.64 5.72 5.78 5.93 182 13.83 13.89 15.50 15.83 16.28 17.22 18.45 19.06 18.83 18.28 17.45 15.39 15.00 14.72 14.56 14.22 13.72 13.28 12.95 12.67 12.45 12.33 12.11 11.89 11.67 11.45 12.67 12.56 13.11 14.61 15.17 16.39 17.61 .00312 .00313 .00303 .00351 .00329 .00333 .00302 .00813 .00829 .00825 .00322 .00298 .00260 .00248 .00249 .00243 .00237 .00239 .00228 .00234 .00238 .00233 .00250 .00250 .00232 .00228 .00291 .00276 .00201 Table C—l . Continued 125. 126. 127. 128. 129. 130. 131. 132. 133. 134. 135. 136. 137. 138. 139. ....I lb 0 141. 142. 143. 144. 145. 146. 147. 148. 149. H U! 0 151. 152. 153. 154. 155. 156. ...: U1 (I .OOOOOOObOOOOOOOOObOOOOOOOOOOOOOOO 83388339238888 8%888883538883388883 .01 183 16.67 14.61 14.45 14.11 13.78 13.56 13.00 12.45 12.00 11.45 10.72 10.61 10.89 11.06 10.78 10.45 10.00 11.50 11.95 13.61 15.95 17.56 18.28 19.11 19.33 17.72 17.06 16.28 15.67 15.56 15.17 14.87 14.28 .00208 .00203 .00281 .00209 .00217 .00221 .00219 .00215 .00205 .00207 .00224 .00227 .00217 .00202 .00189 .00194 .00194 .00231 .00270 .00293 .00291 .00399 .00285 .00276 .00282 .00270 .00247 .00261 .00287 .00247 .00251 Table C—l. Continued 158. 159. 160. 161. 162. 163. 164. 165. 166. 167. 168. 169. 170. 171. 172. 173. 174. 175. 176. 177. 178. 179. 180. 181. 182. 183. 184. 185. 186. 187. 188. 189.0 190.0 OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO O 8.43 .32 SSPPm 8383853 ...: >1 .22 .15 .17 .49 .74 .38 .92 .53 .07 .52 .79 10.83 10.74 10.42 10.10 cooooo«1«1«1<3«1«1 h‘ #4 #4 OOO .909090903959 83388383 7.85 7.71 184 14.00 13.72 14.72 12.83 12.72 12.67 12.39 12.22 14. 14. 16. 18.39 20.61 22.50 23.61 19.11 19.00 18.22 16.39 16.39 15.17 14.17 13.45 12.95 13.06 12.33 12.28 12.00 11.78 11.45 11.22 885 12.39 .00250 .00236 .00194 .00236 .00225 .00225 .00239 .00234 .00267 .00279 .00263 .00407 .00423 .00452 .00291 .00245 .00240 .00229 .00236 .00234 .00228 .00275 .00224 .00225 .00232 .00230 .00230 .00241 .00231 .00221 .00232 Table C—l. Continued 191. 192. 193. 194. 195. 202. 203. 204. 205. 206. 207. 208. 209. 210. 211. 212. 213. 214. 215. 216. 217. 218. 219.0 220.0 221.0 222.0 223.0 ooooooooooooooooboboooooooo O 7.70 7.61 7.58 7.78 8.11 8.68 9.08 9.82 10.32 10.67 10.79 10.67 10.27 9.81 9.40 8.96 8.43 7.96 7.54 7.18 6.95 6.63 6.42 6.00 5.99 5.99 6.17 6.54 7.21 8.01 8.95 9.79 10.22 185 13.83 14.89 16.89 19.33 18.75 20.06 22.00 21.06 20.06 19.45 17.17 15.72 14.78 14.00 13.22 11.83 11.28 10.95 10.61 10.33 10.11 11.06 11.39 13.28 16.39 19.45 21.89 23.56 18.19 18.25 20.95 .00294 .00270 .00285 .00396 .00359 .00300 .00458 .00274 .00252 .00280 .00219 .00226 .00224 .00215 .00213 .00207 .00209 .00201 .00204 .00199 .00197 .00192 .00179 .00201 .00236 .00267 .00268 .00433 .00443 .00412 .00232 .00300 .00283 Table C—l. Continued 225. 226. 227. 228. 229. 230. 231. 232. 233. 234. 235. 236. 237. 238. 239. 240. 241. 242. 243. 245. 246. 247. 249. 250. 251. 252. 253. 254. 255. 256. OOOOOOOObOOObOOOOOOOOOOOOOOOOOOOb 10.60 10.90 10.83 .18 .14 P4 P4 c) #4 .31 9 C9 .93 .42 °°.'“.“9‘.“9‘.‘“.“““9°.°°.°°'~°$° 899838885 .39 9.32 10.21 10.95 11.65 12.13 12.31 12.18 11.74 11.25 10.65 10.25 9.97 9.40 186 19.06 17.20 15.61 15.95 15.22 14.39 13.56 12.78 12.50 12.11 11.83 11. 11. 11. 12. 13. 15. 18.33 21.50 21.11 21.83 16.56 16.45 15.45 13.45 13.11 13.11 11.89 12.17 11.72 11.61 11.72 11.72 588858 .00260 .00252 .00217 .00226 .00213 .00208 .00197 .00194 .00188 .00215 .00209 .00216 .00233 .00263 .00298 .00365 .00489 .00532 .00523 .00145 .00255 .00254 .00269 .00252 .00220 .00218 .00220 .00225 .00226 .00226 .00223 Table C-l. Continued 257. 258. 259. 260. 261. 262. 263. 264. 265. 267. 269. 270. 271. 272. 273. 274. 275. 276. 277. 278. 279. 280. 281. 282. 283. 285. 287. 288. 8 <3 E> c> c> c> c> E> c> c> c> c> c> c> c> c> c> c> c> c> c> c> c> t) c> E) c: c: c: c: c> c> c> c: c> 9.53 9.43 9.29 9.33 9.32 9.33 9.40 9.46 9.58 9.90 10.38 11.03 11.63 12.07 12.49 12. 13. 12. 12. 12. 12. 11.79 11.61 11.54 11.39 11.18 10.95 10.88 10.92 10.82 10.83 10.85 10.92 88888:?»] 187 11.83 11.78 11.78 11.67 11.95 12.06 16.95 18. 20. 22.17 88 23.50 14.45 14.11 13.28 13.78 15.72 14.83 14.11 13.72 13.61 13.61 13.61 13.33 13. 12. 12.67 12.67 12.45 17.39 17.39 18.78 20.95 88 .00220 .00227 .00228 .00221 .00227 .00245 .00241 .00293 .00390 .00430 .00393 .00351 .00321 .00299 .00313 .00315 .00305 .00303 .00306 .00309 .00291 .00305 .00275 .00269 .00262 .00259 .00261 .00258 .00298 .00311 .00382 Table C—l. Continued 290.0 291. 292. 293. 294. 295. 296. 297. 298. 299. 300. 301. 302. 303. 304. 305. 306. 307. 308. 309. 310. 311. 312. OOOOOOOOOOOOOOOOOOOOOO 11. .47 12. 12. 12. 12. 13. 13. 13. 13. 13. 13. 13. 13. 13. 13. 13. 12. 12. 12. 12. 12. 12. 11 17 46 82 888888888885888 31 21 188 23.06 24.45 23.28 18.39 18.45 17.78 17.11 16.78 16.83 16.83 16.95 16.89 16.78 16.33 16.11 15.89 15.61 15.11 14.67 19.39 19.39 20.50 .00410 .00365 .00373 .00374 .00815 .00304 .00290 .00271 .00278 .00282 .00283 .00295 .00291 .00307 .00287 .00267 .00271 .00265 .00259 .00245 .00265 .00268 .00295 189 Table C—2. Simulated hourly corn moisture content and dry matter loss RUG = Corn moisture content by Rugumyo eqns MISRA = Corn moisture content by Misra eqns SMC - Corn moisture content by Sabbah and delGuidice eqns DRUG = Corn dry matter loss ass001ated.wuth Rugumayo eqns DMISRA - Corn dry matter loss assomated with Misra eqns DMS = Corn dry matter loss assoczlated With Sabbah 81 delGuidice eqns _ HOUR RUG NHSRA SMC DRUG DMISRA [NS 1.00 3181 .3188 .3183 .0004 .0004 .0004 2.00 3153 .3155 .3154 .0008 .0008 .0008 3.00 3148 3151 .3142 .0012 0013 .0012 4.00 3133 .3154 .3132 .0015 0017 .0015 5.00 3114 .3148 .3122 0021 0021 .0021 5.00 3084 .3139 3112 .002 0025 .0025 7.00 3039 .3131 .3099 .002 0030 .0029 8 00 3003 .3132 3091 .0032 0034 .0032 9.00 2997 .3128 3084 .0035 0037 .0035 10 00 3032 .3129 3079 .0038 0040 .0038 11.00 3001 .3117 3073 .0040 0043 .0041 12 00 2995 .3114 3057 0043 0045 .0044 13.00 2984 .3108 3052 0045 0049 .0047 14 00 2992 .3104 3057 0048 0052 .0049 15 00 2982 .3100 3053 0050 0055 .0052 15 00 2974 .3095 3048 0053 0057 .0054 17 00 2980 .3094 3044 0055 0050 .0057 18.00 2973 3090 3040 0057 0053 .0059 19 00 2982 3090 3035 0050 0055 .0052 20.00 2970 3085 3032 0052 0058 .0054 21.00 295 3082 3028 0054 0070 .0055 22.00 2955 3078 3024 0055 0072 .0058 23 00 2947 3071 3019 0058 0075 .0070 24.00 2934 3054 3014 0070 0077 .0073 25.00 2939 3051 3010 0072 0080 “0075 25.00 2930 3055 3005 0074 0082 .0077 27 00 292 3051 3001 0075 0084 .0079 2..00 292 3047 2995 0078 0087 .0081 29.00 2915 3043 2991 0081 0089 .0083 30 00 2914 3039 2987 0083 0092 .0085 31.00 2905 3034 2981 .0085 0094 .0087 2.00 "900 3032 2975 .0087 0095 .0089 33 00 2897 302 2970 .0089 0098 .0091 34 00 2898 302 2955 .0090 .0100 .0093 35.00 2898 3022 2951 .0092 .0102 .0095 35 00 2888 3018 2957 .0094 .0104 .0097 37 00 2887 3014 2952 .0095 .0105 .0098 38 00 2 81 3011 2948 .0097 .0108 .0100 39.00 2881 3007 2943 .0098 .0110 .0102 40.00 2871 3004 2939 .0100 .0112 .0103 41.00 2854 3000 2934 .0101 0113 .0105 42.00 2 55 2995 292 .0103 .0115 .0105 43.00 2853 2992 2925 .0104 .0115 .0107 44.00 2851 2988 2921 .0105 .0118 .0109 45.00 2 55 2985 2917 .0105 .0119 .0110 45.00 2844 2981 2912 .0108 .0121 .0111 47.00 2838 2977 2909 .0109 .0122 .0112 48 00 2835 2971 2905 .0110 .0124 .0114 49.00 2844 2959 2904 .0111 .0125 .0115 50.00 2845 2955 2901 .0113 .0127 .0115 51.00 2828 2959 2898 .0114 .0129 .0118 52 00 282 2955 2895 .0115 .0131 .0119 53 00 2824 2951 2892 .0117 .0133 .0121 54 00 2821 2949 2889 .0119 .0135 .0123 55.00 2825 2944 2885 .0120 .0137 .0124 Table C-2 . Continued 56 00 .2311 57 00 .2804 58 00 .2796 59 00 .2791 60 00 .2790 61 00 .2784 2 00 .2778 63 00 .2774 64 00 .2781 65 00 .2768 66 00 .2766 67 00 .2761 68 00 2757 69 00 2754 70.00 .2749 71.00 .2744 \‘VQVVNVQ QWNVVPUN O O M \l U HHHH oooouuuuuaaaau ”HO-CH“ JMFJNM HHHD‘HHH omo‘bUV’OCDO‘kPJ UUUUUUP UlU‘U’Ubbbhbbt-JUUUUUNM OVJDMOOO‘vbMO'OVUbMOOVUbMOOO‘ O O 0 O 0 0 OCKNDOCKNDOCKMDOCKMDOCKNDOCKND OOOOOOOOOOOOOOOOOOOOOOOO puuhupuuuuuuupuuuo—u unuuuwnMHuHHnHHh-MHHH 01301010188840 UQOUOOUUHQO‘JINOQO‘AMOCDO‘JIM'O OOOOOOOOOOOOOOOOOOOOOOOO uuuupnuuuuuuuuuuu O‘O‘O‘U‘U‘UU‘Uhhbbb UNOVU‘U"OOJO‘&UH VO'O‘O‘O‘U‘ 191 Table C-2 . Continued 90 00 2708 2021 .2764 91.00 2709 2818 .2759 2 00 2701 2814 .2754 83 00 2700 2811 .2749 84 00 2709 2807 .2743 B5 00 2692 2802 .2737 B6 00 .2603 .2797 .2730 87.00 .2674 .2791 .2723 88.00 .2666 .2785 .2715 89.00 2659 .2780 2708 90.00 2651 .2775 2700 91.00 2649 .2771 2694 92.00 2642 .2765 2687 93.00 2636 2760 2681 94.00 2635 2755 2675 95.00 .262 .2750 .2669 96 00 .2616 .2742 .2664 97.00 .2615 .2735 .2659 98.00 .2607 2730 .2654 99.00 .2599 2723 .2648 100.00 .2586 2715 .2641 101.00 .2575 2709 .2634 102 00 .2576 2704 .2628 103.00 .2575 2699 .2622 104.00 .2568 2694 .2615 105.00 .2573 2692 .2609 106 00 .2559 2687 .260 107.00 .2550 2682 .2595 108.00 .2543 2676 .2588 109.00 .2535 2671 .2581 110.00 .2531 2666 .2575 111.00 .2525 2661 .2568 112.00 .2521 2656 .256 113 00 .2514 2651 .2556 114.00 .2509 2646 .2550 115.00 .25 2 2641 .2544 116 00 .2498 2635 .2539 117.00 .2494 2630 2534 118 00 2489 262 252 119.00 2455 262 2524 120 00 2479 2613 251 121.00 2474 2608 251 122.00 2465 2303 250 123.00 245 2596 250 124.00 2459 2588 249 125.00 2448 2581 249 126.00 2425 2575 248 56...... 000000000 HMHO‘D‘HO‘MI‘ OOOUQVVVO' V§OOUOUMO OOOQOODOVV 44-43015-4500451 0 ”322222000 «11.103050 Table C-2. Continued 127.00 2424 123.00 2425 129.00 2431 130 00 .2416 1'1.00 .2412 132.00 .2403 133.00 .2404 134.00 .2393 135.00 .2392 136 00 2333 137.00 .2339 133 00 2333 139 00 2375 140.00 .2367 141.00 .2360 142 00 .2359 143.00 .2354 144.00 .2354 145 00 .2353 146 00 .2347 147.00 .2333 143 00 2340 149 00 2 22 100 00 .2313 101 00 .2303 102 00 .2305 103.00 .2295 154 00 .2293 105.00 .2290 106 00 22 7 107 00 .2237 103 00 .2273 159 00 .2270 160 00 .2263 161 00 .2255 162 00 . 2233 163 00 2246 164.00 .2239 165.00 .2236 166.00 .2233 167.00 .2226 163.00 .2220 169.00 .2216 120.00 .2207 1/1.oo .2212 172.00 .2205 1/3.00 .2199 174.00 .2137 175.00 .2179 176.00 .2164. 177.00 .2157 173 00 .2153 179.00 .'143 130.00 .2144 131.00 .2141 132.00 .2133 133.00 .2133 134.00 .2121 135.00 .2120 136.00 .2113 137.00 .2109 133.00 .2103 139.00 .2104 190.00 .2095 191.00 .2107 192 00 .2034 193.00 .2034 194.00 .2073 195.00 .2067 196 00 .2063 U U1 U U1 OOh‘HPJV‘JUUbbbU’O‘O‘VV OU‘OU'VO‘hUIOJi0UIOUHH bLflUU‘UUUU’LfiLfiU‘UL" (t \1 I” 1.)"dePJUMPJDJMPJY‘JFJI‘JFJI‘JMPJ .‘ b m (1) 666666 PJPJMPJMI‘JMPJ mwmuuuuu 0000OF-‘M 0m~m6~vu M .— mo \JUI UUbbU0O‘Vm PJVPmeOVUO HhHD‘MHHO-‘HHHHHHHHHH DJ 1'.) 1'.) 1'.) P.) H 1'.) 1'.) DJ PJ mmmmmmmmmnummmmmmm ."".'21' occuuumm ' ou006m~o 0OHH'U @0000 Table C—2. 00 0(0 .‘Huumnuuuuu Q£mV0U¢UN*O “J P)" \ 5'3 \Q‘A ‘ 1... a: D X‘ f m n 1“ .‘F\ -‘: .3 I. L3 ‘I‘ Q w~wuwvm~ 66666666 '1. . 90809590291010 wwa-‘O VL‘P.‘NM1‘.‘P.‘”J"J"JPJMM UUUU‘UU‘UUUM-‘Oh ‘ U .39_ ”HQ-OBI... I o c - u - o I n u u I o I n u g o u I ~ - o - - . . . . . . . . . . bhhhhthHwh‘b—hO—hfi—“H "wuuumuuuh—HHHHHHHHH Continued ,1 0 CO 0!.) UCCL‘CSCJIUCUCCD‘J JFJFJUébUO‘L‘VGiDLfl U0CJC‘F0UHL‘WOLJC‘J ‘0- Utfi JCCOCOJUC3( a k U033030-‘HFJ’ FJUHH¢50NDU guy uvc C‘C‘O‘C‘C‘t‘NVVVVV’VVVV .‘UubéuL‘O‘O‘ \OvtIULJhUUCIU‘CD '2 UO‘EDD00OOh-fi-f 0‘1o5mU'03‘1U JTJY‘JYUFJMNY'JNPJMMPJYU HHHHHHHHHHHHHH LDUIO‘VO‘C‘VVVVQCH'D00 "JFJMI‘JMY‘JFJYUYUMf-JFJ"JMMPJMMMMMI‘JFJPJFJF Hut-HHHHHHHHwHHHHHHHHh-HHHH “\H'JO‘O0-505H0HU0‘0HMO‘CUHUIVO‘MbPJ‘JlV JN~PPJMUbbUbUU OOOOOOHH’HHHP OflubO‘VOU‘th I o I I O I I - g . ...... (0900(0000000000000000 . . ' . ‘ ' . . . . . . . . . ' . . . n 4 o v D u I u - o . n u a . o . n . a o c u u I n o c o 193 \1 M 00000" UUUUthU‘O‘O‘VVm00OHNMUbb 0000010000100 00 “MN \1 UVNOOthogggguegggg UO0HUhVHU|OU|O(PF-‘QAHIIIUUOUJUMmb-‘blr‘l VVVVVVVQVVVVVVVVV HfiflJMUUU-bb 0000000000000 UIUIUUIU'UIU‘U'U'UIU‘UIUI VUQH0QVUbbUNO ”(unfunny-unwraps“ 000000003 0 6 to O #bbb0hbb uuuuuuuuu QVVO'UU‘00N 0 b N H 20422 Table C—2. Continued ~00000000 meuoauom ”(110001001017thUOHWOO‘FJHVODOU‘ r \r .-FJF~JLJ" A ‘5 .‘ F.‘ "J M "J "J ”J "J 'U M '0 “J "J "J UCJCJGJCOCDCDVVNVVVVV O O L—t-t-ot—I—Ht-ou—L—v—bu—bou—y—Hb—u-Hhh—uu U‘UUUUU-‘J-UO‘C‘C‘C-‘C‘U‘ Neocw~092w~90993993ww O O 'JUC‘N’NCDCDQO u L.) 0 0 umuumnmwu" 0 ' 00061003 31 J"J"."'J 00 W. 00 00. n 00 9N o o 666mmmmmmu DCJ00OOHHU>6 OUO000bCDf‘JO0 (a) 0 PJ 0 O prannHHthhHHh—u—HbuH—t—H uu666666666666 01001370006011.3000! \JN0ONNUHUU0CO" ...-‘0‘ 00“ UVO 0000000000 mummuuumuu JpJpJHHHHHtht-o HOOOJVOUIUMH p 000 U'U'U! PI'U 0000000000000000‘1 O U" M 01 PJPJPJFJPJ J (UV 0 A 00000 UUUIUU‘ OOHF‘HI‘JI‘JLJLJhin'U‘00Vme00 O 01 U 0 U001‘J00bCDMVl‘J0P0fl0H0HVLJDJ 0 0000 HHHHHHHbU—HHHHHHHHHHU—HH U" U ... 00000000 0 O 0 U-‘HHl-Ol-IH 0V0-bUPJ 000 O 000 JNNPJ 0km“ p UU’U‘U‘U‘U‘U‘U‘U‘U‘U‘ 0 0 0 00OOHHNMNUUbUIw 0\HDCD00 UO-b0-b0bO0PJ0UIHEDUED bbDU‘UU‘U'UIU'UIUI CD . I I O I I U l I I 0 0 4 O I I 1 I 8 I U I HHHHHHHHHHHHHHHHHHHHHH (DMVh‘0O APPENDIX D (Listing of the canputer program "FIXED" used to simulate corn drying in a fixed bed with solar heated air) 195 Appendix D PROGRAM FIXED *DECK SOLAR 1NPUT,TAP£61:0UIPUT,IAPE1) (INPUT,OUTPU1,TAPE60 (iiiti P-J )-L:uJ P46 HQD Wm: 0:0 u.) 0: >Ow H2 2H6: Duo LouZ 1—2—4 -v-1 201.0420 RUUTI 8L0 LFY REA ZfR ) 1 E SU (***** (***** (***** (***** (***** (***** FUNCI (***** (***** (***** OH*** Citfiif ,XMO,IAB,TIME ,Hrc T,DELT cmm cv,cu,§an RH PI fi-U >\~4U'1 H(51) 0N6,c0~7,c0~12,c0~13 “U is I-Kc C! \2 WAD ZNU \ \ \ GPP‘ mmz 2V0 ,INAME(3) 99999999,3*.o,510/ S1) 7?) ) 9 VDNQ A II-fi F244 mono»— vv—q UH (JD-PX NUVLLJ i—Zi v-< 03m \ “a.m.— QZUZV- MU 050%: 'Ct OANUVE Lu QNZHz I 1— A. \O \szH hut-U: ‘30. S M \HAHXHJ \ ‘vac- ~90th F-fi'J-zr-mem 1—4 ZW<< Dav—1h X\QZ\U a; \ \bW\>-\mugDu-o: vaum ‘0 r—1 a9 I m PP 0.00 >— >- 02 1-2‘. L‘- ‘I “'3'“ 0219’. Lu 0: >1— wp— 0 tr 7.2 1- cl: «1 0: (PC o 00 4P; 2 u :~* . < N 2 mm HQ! 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APPENDIX E (Listing of the computer program "SDLARUG" used to evaluate a flat-plate solar collector) 257 E. Amen ' lfitfiRMdSOUMEE O Lt)- (P _Jr—c 0U) mm M U> f-H <2 .43 Q U v—r- <4 JP sz OUTPUTqTAPE7) 42 d LLB) OH I [AU UH 2: 4 2% m4 AO HmZ' (Max .UO HQL) N v“)- (Ix OHS a HUM) th' UH 04C) ZDul 0‘42 x46) 0>H ‘RUW F‘LU O NZKMDU ~H1‘Zm Samba: «U .MMJW ‘1'KCKM—ZZ J»Z ge(IKPUT.CUTPUT.TAPE5=IHPUT.TAPES 258 UTINES USED I .J CC”- I PJOZU<

u zmmHmezszJmImomvo ) THRQDAYQHONTHQYEARQSOLQVELQTPIQCLINvTAoAMENvTPZQCOUTQ HXOOH dumumrquwfiaqochvah OMMDZPQ&NJMAUW<:HMJ (H oumuu Shh}: m22h~ QJMHD 1"! ah¥I «oil «was UULK) Cttttl Ctttt Cttttz Cattt3 c....q Cfittts Ctttib Ctrtt? ) SOLQSLF C h TRHGQTRMTQTAQTPI'TPZOTSOLVVEL) 5 I 0P .J9 . A L9}- 00 .02u.cm« u U r GMHLJ mm < \094 4&H2 o n-.J0 4U hJ (N006) OOQQ II QPWMLXFWMDK P aLdeZFMJ >0 CDNfii’HW>- <0+0H0PW“WLW< CHM—I 4ZOPZ L40 0: 00 u. 'WUI .4 >2 U mm mI'Z44I .U o «h UPOUUPU _J 0 _J L4 .- oZp— OI o 0 I4 1 >4 4004042 QI x 00 QimOmO4 2Q u >U XOPmeU OD 0 4CD U)- .h-L...‘ OI 40 P CO 04&90>0 ha 200: hOhiUUm OP HHI4 ZOOO 0 'DFDPOO OPODI4U N t—O 00 z o .4 .0 0 DD 0 \ PU4PO'H (WPH4'DO «u h oooowum umomImG- NP h UZUH IH MICDN xodhommHO :3\ 01x ocn H\h mmm\¢ vomooUM\O hwumfioo'x <.~u1anmnc ZQOJI 'fl mm &\PF®O 00+DUIImi RX #¥**’P Huntmohm 201 260 / {?XQF3.092(2X912)911(1X9F5.1)02(1X9F4.1)01X1F7.1' T( I F5 2 40 {httt END Appen ' PS.INDIC.NRC) ) E Z 50)deOL(SO)9JORD(50)9Y(50)9A(NRC9NRC)9X(A) Catt. 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H ' OOH H LLHU OOmU-‘OV OOCZUVOv HUM! OOH7>O4 DDH7>Q4 fi at a u at a t It i a: «.0 5 Q. ¢ 0 UN UUN N NU N '0 FOR INOIC NEGATIVE OR ZERO STATEMENT DHti Duct continued. dixE. A %M A I 4 m I o D A 4 2 H o 4 Q m b 4 P o m \ c O u: 0 U r- A Z 4 U 3 A4 H 4 4 C) 44 Q U 0 o u,“ 4 CD If) A l‘ to 4V \ o H 0 U 4m 0 O U Q 0 O ~'O U 4 > I 4 a" ZU D O U I- \ Q o v-a. u U) U A 0') WA V) O 0 La. 0 U 74 H 4 O 2 4 O m 0 Ha. I- U 0 c U h D m 4 U H m 2 n w h H h\ m H+ h 0 O \ 4 H 4U L9 4 r 3 A o w u 4U 'm 2A 4 4 I— A U Z 2 mo H 4H 0 O 4 u > I DO H4 ow 0Q m '7 4 U 4 H 04 (DI UU‘) 4 U4 2 I 0 0 D D Q» h D 24 4O 4 4\ H m u o 26 Ow 4 cu h on o I 4 Z vU o \2 4o 2 Z 24 nah h I- U D O .1: AH U 49 O 4I-A Z> o H 4U 4 4m r-4 N UHOOUU O H U I— O? 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DO I 4 O OOQH QOQ UNDU OQAUN/IOM 4 U Q4 mvoo 44 D N 4QD4 4 V2 44 O . 004 4 UUOZO‘Z Z I-4U CKZHZ\44«IIZ\ AZH Z\r—DDZIOD o 4 I UO'AHZIO GU 4OVOI—\I-AOU OH OUUZZO 04 0 km Ahmo H UOo QHmH(m— 40030—04 00+ 00444~ DUIOH4 > < u I4HI4 4 P > o4 h 4 th4 < Hvuu n 0 mp 4 Ho A bob 4 4 400: 4m~m P mmvv u v :2 o QU o mhm 4 I 44U4 - UM U c: O r— WQHQUHQQ QQ 4 4 9* CD 4 #- mo H Ha: 0:2 44 0:44 a: a: ZAAZ 4 o mH u \«\4M\\ 4\\ _ 4na4 m #- (LL 0: ”Ad's LOAA _jAA m u: (9&— LL Q' WA4AM4UU OHI— r— 4 4 ULLQU) u. 4 V) U) 4HCHH4LDCD U00 U) x 4 4 ZUUU) O 4 UV) H 4QUQ UZZ t—ZZ x I O O accza:4 0 HH U4H4U 44 44 I H m m h 4 h (D 4 X \ \UZCZI ZOCCZ *- 0+ +0 2 LL 4>< U ZHZHZH H (I) >-A>-AU) U 4 DU Ca HUHUU I I I l U) H {DHCDHWOOI H 4 UC ;‘ Z ZOU U H O. 0.4 0 0D- U .- _12 H zqdeuHH UHH a: 4 (_JHHDp—H H 4H OHOVUZUU 200 m 4 O\O\UHVSIQ O U U HZHZZ4ZZ 422 m 4 UUUI- \\ 1Q 2 U > PHHHHH44 H44 4 o WUMOQHHQFU 4 U) H UWUU) UHV va 4 U chrZDUHOC O V 2H '- 4V4vzu~vv “we 0 )— U4U4 lLU. 0U 44HU 4 WQZQZ4QH4 QH4 Q Q 4~4vummux> CV34 :1: U‘UHUHOUUH- Umr- O O mwmmz Zr—v— “ om Q hammmmmvv mvv U POHO4II4¥H Q4930. U F 4 4 vv UV mmm—c U U.— HW> <XO4 r-UU H XL]. >IU4 H U3 (no. movtn HHQH tvxa: UHIUO 2H r— 4UIU mo. 4 r—UQQ U. U H!!! >+vm OUQOGH #0 H: Her—UU4Q 267 THE COLLECTOR IS ENGN QHPHP >4H > UO>IHI (Kit—Q .— UUHUQH 24¢“. mtg Ul—IUOU UCKMI (XVII) CD 44-ml4l 4&4 00‘ 0:10 Fag; 0 anft O‘OU) IUD 04 0 UHUOOULLCF- ' ‘ OmH4H 4U> Q I—IO—fl— 4 C) K OIIHLLHfiH U||4HUIIZ IL H U U NON N 2 U i- a: UL) . Z 0 DH: U 4Q mu. 0 u. LLO-D I: O—U 4U Z 4 4UZ LI. UV OW U 4 4mm V) C I C C G O 4 4 i It ¢ 0| 4| in 4! 1n 4- C a- CI i 4 q: t 4- a Cl C: U U U U U U U continued . Appendix E. engOUTINE CALCNIDXOLDoAvNRCQALFG'ALFTQTRHGQIRHTQTAQIPIQTP2QTSOL9 0 TT IS TEDLAR ER TEMPERATURES V O oooooAUGM DIMENSION XOLO(20)oDXOLO(NRC)oA(NRCoNRC) Cttot 268 A ..J N < o p- u 2 O a: N O H. h a: U 0 h.) \ I ..J 0 N .J 0 o 1 (30 o O ()0 ID a 0 N u. 2 o O)- o 4 CD U v—a: CD .1 2m 0 0 H4 0 Z 4 G <1 (L4 '0 N 9— X0: 0 .1 U4 H #4 (u: o P 'MJJ CC LODU \DWUVIU— \DZJU)->->-_J “CZO-J—t—C quu-c—n-«x U P>>>D olMo—n—u—n v-d ZVH/Hflu. (AZOWWVJO QqUo—nu—«H ULL 221:0) oUththJh- U)!— 2 ZUH/H/H/JOILJ o HHHHZNXVO U .0 o o .HMHngfp-JHIIHO U ZWCOMLJIIAII ll WUOCLCLCL ”"7“ v '3 < hudordv .— H _J H 4 IOOOV C: WDXD< UV) COULJUUF- Cote. Caiti Ctttt Ctttt Ct... COO... OLO(I) Catt. ..J O U) .— o O. O— .— .J o C) <1 (I) p. o o O. A I'— N o v q Q I— _1 AA 0 0 C31?) A x o o N 0 Mr! V 0 A F- D o H _JI I .1 o v 0 O In . 0 man x N O _J ¢mn o c O nun/3 A O 4 1x OQJL H * o 1’ou V In" u_ «I m\\ (3 NA 0 O .— p— o o _J 0 03' z ...—4.4 O ow. U) ..— p—vv x .\' P" m z 0 ‘Ah 2 a e_§+ . OAAH uJ '— Pfi’ .Hv “J A orwa H¢\d24 _1 a .J muun mamen U 0v :A ..JCLO. QNROX NC) > (Laun— UNX U \.J O \\.JAUV | a .so (n + ooOJHJOI u Nx o HHUH-O—I O N (1 o 00 vai OXOAG | p—u Zvku XNOI ”.3 LO Q O:\\“._Ul v. 0 0+ o_J Ut—oc‘x 0 ID“ 2c “OFW‘ o op—A o ..JN Hap-am o c- r-c-u-dl N6 (10' L... I lat—maul t—v‘t—xo rmdhca ”_HIHKLD*V~uJ DO—VJII IIQ< _JJQVVO Q. C UVL’HOCCF- X ' I" ”Xi—LL nod X H H O VJuJII IIWMIIVII ll UWQJLOU CLO. LL O—D— p—p—HmZJGJOULJuJHLLQOK-D c..... continued . Appendix E. v i U O m V i fi A m V) N I n 2 V m 0 U a Q U J 4 U 0 P X C + Xx H o H I E 3 Q "a: v— i h A d + m Ad h H 2% n P2 Q V OF M h i O n.0 Q VQ m J OW‘ U 00 Z 0 am * 0 U K UOZ U QM U V DUO W 12 f 1 htU UO In u. In. 9 h N u 3mm 3 0 U OON m 0:0 H 3 1H 0 v filDfl >am 0U UHOOOQLLH Gianni) I—t— . oUwfif—d’ 0 O U <33 Imdlchl m> h n> *2 (”HM llC/Jllt/h-MIIHflCDIIo-~ <1 a ma RU A JMAAHAUUAANUAOZ uoamun¢odmvmnmm o. 0U 00D 0*: 269 HH Hm NNJ Nfih 9 <4 4+ <II Cifitt :1.QO I—NI—N o o 9 o I—OI—o P-OII-i .4: 0! vii—~08 I'- n— 0 ON ON <\<\ I-AI-r‘ o.— oo cI-CI- I- I- Z I Z I p4 H 10.03- (LI-QI- \v v AVA- Q«:D« FUJI-VJ oz .2 UOUO UUJU o o D-III—II sit—VD n.0,“..— HIHI Ctttt \\r-I vvm cont inued . E. Appen ' Citii 271 U (x D .— <1 a U P Q 2 i < U I- r- m 2 2 O d U U z ... Q d U 1 I— 4 AU) Q4 0 #3 U .— IO 4 z 2 3 Q4 4 o h < D A v2 > U D \H U >- \ 0 at P U Q P! n\ U H x >- h at Q > k U I O < a: H 2 H m w 03 H h H m :3 v-c IH GU (I) <1 U C I- (l) 4! U D a: U 4 Q Q ‘2 H Q Q n m m a H quH H 0‘2 (A H k U <1 \Nr— m 0 Q > (H Q OOVU UZI- U [LI-'0: 8.1 2: IL 00 I- QHQ OIIU U I U UGO Htl< O>U A Om H h 39 P0 i m m4: < >02 2 Q on “U 4AA QU 2 PhD < m Au ¢\m Q03 XU m Hmz 2 o QV Haaowhoo m H U mm > ' \ ~HVH_ : QQ x Ium Huc¢m a < Q HHUHJOUNFHK Qu> DIUJ M HH < UHH P «U 24 < < o z w Q n m QQUK t Q 2 I a Hm; U h hUII U U h x Q >UU D 0 u a a «a. « a a a a u l a C «q. i fi ¢ ‘ « I c c ¢ gac a c c i c g a « c .9. ¢ a a o « a U U U UUU U U U U U U continued . E. Appen ' 272 + \ A A D F. O A H o o I . U + n P I \ C O 2 U 4 u 2 m U I'- Q I O Q I U U U a D i U 0 (I) D U a: (I) O H Vast-4 n H \n4 a v A m H 4A U U N O r— 2 _J U U D 1» I O H U. HQZLD I— 3 x\ Q QHLL '<>(H U) U I 22 H< QAU UJO H I H <3: AXI- I-_ UUO U UU < Q cU U mQL >0IU U >. 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