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(,.‘4 “““W‘ ."I----fl-I-n¢ 03‘ ‘ ‘ LIBRARY Ill/lllfllfllflfllllliifllfl/AWM”twigs/Ill!!!l L 11:51:15? “am This is to certifg that the ‘ thesis entitled Thermal Properties of Grain i presented by Edward Arshak Kazarian has been accepted towards fulfillment of the requirements for Ph.D. degree in Agricultural Engineering WM/M Carl W. Hall Major professor Date April 302 1262 THERMAL PROPERTIES OF GRAIN By Edward Arshak Kazarian AN ABSTRACT “Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering 1962 Approved ( Déég (254d «[0. ABSTRACT THERMAL PROPERTIES OF GRAIN by Edward Arshak Kazarian The specific heat, thermal conductivity and thermal diffusivity of a few grains have been reported but the information is usually limited to a narrow range of moisture content. A knowledge of the thermal preperties is necessary before heat-transfer analysis can be used for problems encountered in drying, storing, aeration and refrigeration of grain. The objective of this study was to determine the specific heat, thermal conductivity and thermal diffusivity of soft white wheat and yellow dent corn and to relate these preperties on the basis of moisture content and temperature. The specific heats of the wheat and corn were deter- mined by standard calorimetric tests. A transient heat flow method with a line source of heat was used to determine the thermal conductivity of the grain. The thermal diffusivity was also determined by transient heat flow. Transient heat flow methods of determining thermal preperties of hygrosco- pic materials minimize the problem of moisture migration or moisture changes in the material. The thermal properties of soft white wheat were ii Edward Arshak Kazarian determined at moisture contents ranging from 0 to 20%. The thermal prOperties of yellow dent corn were determined at moisture contents ranging from 0 to 30%. The specific heats of both wheat and corn were found to increase linearly with moisture content. The regression equations were determined. The specific heat of dry wheat was 0.554 Btu/lb-OF. The specific heat of dry corn was 0.350 Btu/lb-OF. There was no significant difference in the specific heat for a difference in mean temperature of 20°F. The thermal conductivity also was found to increase linearly with moisture content for both grains. The thermal conductivity of dry wheat was 0.0676 Btu/hr-ft-OF. The thermal conductivity of dry corn was 0.081u Btu/hr-ft-0F. The thermal diffusivity of wheat decreased with increasing moisture content, but was not a linear function of the moisture content. The thermal diffusivity of dry wheat was 0.00359 sq-ft/hr. The thermal diffusivity of corn decreased with increasing moisture content up to 20%. For moisture contents above 20% the thermal diffusivity of corn increased with increasing moisture content. The thermal diffusivity of dry corn was 0.00395 sq-ft/hr. iii THERMAL PROPERTIES OF GRAIN By Edward Arshak Kazarian A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering 1962 if?) P .104); truth—'2 ACKNOWLEDGMENTS The author wishes to express his deep appreciation to Dr. Carl W. Hall, Agricultural Engineering Department, for his guidance and supervision of this project. His many ideas and suggestions made the project interesting and challenging. Appreciation is also extended to Dr. Merle L. Esmay, Agricultural Engineering Department, Dr. Donald J. Montgomery, Physics Department, Dr. Edward A. Nordhaus, Department of Mathematics, and Prof. Donald J. Renwick, Mechanical Engineering Department, for their cooperation and assistance. Acknowledgment is extended to Prof. A. w. Farrall, Head of the Agricultural Engineering Department, for his interest and support of the project. Sincere thanks are extended to Mr. James Cawood and Mr. Glen Shiffer for their help in the research laboratory. VITA Edward Arshak Kazarian candidate for the degree of Doctor of PhilosOphy Final examination: April 13, 1962; 10:00 A.M.; Room 218 Agricultural Engineering Building Dissertation: Thermal PrOperties of Grain Outline of studies: Major subject: Agricultural Engineering Minor subjects: Mathematics Mechanical Engineering Biographical items: Born: April 2, 1931; Hamburg, Michigan Undergraduate studies: Michigan State University B.S.A.E., 19Sh Graduate studies: Michigan State University M.S.A.E., 1956 Michigan State University 1957-1962 Experience: l95h-1955 Graduate Research Assistant, Michigan State University 1955-1962 Instructor, Agricultural Engineering Depart- ment, Michigan State University Member of: American Society of Agricultural Engineers Sigma Xi vi TABLE OF CONTENTS Section Page INTRODUCTION . . . . . . . . . . . . . . 1 REVIEW OF LITERATURE . . . . . . . . . . . A METHOD AND APPARATUS . . . . . . . . . . . 13 Specific heat . . . . . . . . . . . . 13 Thermal conductivity . . . . . . . . . . 1h Thermal diffusivity . . . . . . . . . . l9 PROCEDURE . . . . . . . . . . . . . . . 23 Temperature measurement . . . . . . . . . 23 Grain samples . . . . . . . . . . . . 2h Density measurements . . . . . . . . . . 27 Specific heat . . . . . . . . . . . . 27 Temperature correction . . . . . . . . . 30 Thermal conductivity . . . . . . . . . . 33 Thermal diffusivity . . . . . . . . . . 38 RESULTS AND DISCUSSION . . . . . . . . . . . NB Density . . . . . . . . . . . . . . h3 Specific heat . . . . . . . . . . . . #3 Thermal conductivity . . . . . . . . . . 53 Thermal diffusivity . . . . . . . . . . 59 CONCLUSIONS . . . . . . . . . . . . . . 65 SUGGESTIONS FOR FURTHER STUDY . . . . . . . . 67 REFERENCES . . . . . . . . . . . . . . . 68 Section OTHER REFERENCES . . . APPENDIX . . . . . Sample calculations viii Page Table 1. 2. 10. ll. 12. 13. m. 15. 16. LIST OF TABLES Reported thermal properties of grain . . . . Comparison of temperatures measured with recording potentiometer and manual potentiometer Moisture content of wheat and corn samples used for determining the thermal properties . Comparison of specific heat determined for paraffin-coated and uncoated wheat . . . . . Effect of current flow on the thermal conductivity determination of corn . . . . . Effect of total heating time on the thermal conductivity determination of corn . . . . . Comparison of thermal diffusivity of wheat using different size slabs. . . . . . . . Comparison of the measured and published thermal preperties of quartz sand . . . . . Specific heat values of soft white wheat at 70.90F (51.2 to 8900031). e o e e o e 0 Specific heat values of yellow dent corn at 68.90F (su.0 to 83.8°E). . . . . . . . Specific heat values of soft white wheat at 93.l°F (77.0 to 115.10F) . . . . . . . Specific heat values of yellow dent corn at 95.30? (80.0 to 115.40F) . . . . . . . Thermal conductivity values for soft white wheat Thermal conductivity values for yellow dent corn Thermal diffusivity values for soft white wheat. Thermal diffusivity values for yellow dent corn. ix Page 12 0A 30 35 35 to E2 146 LLB A9 53 53 S7 S9 60 Table 17. 18. Page Summary of the thermal preperties of soft white wheat . . . . . . . . . . . . 6h Summary of the thermal prOperties of yellow dent corn . . . . . . . . . . 6h I Figure 1. 9. IO. 11. 12. 13. 1h. LIST OF FIGURES Apparatus for determining the specific heat or grain - o e a e e e e e e 3 e Apparatus for determining the thermal conduCtiVity Of grain e e e e e e e The rectangular boxes used for the thermal diffusivity determinations . . . . . . Apparatus for determining the thermal diffusivity of grain . . . . . . . . Typical time-temperature curve obtained from calorimetric tests for determining the specific heat of grain . . . . . . . . . . Typical time-temperature curve obtained for thermal conductivity determinations of grain . Typical cooling curve obtained for the thermal diffusivity tests of grain . . . . . . Relation between density and moisture content for soft white wheat . . . . . . . Relation between density and moisture content for yellow dent corn . . . . . .. . Relation between specific heat and moisture content for soft white wheat at 70.90? . . Relation between specific heat and moisture content for yellow dent corn at 68.9°F . . Relation between specific heat and moisture content for soft white wheat at 93.10F . . Relation between specific heat and mgisture content for yellow dent corn at 95.3 F . . Relation between thermal conductivity and moisture content for soft white wheat . . xi Page Figure Page 15. Relation between thermal conductivity and moisture content for yellow dent corn . . . . 58 16. Relation between thermal diffusivity and moisture content for soft white wheat . .. . . 61 1?. Relation between thermal diffusivity and moisture content for yellow dent corn . . . . 63 xii b E: :y o 4} l “ *3 NOMENCLATURE thermal diffusivity, sq-ft/hr specific heat, Btu/lb-OF base of natural logarithm thermal conductivity, Btu/hr-ft-OF moisture content, % w.b. -1 -1 %(o U 0 ll Sample Sample B, - 0.301 + 0.00733 M O I Sample C, c 0.288 + 0.00828 M where c is the specific heat of the wheat and M is the moisture content, %, w.b. Pfalzner concluded that the apparent specific heat of bound water does not differ appreciably from that of free water over the range of moisture contents used. Moote (1953), using the same method and procedure as Babbitt,studied the effect of moisture content on the thermal properties of hard wheat. The thermal conductivity, thermal diffusivity and density were measured for 2 samples of wheat. The moisture content of sample A was varied from 1.11% to 7.11% by intermittently adding water to the wheat. T?n3.moisture content of sample B was varied by intermittently drfiring from 13.6% to 5.3%. The specific heat was calculated frcun the measured values of the thermal conductivity, therunal diffusivity and the density. TThe thermal conductivity was reported to vary linearly with moisture content for both samples of wheat, with sample B having a slightly lower value than sample A. The conductivity values of sample A ranged from 0.0755 Btu/hr-ft-°F at 1.4% moisture to 0.0874 at 7.4% moisture content. The thermal conductivity values for sample B varied from 0.0794 at 5.3% moisture content to 0.0967 at 15.6% moisture. The calculated values of the specific heat were found to vary linearly with the moisture content. The specific heat of sample A ranged from 0.619 at 1.4% moisture to 0.407 at 7.4% moisture content. For sample B the specific heat varied from 0.557 at 5.3% moisture content to 0.460 at 10.6% moisture content. No attempt was made to relate the thermal diffusivity of the wheat to the moisture content. Moote concluded that the thermal progerties of dry wheat are as follows: thermal conductivity. 0.0726 Btu/hr-ft-OF; thermal diffusivity, 0.00460 sq-tt/hr; and specific heat, 0.31 Btu/lb-oF. Disney (1954) reported the specific heat of Manitoba and Bersee hard wheat as measured by an ice calorimeter. The method used was to dr0p a known weight of the wheat at room temperature into the ice calorimeter and to measure the amount of ice melted. The specific heat of the Manitoba wheat was measured N at seven different moisture contents ranging from 1.29% to 17.5%. The moisture content was changed by intermittently drying the wheat. Values of the specific heat reported ranged from 0.510 Btu/lb-OF at 1.29% moisture content to 0.447 at 17.5% moisture content. Specific heat measurements at twenty different moisture contents were reported for the Bersee wheat. Fifteen of the tests were run at moisture contents obtained by intermittently drying the wheat from 33.6 to 0.14%. Five tests were run after the moisture content of the sample was changed from 0.14 to 18.2% by the addition of water. The specific heat after conditioning the wheat to the various moisture levels by desorption was found to vary from 0.582 Btu/lb-OF at 33.6% moisture content to 0.507 at 0.14% moisture. Conditioning the wheat by absorption gave specific heat values that ranged from 0.506 at 1.99% moisture content to 0.457 at 18.2% moisture content. Disney did not eXpress his data on Specific heat as a linear relationship with moisture content. Haswell (1954), using the same method and procedure as Disney. reported the specific heat of rice, oats and ‘groats. For rough rice at moisture contents of 10.2. 15.5 pand 17.0%. he expressed the specific heat by the regression equation: 0 = 0.265-* 0.0107 M. For shelled rice at 9.8, 14.5 and 17.6% moisture content, the data were eXpressed 10 by the equation: c = 0.287 + 0.0091 M. Determining the specific heat of finished rice at moisture contents of 10.8, 14.6, and 17.4 gave the equation: c = 0.282 + 0.009 M. Working with oats at 11.7, 14.8, and 17.8% moisture content, the specific heat was given by: c = 0.505 + 0.0078 M. For groats at 11.8, and 17.6% moisture content, the linear relationship was reported as c = 0.257 + 0.0119 M. A transient heat flow method of determining thermal conductivities was reported by H00per and Chang (1955). The method is based on using a line heat source of constant strength in a homogeneous, initially isothermal material. By measuring the amount of heat supplied, the temperature rise near the heat source and the time of heating, the thermal conductivity can be determined from the equation for heat flow from a line source of heat. Among the thermal conductivities of various materials that were reported was a single value of 0.077 Btu/hr-ft-OF for wheat. The moisture content of the wheat was not specified. The development of the transient heat flow method of determining the thermal conductivity of materials was reported in detail by H00per and Lepper (1950). A thorough discussion of the apparatus and procedure and the solution to the basic equation was presented. D'Eustachio and Schriener (1952) used the method of 11 heat flow from a line source to determine the thermal conductivity of cellular glass and silica gel. Their results were the same as results obtained using the guarded hot plate. Lentz (1952) and DeVries (1952) individually reported on the thermal conductivities of soils as determined by using the line source of heat. The reported thermal pr0perties of grain are summarized in Table 1. 12 .mQOC090M0h 05”.. OD .Hmkmfi mHODESZ .x. eao.o “my neon: 5:3.0 m.efi som.o H.0H mmm.o 9.: oam.o om.H Aspouaaazv mmm.o e.mm mmm.o m.mm 65:.0 a.aa mo:.o ~.ma mmm.o «.3 Aoomhomv aom.o :H.o “ml each: 50:00.0 :emo.o eo:.o o.mm 3.5 63:00.0 mmeo.o oam.o m.mm :.H AHHV seen: mom.o 0 “may paws: 64:00.6 Hamo.o oem.o o.mm oma 0s as m.e “He uses: omeo.o mm on om m.aa memo.o mm 0s om .HH “mav amen: mem.o o on seam meo.o m.ma Amav sumo mom.o 0 Rev memo :amo.o m.:m amo.o a.m Amy memo moa.o mm on om m.ma *fimav aaoo as\pm-am ao-paasn\spm mosna\spm .n.3.w .apaeamsaaae .hsaeaposeaoe .eaos .suuao\nH so .pcopcoe HmEhonB Hashona caudoomm .hpwmcon .mHSponmEme ohsumdoz Gamma .cammw mo modpnoaomm Hashes» vmuhomom .H magma 13 METHOD AND APPARATUS Specific Heat The standard method of determining the specific heat of materials is by using a calorimeter. The material is heated to a constant temperature and then drOpped into water at a known temperature in the calorimeter cup. This method is referred to as the method of mixtures. The temp- erature rise of the water is recorded until thermal equilibrium is reached. The weight of the sample, calorime- ter cup and water are also measured. Then the specific heat of the material is calculated by equating the heat content of the material to that of the calorimeter cup and the water. Any factors that would affect the temperature measured in the calorimeter such as heat gain or loss, heat of stirring, etc., are combined into a temperature correction term. The equation for the method of mixtures is: wlcl(Atl + ¢) = w2c2(At2 - 4») + w3c3(At2 - ¢> where: w1 = weight of the sample, gm c1 = specific heat of the sample, Btu/1b-°F Aml = temperature change.of the sample, 0F temperature correction term, 0F +5 u weight of the calorimeter cup, gm specific heat of the calorimeter cup, Btu/1b-OF o N ll ILL Ata = temperature change of calorimeter cup and water, oF w3 = weight of water, gm c3 = specific heat of water, Btu/lb-OF The specific heat of the sample is calculated from the t - equation; cl = ("202 + "363) (ALE. ¢) w1(At1 + ¢) The specific heat determinations of grain were carried out with a Dewar-flask calorimeter. The calorimeter was further insulated with two inches of fiber-glass insulation to reduce the temperature correction for heat gain or loss from the surroundings. The weights of the sample, calorimeter cup and the water were measured with a balance graduated to 0.01 gm. The temperatures of the sample and water were measured and recorded with a 30 gauge copper-Constantan thermocouple and a recording potentiometer. The recording potentiometer was set to record every 30 seconds. The apparatus for the specific heat measurements is shown in Fig, 1, Thermal Conductivity The majority of the reported values for thermal cond- uctivity of grain have been determined by steady-state heat flow across the grain. The objections to steady-state lmeasurements are: (1) the long time required to attain 15 ._ f' . , " ; m Ill 1 5') ._ , . ,. wo'xzo 140- Fig. 2. Apparatus for determining the thermal conductivity of grain. 16 the steady—state conditions; and (2) the possibility of moisture migration due to maintaining the temperature difference across the grain for long periods of time. Both of these difficulties can be minimized by transient heat flow methods. The method chosen for determining the thermal conduct- ivity of grain was the transient heat flow in an infinite mass, initially at a uniform temperature, heated by a line heat source of constant strenght. The basic equation for the heat flow from a line source is: at (azt 1 at .—... =0< -—-—2+ £99 E9r rEBr ; temperature at radius r where; t 9 time r = radius from the heat source o<= thermal diffusivity of the material The solution for the temperature is given by Hooper and Lepper (1950) as; t = -——- I(rn) 27k Where t = temperature, 0F Q = heat input, Btu/hr-ft k = thermal conductivity of the material, Btu/hr-ft- °F r = distance from heat source, ft n = as era. rt‘l 17 (Ni)2 (rn)u The function I(rn) = A - loge (rn) + -E- - -——- + ... 8 where A is a constant. If (rn) is sufficiently small, all the terms of the series except the first two may be drOpped. Then I(rn) = A - log (rn), and the temperature is given by: e -._Q.[- ' t " Zflk A 108e (rn)J The temperature rise between times 81 and 82 is given by: 152 'ti = m 103.3(92/91) temperature at time 8 where: t1 1 t2 temperature at time 02 and finally: Q loge (82/91) LLM ta-tIT The thermal conductivity is then calculated from the measured quantities of Q, 81, 82, t1, and t2. The apparatus for the thermal conductivity tests consisted of a hollowpbrass cylinder 11 inches high and 5% inches in diameter. The wall thickness of the cylinder was 1/32 inch. Both ends of the cylinder were plugged with 3/h inch thick pieces of wood. A 6% inch length of bare resistance heating wire was stretched between copper leads on the axis of the cylinder. The heater wire was surrounded by 2 3/h inches of grain in the radial direction and 1 1/2 18 inches in the axial direction. A heater wire with a resistance of S.h5 ohm/ft was used. Power for the heater wire was supplied by a 6 volt storage battery. A variable resistor was used to control the flow of current in the circuit. The current was measured by a 0-1 amp direct current ammeter graduated in 0.01 amp. A 30 gauge copper-Constantan thermocouple was secured to the middle of the heater wire. The thermocouple was insulated from the bare heater wire by a single layer of plastic electrical tape at the point of attachment. The thermocouple was placed at approximately 1/6h inch from the heater wire. Temperatures were again recorded with the recording potentiometer. The apparatus for the thermal conductivity tests is shown in Fig. 2. A discussion of the possible sources of error using this method of determining the thermal conductivity of materials is given by Hooper and Lepper (1950). There are two sources of error that may affect the results. The first is the effect of drOpping the terms in the I series and the second arises from the fact that the heat source is finite in diameter and length. For the apparatus constructed for these tests, the error caused by dropping the terms in the I series can be shown to be negligible. The radius of temperature measurement r, is l/6h inch or 0.00130 ft. If the thermal diffusivity of the grain is assumed to be 0.00h sq-ft/hr, and the time is arbitrarily chosen as 1 minute, 19 .1. - n is found from the relation: n = a...) 2 to be 61.3 ft 1. The quantity (rn) is then = 0.00130(6l.3) = 0.0797. The quantity (rn)2/2 = 0.00317. Dropping this term would cause an error of 0. 125% which is within the limits of experimental error. The higher powers of (rn) would be smaller than the second power of (rn) and can also be dropped from the series. ‘ The error caused by the finite heat source is determined from the test data and is discussed in the results of the thermal conductivity tests. Thermal Diffusivity The method chosen for determining the thermal diffusivity of grain was transient heat flow in a slab, initially at a uniform temperature, with the faces suddenly lowered to and held at zero. The basic equation is; at Bet ..— =0( .—2 369 3:: where: t = temperature 8 time a< = thermal diffusiv'ity x = distance from face of the slab The solution of the equation for the temperature at the center of the slab is given by Ingersoll, L.R., Zobel, 0.J. and Ingersoll, A.C. (195h) as: tc = to 8(2) 0 ‘Where: tc - temperature at center of the slab, F 20 initial temperature of the slab, OF 2 _ 2 _ z u/% (e-flz ' 1/36 977 Z + 1/50 251' z :- eee) z -..-. o< e/xz, dimensionless t o S(z) The series S(z) has been evaluated for values of z and is also given in Ingersoll, L.R., Zobel, 0.J. and Ingersoll, A.C. Therefore, for selected values of S(z) = tc/to, the values of z can be obtained, and with the measured values 2 of 8 and x , the diffusivity is calculated from the relation, GK = zxZ/e . The thermal diffusivity tests were OOHdUCted by enclosing the grain in a rectangular box. Three different :size boxes were made to determine if the size of the sample had any effect on the measured thermal diffusivity. The inside dimensions of box #1 were 1.95 inches thick, 6 inches wide and 6 inches high. Box #2 had inside dimensions of 1.35 x 6 x 6 inches and box #3 was made with inside dimensions of 1.35 x 9 x 9 inches. The boxes were made by fastening two sheets of 2h gauge (0.025 inch) copper to a wood framework. A nylon thread was stretched at the center of the rectangular area and three 30 gauge cOpper-Constantan thermocouples were mounted on the thread. The thermocouples were located at the % points along the thread. All the joints in the boxes were water-proofed with a mastic and the boxes were tested for leaks under water. The thermo- couple wires leading from the boxes were wrapped with water-proof tape. A hole was provided in the t0p of the 21 boxes for filling and removing of the grain sample. The three boxes are shown in Fig. 3, The temperatures at the center of the boxes were again recorded with the recording potentiometer. The apparatus consisting of one of the boxes and the potentiometer is shown in Fig )4. 22 _; fiat, ' '7 . . ".17 ‘- . g _ Hg . Fig. 3. The rectangular boxes used for the thermal diffusivity determinations. Fig. h. Apparatus for determining the thermal diffusivity of grain. 23 PROCEDURE Temperature Measurement The accuracy of the thermocouple and recording potentiometer was checked against a second thermocouple and a manual potentiometer. Both thermocouples were made from the same spool of wire and were of equal length. The two thermocouples were immersed in ice water and the recording potentiometer was adjusted to read the same temperature as obtained from the manual potentiometer. Then temperatures were read at intervals from both potentiometers while the water warmed up to room temperature. The results of tests on four different thermocouples used with the recording potentiometer are shown in Table 2. The temperatures measured over a 60 oF range with the recording potentiometer were found to vary from 0.2 to 0.3 0F from those measured with the manual potentiometer. Within a range of 15 to 20 0F, the temperatures measured with the recording potentiometer varied by 0.1 °F from the manual potentiometer. The thermal prOperties of grain were based on equations requiring only temperature differences so the recording potentiometer was sufficiently accurate . 2h Table 2. Comparison of temperatures measured with recording potentiometer and manual potentiometer. Temperature °F Thermocouple_l Thermocouple 2 Thermocogple 3 Thermocouple 3 Man. Record. Man. Record. Nan. Record. Man. Record. 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.1 32.6 32.6 32.1 32.1 32.1 32.1 32.1 32.1 3a.? 3h-8 33.6 33.6 3h.2 3h.3 35.1 35.1 37.2 37.2 39.8 39.8 uh.9 uh.9 37.8 37.8 h6.9 h6.8 h%.3 h%.3 h9.0 h9.o h2.2 h2.3. 52.1 52.3 h .1 h .1 50.1 50.1 #5.3 #5.3 55.2 55.2 51.2 51.3 53.8 53.8 u8.0 #8.0 57.5 57.5 52.9 52.9 56.1 56.2 h9.9 50.0 59.3 59.% 5h.5 5h.5 58.5 58.6 Sleu 510% 6007 600 55e6 SSe7 59e8 59.9 52.7 52. 62.1 62.3 57.0 57.1 60.6 60.6 53.7 53.7 63.0 63.2 58.6 58.7 61.2 61.2 511.8 511.8 611.1 611.2 60.1 60.3 61.8 61.9 55.5 55.7 6h.5 6h.7 62.h 62.6 62.3 62.h 56.2 56.3 65.1 65.3 63.11 63.7 62.8 63.0 57.0 57.0 65.7 65.9 6h.2 6h.6 63.6 63.7 57.5 57.7 65.9 66.2 65.6 65.8 6h.0 6h.2 58.0 58.1 66.2 66.% 66.1 66.h 6h. 6h.5 58.5 58.7 66.6 66. 66.8 67.1 58.9 59.1 66.7 67.0 67.3 67.6 59.3 59.5 67.7 68.0 Grain Samples Samples of soft white winter wheat and yellow dent corn were obtained and the moisture content of the grains was determined. Initial moisture content of the wheat was 12.7% and the moisture content of the corn was 13.2%. It was shown by previous investigators that significant 25 differences in the thermal properties of grain could be measured if the moisture contents of the grain samples differred by h to 5%. Therefore, it was planned to measure the thermal prOperties of the grains at moisture content increments of approximately 5%. The samples of wheat and corn were divided into two parts. One half of the grain was dried to approximately 10%:moisture content. The other half of the sample was conditioned to about 15% moisture content by the addition of water. Disney (195h) had reported that wheat conditioned to higher moisture contents by the addition of water has the same thermal prOperties as wheat initially obtained at the higher moisture level. After determinations for the thermal preperties were made on the grains at the 10%fmoisture level, the grains were dried to about 5%Kmoisture content and eventually to 0%1moisture content. Thus the data obtained at C. 5 and 10% moisture levels for both grains were on the same sample of grain. The sample of wheat at 15% was tested and subsequently conditioned to 20% moisture content. The corn sample at 15%“was conditioned to moisture levels of 20, 25 and 30%‘with determinations being made at each moisture level. Because the tests were conducted over a long period of time, the grains were _kept in a 32°F temperature box when not being used. The moisture content of the grain was determined by the oven drying method. After the grain had been conditioned 26 to approximately the desired moisture levels, 60 gram samples were obtained and dried in a 200°F oven for 3 to h days. The final weight was recorded and the moisture content calculated on the wet basis. After running a series of tests to determine the thermal conductivity of the grain, a second 60 gram sample was obtained and another moisture determination was made. The moisture contents of the two samples did not vary over 1 2%, therefore no further moisture determinations were made. The values of the moisture content from the two samples were averaged and used as the moisture content of the grain. The moisture levels used for determining the thermal pr0perties of the wheat and corn are shown in Table 3. Table 3. Moisture content of wheat and corn samples used for determining the thermal properties. Moisture content, %w.b. Grain Sample 18 Sample 2 Average Wheat 0.68 0.68 0.68 Echo 5050' 5-95 10.1 10.5 10.3 1h.h 1h.h 1h.h 20.h 20.2 20.3 Corn 0.88 0.93 0.91 5010 5007 5.08 9.73 9.90 9.81 1h.7 1h.8 1h.7 20.2 20.1 20.1 2h.8 2h.6 2h.7 30.h 30.1 30.2 a. Moisture content determined before any to 8 ts were run. 27 Density Measurements It was not practical to measure the density of the grain samples for each of the tests conducted. Although the exact volume of the container holding the grain was known, the container could not be filled completely without vigorous and undue vibration. The density of the grain was therefore determined by filling a one liter graduate and weighing the amount of grain. An attempt was made to fill the graduate in the same manner as the test containers would be filled. Since the density could vary widely depending on how the container is filled, a total of ten determinations were made. The average of the ten.tests was used as the density of the grain. The density measurements wereczonducted before any of the tests to determine thermal pr0perties were conducted. Specific Heat Several attempts were made to conduct the specific heat tests with the grain enclosed in a container. A small cepper capsule, aluminum foil and polyethylene bags were used to contain the sample of grain dropped into the calorimeter. However many' difficulties were encountered and consistent data could not be obtained. The main objection to this method was that unless a very small sample of grain was used the time to reach equilibrium 28 was 15 to 20 minutes. Consequently the temperature correction term was large compared to the measured temperature change in the calorimeter. When smaller samples were used, the temperature change in the calorimeter became too small to be accurately measured with the recording potentiometer. In order to attain equilibrium between the grain sample and the water in a relatively short time, the grain was drOpped directly into the calorimeter. When equilibriumeis reached in a relatively short time the temperature change in the calorimeter would be greater and the temperature correction term would be smaller. Since the specific heat of grain is one-third to one-half that of water, the maximum temperature change in the calorimeter for a given amount of grain was obtained when a minimum amount of water covering the grain was used. For 60 grams of grain, ho grams of water would give the largest temperature change without an excess of grain in the calorimeter. The grain samples were held at room temperature and then dropped into cold water in the calorimeter. For each test, ho grams of ice water were placed in the calorimeter cup and allowed to warm up to approximately hOOF. Then the grain sample was dropped into the calorimter and the calorimeter was shaken by hand to agitate the grain-water mixture. Equilibrium was reached in less than 30 seconds for the majority of the tests. Tbmperatures were recorded for 2 to 3 minutes after :‘)liv|14(l\,1 (1 (i . X 29 equilibrium was reached. Dr0pping the grain directly into the water in the calorimeter cup may have introduced two sources of error. First, the grain may undergo a change in moisture content and second, the heat of wetting may influence the measured temperature change. it was not possible to measure directly if the moisture content of the grain was changed appreciably when dr0pped into the water for the period of 2 to 5 minutes required to run the test. The grain would be covered with surface water which could not be removed easily. Therefore an indirect method was used to determine if this was a source of error. Dry wheat was divided into ten 60 gram samples. Five of the samples were coated with paraffin by immersing the grain in melted paraffin. The grain was weighed after dipping to determine the amount of the paraffin coating. The other five samples of wheat were left uncoated. Tests were conducted on the ten samples to determine the specific heat. The data obtained for the uncoated and coated wheat are shown in Table 4. Statistical analysis of variance of the data showed that there was no significant difference at the 5% level between the coated and uncoated wheat. Although the uncoated wheat may have undergone a slight change in moisture content, it would not affect the results of the specific heat determinations. 30 To determine if the heat of wetting would affect the measured temperatures inthe calorimeter, wheat and water, both at room temperature were mixed together in the calorimeter. There was no measurable temperature change in the mixture after 10 minutes elapsed. This indicated that any heat evolved was too small to affect the temperature measurements. Since the two expected sources of error were found to be negligible, the procedure described was used to determine the specific heat of wheat and corn at various moisture levels. Table h. Comparison of specific heat determined for paraffin coated and uncoated dry wheat. Specific heat, Btu/lb-OF Uncoated Coated with Paraffin 0.381 0.370 0.36 0.3h8 0.34 0.3h5 0.351 0.359 0.29g 0.38] Average 0.3h7 0.362 Temperature Correction A typical time-temperature curve obtained during the calorimetric tests is shown in Fig. 5. The temperatures obtained bbfore the sample of grain was dropped into the water are referred to as the initial rating period. Since the heating of the water in the calorimeter cup is 31 .dame mo amen camaoodm one wdfidasaepop mom memo» casposaaoamo Soak pecamuno o>mso endpmaeQEeuieEHp Hddfiahe .m .mfim ...e .mmahqmmdsm... om om on. ow 0m oe . _ _ n _ _ < [I mmbszofiao 2. cut; ...0 i um3hfiposecoo HmEAonp one you vecawpno o>aso ensueaeQEeunoEfiu Heodmha .0 .mam 3.52:: .92: o. m m b m m e m _ o _ . _ _ _ _ . _ _ .0m 00 «1 10m .60. 11 mmakdeQEMP. lo: s . ‘sanlvaadwsl 38 time; that is, a time correction is subtracted from each observed time. The time correction can be obtained by plotting the values of de/dt against time and reading the value of time at de/dt = 0. For the data presented in Fig. 6, values of de/dt were obtained by drawing tangents to the time-temperature curve and determining the slope. Then the values of de/dt were plotted on the same graph to obtain the desired time correction. For the data given in Fig. 6, the time correction was 5 seconds. Hooper and Lepper (1950) have also shown that the time correction for most materials, and for a particular apparatus, is nearly constant. The time correction for one other test was determined and found to be 7 seconds. Therefore the corrections from the two tests were averaged and used as the time correction for all the conductivity tests. Thermal Diffusivity The method chosen for determining the thermal diffusivity was transient flow in one direction across the material. The first step was to determine if the apparatus was closely approximating this condition. The three boxes constructed for the thermal diffusivity tests were filled with dry wheat and tests were conducted with each box. Using the three thermocouples mounted on the nylon string stretched at the center of the box, the temperatures were measured at the three locations. If the temperatures measured at the 39 two end locations fell on the cooling curve plotted by the center temperature, the heat flow would be unidirectional. For boxes 2 and 3, where the thickness was 1.35 inches, the temperatures measured at the l/h and 3/h locations fell exactly on the curve plotted by the center temperature. For box 1, where the thickness was 1.95 inches, the tempera- ture at the end locations fell on the center temperature cooling curve for the first 30 to no minutes of cooling. After this time, the temperature at the end locations varied slightly from the center temperature. If the tests were limited to 30 or to minutes, any of the three boxes could be used. To determine if the size of the slab had any effect on the measured thermal diffusivity, tests were run on dry wheat using the three boxes. Five tests were conducted using boxes 1 and 2, and three tests were conducted with with box 3. The results of these tests are shown in Table 7. Analysis of variance showed that there was no significant difference at the 5% level between the data obtained from the three boxes. It was decided to use Box 1 for the remaining tests because it would give a larger sample with which to work. For each test the sample of grain was placed in the box and then held at room temperature until thermal equilibrium was assured. Then the box was placed in the ice bath and the temperature at the center was recorded to every 30 seconds. The sample was cooled until the temperature at the center reached % of the difference between the initial temperature and 32°F. Finely crushed ice was continually added to the ice bath to maintain a constant temperature. After each test, the grain was removed from the box until it reached room temperature before another test was conducted. Table 7. Comparison of thermal diffusivity of wheat using different size slabs. Thermal diffusivity, sq-ft/hr Box 1 Box 2 Box 3 _(1.95"x6"x6") (1.35"x6"x6") 12435'5‘9'5‘91) u 0.00328 0.00359 0.00352 0.003u5 0.00361 0.00355 0.00368 0.00362 0.00348 0.00359 0.0035h 0.00359 0.00360 Average 0.00352 0.00359 0.00352 A typical cooling curve, obtained by plotting the temperature at the center of the slab against time is shown in Fig. 7. The thermal diffusivity was calculated for five points on the curve. The points were chosen at ratios of center temperatures to initial temperatures of 0.9, 0.8, 0.7, 0.6 and 0.5. The time required to reach the tempera- tures described by the ratios was determined and the diffusivity was found from the relation: CK = zxd/G. The LLl O¢ .cdeam we mummy hpabamsumav Hashes» er» tom cecawpno e>ASo mafiaooo Heoamme $52.: as: on on mm mm m. o. m _ é .wE . r _ _ - _ _ — M l to In ‘aanlvsadwsl 1 C) (O do A2 average of the five calculations from each curve was used as the thermal diffusivity of the sample. The thermal prOperties of dry quartz sand were deter- mined. The measured values of the thermal prOperties were then compared to the published values to determine the accuracy of the methods and procedures used. The comparison of the measured values and the published values is given in Table 8. The published values were taken from Ingersoll, Zobel and Ingersoll (195A). Table 8. Comparison of the measured and published thermal prOperties of quartz sand. Density Specific Thermal Thermal lb/cu-ft heat 0 conductivity diffusivity Btu/lb- F Btu/hr-ft-OF sggft/hr Measured 90.0 0.172 0.136 0.00838 Published 193__ 9:12_ 0.1 0.008 %'Variation 12.6 10.5 6.66 h.75 A direct comparison could not be made because the quartz sand used in the tests had a density of 90 lb/cu-ft, and the published values were for sand of 103 lb/cu-ft. However the differences in percent between the measured and published thermal prOperties were less than the difference in density. Therefore, the apparatus was considered suitable for determining specific heat, thermal conductivity and thermal diffusivity of grain. 43 RESULTS AND DISCUSSION Density . The results of the density measurements for the soft white wheat are shown in Fig. 8. For moisture contents of 0 to 10% the density of the wheat was fairly constant with an average value of £184 lb/cu-ft. Above 10% moisture content, the density decreased by 0.23 lb/cu-ft for a 1% increase in moisture content. This is expected since drying would shrink the kernels to a point beyond which very little shrinkage would occur by further removal of moisture. The same results were obtained for the density measurements on the yellow dent corn. The density was approximately constant at h6.8 lb/cu-ft for moisture contents from 0 to 15%. The density decreased by 0.27 1b/cu-ft for an increase of 1% in the moisture content from 15 to 30%. The relation between density and moisture content for corn is shown in Fig. 9. Specific Heat The specific heat values of soft white wheat obtained by dropping the grain into cold water are shown in Table 9. The mean temperature was taken as the average of the initial and final grain temperatures for all the tests. .aens: ends: uMOm sou pceucoo endumfios due zcamzeo Coozuon coapwaem .w .me ezuomma Hzmezoo $35.02 ea cu m. o. m o q — _ _ V 3mm: 0. ...o .e>< 2.2.0.. :03. l I ‘0 q. I Q q. 1 C) It) 1:1 °n0/‘s1 ‘Ailswao 115 .caoo anon SOHH05 now uceunoo endpmfios use apqncno nemxnen compeamm ...zmommm ....ZMFZOU mmzhwaz .o .mE on mm ON m. 0. n O _ _ _ _ a _ N 9..wa o. no .o>< ._.Z_On. Io< ._.Z_On_ Io< ._.Z_Om Io< ._.Z_On_ Io< 5.0a :03 .00 \o\ s. 288.0 83.08 \ -10 -nd to 3.81/018 117% 01-110st 55 The thermal conductivity values of the wheat appeared to be linearly dependent on the moisture content and there- fore were analyzed by linear regression. The regression equation was k = 0.0676 + 0.000654 M and the standard error was 0.00118. The data and regression line for the thermal conductivity of wheat are shown in Fig. 14. The mean temperature for the wheat was determined in the following manner. A time-temperature curve was drawn using the average temperatures from all the tests on wheat. The curve drawn represents the temperature at a radius of 1/64 inch from the hot wire. For temperatures at increasing radii, the curves would be similiar but would fall below the curve for the 1/64 inch radius. The temperature curve for a radius of 2 1/4 inches would be nearly constant and equal to the initial grain temperature. Therefore the temperatures in the entire sample may be represented by the area under the time-temperature curve. This area was measured with a planimeter. 'The temperature where the area under the curve would be equal to one half of the total area was determined. This temperature was taken as the mean temperature for the grain. The mean temperature for the wheat was 87.7OF. The temperature range of the tests was 69.8 to 111.4 OF, The thermal conductivity values on the yellow dent corn are given in Table 14. 56 mm .weosz ouanz whom mom unopcoe easemaos pee hpa>fiposmcoe Hashes» neezpen coapeaom hzuomma .FZUPZOU 912.902 0.0. m. 0_ m _ _ _ d mkmu... m “.0 .0>< Fz_0n_ :04w .2 380090 + 2.8.0.0. \\ .:H .waa 1 050.0 I nh0.0 1 000.0 3.1:1'aH/nia ‘AilAliOnONOO 11711133141 57 Table 14. Thermal conductivity values for yellow dent corn. Thermal conductivity, Btu/hr-ft-OF Moisture content, 0.9;, 5.08 9.81 14.7 20.1 2437 30.2 0.0820 0.0855 0.0886 0.0910 0.0907 0.0955 0.102 0.0834 0.0848 0.0863 0.0919 0.0947 0.0990 0.107 0.0794 0.0834 0.0894 0.0894 0.0964' 0.0964 0.0964 0.0834 0.0843 0.0855 0.0927 0.0964 0.101 0.0900 0.0780 0.0855 0.0894 0.0945 0.0947 0.0990 0.103 Avg. 0.0812 0.0847 0.0878 0.0919 0.0945 0.0982 0.996 The data were again analyzed by linear regression resulting in the regression equation k = 0.0814 + 0.000646 M. The standard error of estimate was 0.00085. Fig. 15 shows the thermal conductivity data for the corn. The mean temperature for the corn was determined in the same manner as for wheat. However since two different times were used for the conductivity tests on the corn, the mean temperatures were determined for each test separately. Sixteen minutes were used for the tests on the corn from 0 to 14.7%.moisture content. The mean temperature for these tests was 89.50F with a range of 70.0°F to 118.6OF. The time for the test on 20.1, 24.7 and 30.2% corn was 10 minutes. The mean temperature for these tests was ‘95.4°F with a range of 69.4 to 126.6OF. 58 .caoe peep zoaaoh how pconcoo manumdos one hua>flposvcoo Hester» soezpep cowueaem .mH .wam ...zwomwm . ...ZMhZOU mmDhQO—z on mm on m. o. m o _ d _ d _ _ I. w ...... game n so .e>< Sad :93 t moo m \\ W flu \\ nu s. eeeooodéaooé \ w m 1onu M l .A 1 9 0 :1. 1.11111 /nls Thermal Diffusivity The results of the thermal diffusivity values for soft white wheat are shown in Table 15. Table 15. Thermal diffusivity values for soft white wheat. Thermal diffusivity, sq-ft/hr. ‘Mgisture content, % 0.68 5.45 10:3 14.4 20.3 0.00359 0.00340 0.00327 0.00312 0.00301 0.00361 0.00349 0.00333 0.00316 0.00315 0.00362 0.00346 0.00339 0.00312 0.00304 0.00354 0.00354 0.00326 0.00324 0.00314 0.00360 0.00348 0.00331 0.00322 0.00316 Average 0.00359 0.00347 0.00331 0.00318 0.00310 The mean temperature for the thermal diffusivity tests was obtained in the same manner as described for the thermal conductivity tests. The mean temperature for the tests on the soft white wheat was 57.00F with a range of 48.3 to 73.80F. Table 16 shows the thermal diffusivity values for the yellow dent corn. The mean temperature for the corn was 56.80F with a range of 47.7 to 74.00F. 60 Table 16. Thermal diffusivity values for yellow dent corn. Thermal diffusivity, sq-ft/hr M, 5 0.91 5.08 9.81 14.7 20.1 2437 30.2 0.00387 0.00389 0.00358 0.00342 0.00330 0.00344 0.00367 0.00399 0.00376 0.00371 0.00360 0.00332 0.00333 0.00369' 0.00396 0.00389 0.00366 0.00352 0.00335 0.00348 0.0034 0.0039 0.00378 0.00359 0.00350 0.00343 0.00345 0.0034 0.0039 0.00373 0.00367 0.00352 0.00338 0300350 0.00364 Avg 0.00395 0.00381 0.00364 0.00351 0.00336 0.00344 0.00358 The thermal diffusivity of the wheat decreased with increasing moisture content. The diffusivity of the corn decreased with increasing moisture content up to 20%, and for higher moisture contents the diffusivity was found to increase. This can be explained by the variation in the density with moisture content. As previously discussed the density was not a linear function of the moisture content for both wheat and corn. Since the thermal diffusivity can be obtained from the equation; o< = k/cfl , and with k and c varying linearly, o< would vary inversely with the density, and would not be linear with moisture content. The measured values of the thermal diffusivity compared to the calculated values for soft wheat are shown in Fig. 16. The calculated values of the thermal diffusivity were 6.1 to 11.6% greater than the measured values for the wheat at the various znoisture levels. The difference in the measured diffusivity and the calculated diffusivity can be shown to be acceptable. 61 noon: moan: phom mom pseudOo ensemdos new mufi>amsmmfic assuage cmozuon oofiumaom .bH .mfim ...zwomma ....zwhzoo $5.552 mm om m. o. m . o _ _ _ _ . mkmm... m ...—o .o>< ._.z_on_ Io4 ._.Z_On_ Io4w [mood 400.0 034430440 9! I ll 'L-IH/‘iJ'OS ‘AilAlSflJJIG 1vwa3Hi 64 A summary of the thermal prOperties determined for soft white wheat is shown in Table 17. The thermal prOperties for yellow dent corn are summarized in Table 18. Table 17. Summary of the thermal prOperties of soft wheat. Moisture Density Specific Thermal Thermal content, lb/cu-ft heat, conductivity, diffusivity, % BtuZlb-OF BtuZhr-ft-OF sqeft/hr 0.68 48.2 0.347 0.0679 0.003 9 5.45 48.5 0.375 0.0706 0.003 7 10.3 48.6 0.428 0.07%? 0.00331 14.4 47.7 0.500 0.07 6 0.00318 20.3 46.3 0.522 0.0798 0.00310 Table 18. Summary of the thermal properties of yellow dent corn. Moisture Density Specific Thermal Thermal content, lb/cu-ft heat, conductivity, diffusivity, Btg[lb-°F Btu/hr-ft-OF sq¢ft/hr 0.91 47.1 '0.366 0.0812 0.00395 5.08 46.9 0.40 0.0846 0.00381 9.81 46.6 0.43 0.0878 0.00364 14.7 46.7 0.484 0.0919 0.00351 20.1 45.2 0.531 0.09 5 0.00336 “24.7 44.3 0.567 0.09 2 0.003 30.2 42.6 0.588 0.0996 0.0035 The temperature range of all the various tests conducted was from 47.7 to 126.6 CF. Since the effect of temperature on the thermal properties is small, the data obtained may be used over this range. The conditions for many problems encountered fall within these temperatures. CONCLUSIONS The results of this study and of other investigators show that the specific heat and thermal conductivity of grain is a linear function of the moisture content. The thermal diffusivity of grain is not a linear function of the moisture content. The specific conclusions regarding the thermal prOperties of the grains used for this study are: 1. The specific heat of soft white wheat is a linear function of moisture content and is expressed by the equation, c = 0.334 + 0.00977 M for a temperature range of 51.2 to 89.0 °F. 2. The specific heat of yellow dent corn is a linear function of moisture content also. The relation for corn is c = 0.350 + 0.00851 M for a temperature range of 54.0 to 83.8 0F. 3. The thermal conductivity of soft white wheat is a linear function of moisture content expressed by the equation k = 0.0676+ 0.000654 M for a temperature range of 69.8 to 111.4 OF. 4. The thermal conductivity of yellow dent corn is a linear function of moisture content expressed by k = 0.0814 + 0.000646 M for a temperature range of 69.4 to 12606 OF. 65 66 5. The thermal diffusivity of grain is not a linear function of moisture content. For soft wheat the thermal diffusivity varied from 0.00359 sq-ft/hr at 0.68% moisture content to 0.00310 sq-ft/hr at 20.3% moisture. The thermal diffusivity of yellow dent corn varied from 0.00395 sq-ft/hr at 0.91%?moisture content to a minimum of 0.00336 sq-ft/hr at 20.1% moisture, then increased to 0.00358 sq-ft/hr at 30.2% moisture. SUGGESTIONS FOR FURTHER STUDY 1. The effect of temperature on the thermal prOperties of grain should be more thoroughly investigated. 2. The thermal properties of other grains and agricultural products should be determined. 3. Other prOperties such as absorptivity and emissivity should be investigated for analyzing radiant drying of grain. 4. Surface heat-transfer coefficients for grain and other products should be studied. 5. The linear and volumetric coefficients of thermal expansion should be determined. 67 2. 7. 10. REFERENCES Babbitt, E.A. 1945 The thermal prOperties of grain in bulk. Can. J. of Research F23z388-401. Bakke, A.L. 1935 Thermal conductivity of stored cats with different moisture content. Plant Physiology 10:521-524. D'Eustachio, D. and Schreiner, R.E. 1952 A study of a transient heat method for measuring thermal conductivity. Amer. Soc. Heat. and Vent. Engr. Trans. 58:331-339. DeVries, D.A. 1952 Non-stationary method for determining thermal conductivity of soil in situ. Soil Science 73:83-89. Disney, R.W. 1954 The specific heat of some cereal grains. Cereal Chemistry 31:229-334. Haswell, G.A. 1954 A note on the specific heat of rice, oats, and their products. Cereal Chemistry 31:341 343. H00per, F.C. and Lepper, F.R. 1950 Transient heat flow apparatus for the determination of thermal conductivities. Amer. Soc. Heat. and Vent. Engr. Trans. 56:309-322. Hooper, F.C. and Chang, 8.0. 1953 Development of the thermal conductivity probe. Amer. Soc. Heat. and Vent. Engr. Trans. 59:463-472 Ingersoll, L.R., Zobel, 0.J. and Ingersoll, A.C. 1954 Heat Conduction. The University of Wisconsin Press Madison, Wisconsin“ 325pp Lentz, C.P. 1952 A transient heat flow method of determining thermal conductivity. Can. J. Tech. 30:153-166 68 11. 12. 13. 14. 69 Moote, I. 1953 The effect of moisture on the thermal properties of wheat. Can. J. Tech. 31:57-62. Oxley, T.A. 1944 The properties of rain in bulk. Soc. Chem. Indus. J. Trans. 3:53-57. Pfalzner, P.M. 1951 The specific heat of wheat. Can. J. Tech. 29:261-264. Rodenwald, H. and Kattein, A. 1900 The specific heat of wheat starch. Zeits. fur Physik. Chem. 33:540-548. OTHER REFERENCES Allcut, E.A. 1949 Thermal conductivity tests and results. Instn. Heat. and Vent. Engr. J. 17:151-159. Blackwell, J.H. 1954 Transient flow method for determination of thermal constants of insulating materials in bulk. J. Applied Physics 25:137-144. Hall, C.W. 1957 Drying Farm Cr0ps. Edwards Brothers, Inc. Ann Arbor, Michigan, 336pp Hearmon, R.F.S. and Burcham, J.N. 1956 Specific heat and heat of wetting of wood. Soc. Chem. Indus. 31:807-812. Ingersoll, L.R. and Koepp, O.A. 1924 Thermal diffusivity and conductivity of some soil materials. Phy. Review 24:92-93. Jespersen, H.B. 1935 Thermal conductivity of moist materials and its measurement. Inst. Heat. and Vent. Engr. Trans. 21:157-174 Joy F.A. 1957 Thermal conductivity of insulation containing moisture. Amer. Soc. Test. Matls. Spec. Tech. Publication n217:65-73 MacLean, J.D. 1941 Thermal conductivity of wood. Amer. Soc. Heat. and Vent. Engr. Trans. 47:323-354. Rowley, F.B. 15933 The heat conductivity of wood at climatic temperature differences. Amer. Soc. Heat. and Vent. Engr. Trans. 39:329-356. Short, B.E. 15944 The specific heat of foodstuffs. Engr. research Series No. 40, Bureau of Engr. Research. The University of Texas, Austin, Texas. 39pp 7O 71 Stark, A.L. 1956 Correlation of specific heat and percentage of water in applewood. Plant Physiology 8:168-170. White, W.P. 1928 The Modern Calorimeter. The Chemical Catalog Company, Inc. New YorK. 194pp. Yegorov, G. 1957 Relationship between the thermal prOperties of \ wheat and it's moisture content. Mukomol' Noelevatornaia Promyshlennost' 25(1}:18-2l .APPENDIX Sample Calculations Specific Heat The equation for specific heat is; (W202 + W383)0At2_: 0) W1 (A151 + (b) C 1: For wheat at 0.68% moisture content; cl specific heat of sample "1 = weight of sample, 60.0 gm c = specific heat of calorimeter cup, 0.220 Btu/lb-OF w2 = weight of calorimeter cup, 49.1 gm 0 ll specific heat of water, 1.00 Btu/lb-OF weight of water, 40.0 gm corrected temperature change of water and D d re I 4} u calorimeter cup, 13.4 0F (At1 + 0) = corrected temperature change of sample, 1 29.8 OF ‘ substituting into the equation; ( 9.1)(0.220)+(40.0)(1.00) (13.4) cl = [4. __ __» -] —— = 0.381 Btu/lb-OF <60.0)(29.8) 73 Thermal Conductivity The equation for thermal conductivity is; Q loge(02/01, For wheat at o.68% moisture content; k = thermal conductivity of sample, Btu/hr-ft-OF = heat input = 12R(3.42) current, 0.490 amp :1! HQ ll = resistance of heater wire, 5.45 ohm/ft 0 = time, 7.0 min = time, 1.0 min = temperature at time 02, 106.4 OF t = temperature at time 91, 96.3 OF substituting into the equation; (0.490)215.45)(3.42) 1oge(7.0/1.0) 4(3.14)(106.4 - 96.3) - 0.0684 Btu/hr-ft-OF k: W I Thermal Diffusivity The equation for thermal diffusivity is; OK = zx2/8 For wheat at 0.68% moisture content; 6K = thermal diffusivity of sample, sq-ft/hr z = value obtained from S(z), for S(z) = tc/to = 0.5, 2 = 0.0947 x = distance from face of slab, for Box #2, x = 0.1131 74 0 = time, 0.338 hr substituting into the equation; a< = 0.0947(0.113)2/0.338 = 0.00359 sq-ft/hr MICHIGAN STATE UNIV. LIBRARIES lllVI”WI“HHWHWHIWWWWHINUHI 31293200206823