simulation study of solar air heater

Solar Energy 74 (2003) 309–317

S imulation study of solar air heater*Nidal H. Abu-Hamdeh

Jordan University of Science and Technology, P.O. Box 422, Irbid 21110, Jordan

Received 2 May 2002; received in revised form 28 October 2002; accepted 23 April 2003

Abstract

A mathematical model for predicting thermal efficiency, heat gain, and outlet air temperature of a covered plate attic solarcollector under steady conditions was developed. The model presented in this paper utilizes the basic principles andrelationships of heat transfer to simulate the behavior of the solar air heaters under various conditions. The model wasvalidated by comparing the predicted outlet air temperatures and collector efficiencies to those measured during dryingoperation of an attic solar collector. The effect of the air speed inside the collector and wind speed above the collector on thecollector efficiency were investigated using the mathematical model. 2003 Elsevier Ltd. All rights reserved.

1 . Introduction the walls of grain bins, machine storage buildings, andcrop drying sheds. The heat provided by solar energy hasbeen used successfully to dry small grains, peanuts, hay,The increased costs during the past decade for fossiland tobacco (Scanlin, 1997, 1999; Brooker et al., 1974;fuels used for drying crops led to a search for methods ofButts et al., 1980; Foster and Peart, 1976; Boonlong, 1984;drying crops that consume less energy.Brooker et al.Soponronnarit and Peyre, 1982; Morrison and Shove,(1974) noted that conventional high temperature continu-1979; Ahmad, 2001; Hussein et al., 2001).ous and batch-drying processes require up to 6.9 MJ of

Troeger and Butler (1979)have reported on dryingenergy per kg of water removed during drying.experiments in which solar energy is utilized as an energySolar energy is one of the most promising renewablesource for the drying of peanuts. They estimated the size ofenergy sources in the world. Compared to non-renewablesolar collectors and rock storage facilities which would besources such as fossil fuels, the advantages are clear: it isrequired for drying peanuts under normal weather con-totally nonpolluting, has no moving parts to break down,ditions. Harner et al. (1981)reported improved efficiencyand does not require much maintenance. Solar generatorsof energy utilization in peanut curing with the use of aircan be installed in a distributed fashion, on each farm orrecirculation. The roof of a peanut drying facility wasbuilding, using area that is already developed, and allow-retrofitted to incorporate a bare plate solar collector. Theing individual users to generate their own power, quietlyexhaust air from the trailers was directed toward the inletsand safely.of the bare plate collector, thus achieving some recircula-The concept of a dryer powered by solar energy istion of the air. Understanding the heat transfer characteris-becoming increasingly feasible because of the gradualtics of covered plate attic collectors is very important whenreduction in price of solar collectors coupled with thetrying to control costs of a commercial drying operation.increasing concern about atmospheric pollution caused byTherefore, the objectives of this research were to:conventional fossil fuels used for drying crops. Farm

buildings provide sizeable amounts of surface for use as 1. develop a mathematical model for predicting steadysolar collectors. Such collectors have been integrated into state thermal performance of covered plate attic solar

collectors;2. validate the model using experimental data;3. provide performance data for covered plate attic solar*Tel.: 1962-2-709-5111x22330; fax1962-2-709-5018.

E-mail address: [email protected](N.H. Abu-Hamdeh). collectors upon which design decisions could be made.

0038-092X/03/$ – see front matter 2003 Elsevier Ltd. All rights reserved.doi:10.1016/S0038-092X(03)00189-0

mailto:[email protected]

310 N.H. Abu-Hamdeh / Solar Energy 74 (2003) 309–317

Nomenclature

2A area, m21 21c specific heat, kJ kg K

F9 collector efficiency factor, dimensionlessF collector heat removal factor, dimensionlessR

22 21h convective heat transfer coefficient, W m K22 21h linearized radiant heat transfer coefficient between absorber plate and the cover, W m Kr

22E solar radiation, W m21~m mass flow rate through collector, kg s

m mass, kg22R resistance to radiative heat transfer, m

T temperature, K22 21U overall heat transfer coefficient through the bottom, W m K

22 21U heat transfer coefficient from the absorber plate to the main room, W m Kb22 21U collector loss coefficient, W m KL

U heat transfer coefficient from the cover to the outside atmosphere including radiation to the sky,t22 21W m K

22V wind speed, mh collector efficiency, %u incidence angle, degrees

22 24s Stefan–Boltzman constant, W m Kt transmittancea absorptance´ emittancet time, sDt time increment, s

Subscriptsa air moving through the collectorai from air in collector to inclined coverav from air in collector to vertical covero outside atmosphere (ambient)i inclined coveria from inclined cover to air in collectorin at collector inletip from inclined cover to absorber plateiv from inclined cover to vertical coverm main roomout at collector outletp absorber platepa from absorber plate to air in collectorpi from absorber plate to inclined coverpv from absorber plate to vertical coveru usefulv vertical coverva from vertical cover to air in collectorvi from vertical cover to inclined covervp from vertical cover to absorber platew due to wind

N.H. Abu-Hamdeh / Solar Energy 74 (2003) 309–317 311

2 . Experimental methods and materials reducing total energy collected over the day as given bythe Solar Livestock Housing Handbook (1983).

A drying facility utilizing the use of solar energy was Temperature within the structure is maintained by eitherdesigned and constructed at a farm location in Jordan.Fig. pulling air through the solar attic or by adding heat with1 is a schematic drawing of the system which consists of a supplemental LPG heaters. Two supplemental gas heatersmain drying room and an attic in which solar energy is having a normal input rating of 60 kW and a thermal

2collected. The total floor area of the structure is 130 m . output capacity rating of 46 kW were used. If the tempera-The main drying room is 16 m long and 7 m wide. The ture in the main drying room is below 308C and the atticceiling height of the main drying room is 3 m resulting in a temperature is high enough to provide energy (358C), then

3total volume of the room of 336 m . the attic vents and shutters open so that air passes up fromThe ceiling of the drying room was formed by attaching the front of the main drying room, through the attic, down

plywood (9.5 mm) to the bottom of the lower chord of the through a main duct in the rear, and back into the dryingroof trusses. Trusses, roof purlins, and the plywood were room. If the solar energy collection of the attic is in-painted flat black in order to provide the absorber surface sufficient to maintain the setpoint temperature in the mainarea. Black-painted plywood has an absorptance (a) of drying room (308C), then the supplemental LPG heaters0.94 and emittance (´) of 0.92. The roof was covered with are turned on and shutters opened to pull air from aroundclear corrugated fiberglass panels having a transmittance the heaters into the main duct for distribution into the main(t) of 0.86 and an absorptance (a) of 0.09 as given by the room. If the attic temperature is below the setpoint of theSolar Livestock Housing Handbook (1983).Panels were attic (358C), then all heating is from supplemental heatersinstalled with self-drilling screws with aluminum washer and the dampers and shutters to the attic are closed toand neoprene washer. The slope of the roof was set for prevent energy loss at night.maximum solar energy collection throughout the drying If the relative humidity within the facility becomesseason (the month of September in this study) (Solar higher than the desired for proper drying of the grains, thenLivestock Housing Handbook, 1983). For Jordan, this inlet dampers open and the fan on the main duct in the rearcorresponds to an angle of 268 towards south. However, of the facility draws in fresh (less humid) air from outside.the building was oriented so that the fiberglass panels for An equal mass of humid air is exhausted through gravitysolar collection face 238 east of due south (slope of vents in the front of the facility. The two duct fans arepanels5268). This orientation was chosen to maximize 0.8 m diameter, industrial, ventilation fans with a capacity

3 3early morning solar energy collection without greatly of 1.8 m /s at 120 Pa static pressure and 5.1 m /s at 30 Pa

Fig. 1. Schematic drawing of the drying system with solar attic.


static pressure. They are equipped with 1.15 kW, 240 V, 5. Natural convection was considered as the mode ofand 3-phase motors. convective heat transfer between the interior surfaces

An attic exhaust fan is used to prevent excessive attic (inclined cover, vertical cover, and absorber plate) andtemperatures. This fan is set to operate if attic temperature the air when the fans were not in operation. Forcedexceeds 658C. The fan selected is a 0.9 m diameter, convection over a flat plate was considered as the mode

3greenhouse fan with a capacity of 4.1 m /s at 36 Pa static of convective heat transfer between the absorber platepressure. It is equipped with a 0.35 kW, 240 V, and 3-phase and the air when the fans were in operation.motor, fan housing, and motorized shutter. 6. The absorber plate was defined as the horizontal surface

Data were recorded during grain drying operations at the of the attic and considered to be at a uniform tempera-experimental site. Ambient temperature, air temperature at ture.the inlet and at the outlet, temperature of the absorber Considering the above assumptions, the energy balanceplate, temperature of the two covers, and temperature in can be formulated for each component of the collectorthe main drying room were measured by copper constantan system, namely the absorber plate, the inclined cover, thethermocouples and recorded by a data logger (model: vertical cover, and the air inside the collector.Doric 205). Accuracy was approximately61 8C with Energy transferred to the inclined cover was due torepeatability of 0.18C. Recording was done every 20 min convection from the air and radiation from the absorberand the average value over an hour interval was used in plate (Fig. 1). Energy losses were due to convection bycalculations. The air velocity profile in the duct was wind and radiation to both the vertical cover and to themeasured by a pitot tube. The air flow rate was the product outside atmosphere. According to assumption 3, energyof the average velocity and the duct cross-sectional area. absorbed by the cover material was considered negligibleWind velocity above the solar collector was measured by a because temperature measurement during the experimentcup anemometer. Readings were done instantaneously.indicated that the cover of the collector remained nearWind velocity was normally less than 2 m/s. Global solar ambient temperatures. An equation based on energy bal-radiation was measured by a solar pyranometer and ance was formulated for the inclined cover as follows:integrator (Kip and Zonnen, model: CC12). It had an

(radiation from absorber)1 (convection from air inaccuracy of60.1%. This measured value was employedfor calculating the thermal efficiency of the solar collector. collector)5 (convection by wind)1 (radiation to verticalTesting was done between 09:00 and 16:00 h for clear sky

cover)1 (radiation to outside atmosphere)conditions. Inlet air temperature was allowed to vary atleast for four or five different values. At each temperature,

s 4 4]the solar collector was heated for about 30 min by solar (T 2 T )1 h A (T 2 T )5 h A (T 2 T )p i ai i a i w i i oR ipradiation, in order to obtain a nearly steady condition,sbefore taking data. 4 4 4 4]1 (T 2 T )1s´ A (T 2 T ) (1)i v i i i oR iv

where the general expression forR is given by:3 . Analysis and mathematical modeling

A1 1X] ] ]1 21S D´ A ´The drying system considered in this study consists of a X Y Y]]]]]R 5 .XYmain drying room and an attic in which solar energy is AX

collected. The horizontal surface of the attic was defined asDuffie and Beckman (1980)presented the followingthe absorber plate. To develop a model to simulate the

method for determining the convective heat transfer coeffi-dynamic behavior of the covered plate attic solar collectorcient due to the wind moving across a solar collectorused in this study and shown inFig. 1 under variouscover, h , and wind speed,V, as the following:conditions, the following assumptions were made. w

1. The collector operated under steady state conditions.h 52.81 3.0V. (2)wThis implied that the conditions would be constant over

a given time.2. The effects of the heat transfer from the ends of the In the case of vee-corrugated covers, the convective

collector were negligible. coefficients in the cavity were adjusted by the ratio of the3. The energy absorbed by the cover material was negli- cover area in contact with air divided by the cover area,

gible compared to that absorbed by the remaining h 5 h /sin (u /2) where u is the angle between vees ofcomponents of the attic solar collector. corrugated surface in degrees.

4. The temperature of the air moving through the collector The relationship that defined the energy balance for theis the average of the air temperatures at the collector vertical cover was developed using an analysis similar toinlet and outlet. that for the inclined cover as follows:


(radiation from absorber)1 (convection from air in h A (T 2T )1 h A (T 2T )1 h A (T 2 T )ia i i a va v v a pa p p a

collector)5 (convection by wind)1 (radiation to inclined ~5m c (T 2T ). (5)a a out in

cover)1 (radiation to outside atmosphere)The mathematical model developed was used to predict

s steady state performance of the covered plate attic solar4 4](T 2T )1 h A (T 2 T )5 h A (T 2 T )p v av v a v w v v oR collector. A computer program was written to solve thevp

system of nonlinear equations. The resulting system ofs 4 4 4 4]1 (T 2 T )1s´ A (T 2T ). (3) equations was solved using a computer subroutine, ob-v i v v v oRvitained from the International Mathematical and StatisticalLibrary (IMSL Reference Manual, 1980), which solvesThe application of energy balance to the absorber platesystems of nonlinear equations using the secant iterativesurface revealed that energy was transferred to the plate intechnique. The temperatures required to present a solutionthe form of solar radiation while losses occurred in theto the simultaneous equations are:form of longwave re-radiation to the covers, conduction to

the main room below, and convection to the air in the 1. the temperature of the absorber plate;collector. The difference between the energy transferred to 2. the temperature of the vertical cover;the plate and energy losses must equal to the change in the3. the temperature of inclined cover;internal energy of the absorber plate as in the following: 4. the temperature of the air at the collector outlet;

5. the average temperature of the air in the attic;(solar radiation) 6. the temperature of the main drying room.5 (longwave re-radiation to inclined cover) After the equations were solved, the useful energy gain

by the air was determined from1 (longwave re-radiation to vertical cover)

~Q 5m c (T 2 T ). (6)1 (conduction to main room) u a a out in

1 (convection to air in collector)Thermal efficiency of solar collector,h, is defined as the

1 (change in the internal energy of absorber) ratio of useful energy gain by the air to solar radiationincident on the plate of the collector:

EA [(ta) cosu 1 (ta) cosu ]p i i v v Qu]]h5 . (7)s s4 4 4 4 EAp] ]5 (T 2 T )1 (T 2 T )p i p vR Rpi pv

In terms of standard non-dimensional parameters for1UA (T 2T )1 h A (T 2 T )p p m pa p p a collectors, the thermal efficiency of a solar collector can be

m c written as:p p]]1 [T (t)2 T (t 2 1)]. (4)p pDt F U (T 2T )R L in o

]]]]h5F [(ta) cosu 1 (ta) cosu ] 2 (8)R i i v v EThe absorber absorbs a portion of the solar energypassing through the covers while the remainder is diffusely in whichreflected. Since not all of the reflected energy is lost but is

~[ A U /m c ]p L a a~F 5 (m c /A U ) 12 e (9)s dreflected back again by the covers, the transmittance– R a a p L

absorptance product (ta) defined byDuffie and Beckmanand by assumingh 5 h 5 h, thenav ai(1974) was used to account for the multiple reflection of

energy within the collector, and was multiplied by the 2h 1 2hh 1 hUr bincidence angle of radiation for each plate. The product ]]]]]]]]F95 (10)2(h 1 h 1U )(h 1 h 1U )2 hr t r b r(ta) was used because the cover of the attic collectormight consist of material with different radiant properties 2(U 1U )(h 1 2hh 12hU U )b t r b t(t). ]]]]]]]]U 5 (11)L 2h 1 2hh 1 hUAn analysis of the energy balance of the air in the r b

collector showed that heat was transported by convectionwhereF was determined byDuffie and Beckman (1980)Rfrom the two covers and the absorber plate to the air, andby assuming thatF9 and U were independent of theLthis amount of energy must equal to the change in theposition of a collector. To obtain values ofF9 andU , it isLinternal energy of the air in the collector as follows:necessary to determine heat transfer coefficients,U , U , h,t b

and h .r(convection from inclined cover)1 (convection fromThe model was validated by comparing the predicted to

vertical cover)1 (convection from absorber) the measured values of air temperatures at the collectoroutlet and collector efficiencies. The measured data were5 (change in internal energy of air in collector)


obtained from the attic solar collector described in the heat was gained by the air since it dissipated some of itsprevious section. heat energy to increase the absorber plate temperature

above the average air temperature. Thus, the simulatedoutlet temperatures and efficiencies were higher than those

4 . Results and discussion experimentally measured. During the late afternoon, someof this stored heat was released as the temperature of the

The mathematical model developed in this study was air inside the collector and the incident solar radiationused to predict steady state performance of a covered plate began to decrease. As a result, measured outlet air tem-attic solar collector. Validation of the model was achieved peratures and efficiencies were higher than those simulatedby comparing predicted and measured outlet air tempera- by the model.tures and collector efficiencies. Data were collected for a As shown inFig. 4, the relationship between measuredperiod of 12 days at the experimental site described before. and simulated thermal efficiency and (T 2 T ) /E wasin o

During this time, normal grain drying management prac- linear, i.e. efficiency decreased when (T 2 T ) /E in-in o

tices were performed by local farmers. The average data creased. A comparison of the experimentally measured andfrom the 12 days for every hour from 09:00 to 16:00 h the simulated efficiencies shows that the mathematicalwere presented. In addition, the effect of air speed inside model was relatively accurate for predicting steady statethe collector and wind speed above the collector was performance of the cover plate attic collector.investigated by mathematical simulation. The effect of air speed inside the collector and wind

Fig. 2 shows comparative results for measured and speed above the collector was investigated by mathemati-simulated outlet air temperatures of the covered plate attic cal simulation.Fig. 5 shows the simulated results relatingsolar collector. The resulting air temperature at the outlet efficiency and air speed for constant wind speed for theof the collector was different from that measured at some solar collector. As seen in the figure, efficiency increasedhours of the day during the drying operations. A closer when air speed is small and increased slowly when airexamination of the results from the model revealed that speed is high, at constant wind speed. Lower air speed willmost of the errors occurred when conditions were simu- result in low efficiency but higher air speed may result inlated during the morning hours just after sunrise and an excessive pressure drop inside the collector. Theduring the late afternoon just prior to sunset. The resulting optimum air speed for the attic solar collector investigatedprediction of the outlet air temperature simulated the actual in this study should be around 4–6 m/s. The same figureconditions more closely during the noon time. The simu- indicates that wind speed above the solar air heater has anlated temperature increased at a lower rate and to a higher effect on the performance of the covered plate attic solarvalue as the sun rises but cooled faster and to a lower collector. The efficiency dropped when wind speed in-temperature as the sun sets. This phenomenon was ob- creased because of increased heat loss.Fig. 6 shows theserved in the measured and simulated efficiency curves of simulated results relatingF and air speed for constantR

the collector as shown inFig. 3. This can be explained by wind speed for the solar collector. As seen in the figure,FR

knowing that useful heat can be obtained only when the increased rapidly when air speed is small and increasedplate temperature is above the air temperature. During the slowly when air speed is high, at constant wind speed.morning hours just after the sunrise, lower measured useful The program developed was used to investigate the

Fig. 2. Comparison between measured and simulated outlet air temperatures (8C) of the covered plate attic solar collector.


Fig. 3. Comparison between measured and simulated collector efficiencies of the covered plate attic solar collector.

effect of using different material on the roof on the 5 . Cost analysissimulated average daily collector efficiency. The roof wasassumed to be covered with white fiberglass panels having A cost analysis of two possible alternatives, a dryinga transmittance (t) of 0.60 and an emittance (´) of 0.55 as facility utilizing the use of solar energy (the systemgiven by theSolar Livestock Housing Handbook (1983). discussed in this paper) and conventional drying systemThe simulated average daily collector efficiency in case of using similar facility but utilizing LPG heaters only wasusing clear corrugated fiberglass was found to be 0.47 investigated.while it was found to be 0.38 when white fiberglass was Similar loads of peanuts were placed in both dryingused. The white fiberglass on the roof adversely affected facilities in a manner which would be typical of normalthe performance by not allowing as much of the radiation peanut drying management practices. The range of initialto reach the absorber. moisture contents of the peanuts placed in the structures

It can be seen that the model satisfactorily predicted was from|30% wet basis to 35% wet basis. Loads of wetdaily performance of covered plate attic solar collectors. In peanuts were weighed before being placed in the dryingorder to improve the diurnal behavior of these systems, the facilities and then weighed again after the drying processeffects of two- or three-dimensions should be included. in order to obtain the total mass of water removed in the

Fig. 4. Measured and simulated collector efficiencies of the covered plate attic solar collector as functions of (T 2 T ) /E.in o


Fig. 5. Effect of air speed inside the collector and wind speed above the collector on thermal efficiency of the covered plate attic solarcollector.

drying process. Gas meter readings were taken at the GJ, the total energy costs per unit of water removed werebeginning and at the end of the drying period. $0.15/kg and $0.02/kg for the conventional dryerH O H O2 2

Samples of peanuts were taken periodically during the and solar dryer, respectively. For the solar dryer, thedrying process and moisture measurements of the kernelscontribution of the collector cost to the total energy costswere made on a Dick-john Model GAC II moisture meter. per unit of water removed should be calculated. The totalLoads of peanuts were considered dry when the moisture costs were calculated using the amortized values for thecontent of peanuts dropped below 10% wet basis. attic solar collector alone. An estimate of the construction

The loads in each drying facility contained over costs including installation and materials resulted in a total11.8 tons of peanuts from which|2.8 tons of water were estimated initial cost of $1434. Cost for maintenance wasremoved. Total gas energy consumption per unit of water also calculated for the collector. The attic solar collectorremoved was 13 840 kJ/kg and 2269 kJ/kg for the was amortized over 10 years at 10% interest per year. TheH O H O2 2

estimated annual cost for the collector was found to beconventional dryer (which utilizes LPG heaters only) and$273.4, and when divided by the total amount of waterattic solar collector dryer, respectively. The gas energyremoved and added to the total energy costs per unit ofconsumption is based on an assumed heat content of thewater removed gave a total of $0.11/kg for the atticgas of 25 447 kJ/ l of gas. H O2

The data do show that significant savings in fuel costs solar collector drying system. This indicated that investingcan be achieved. Based on an assumed gas cost at $11 per in an attic solar collector air heater is quite attractive.

Fig. 6. Effect of air speed inside the collector and wind speed above the collector onF of the covered plate attic solar collector.R


B utts, C.L., Harner, J.P., Baker, J.L., Vaughan, D.H., 1980.6 . ConclusionsCombination drying of grain using solar energy. In: GrainConditioning Conference Proceedings, pp. 52–68.A mathematical model for predicting thermal perform-

D uffie, J.A., Beckman, W.A., 1974. Solar Energy Thermal Pro-ance of a covered plate attic solar collector was developed.cesses. John Wiley, New York.Validation of the model was achieved by comparing

D uffie, J.A., Beckman, W.A., 1980. Solar Engineering of Thermalsimulated and measured outlet air temperatures and collec- Processes. John Wiley, New York.tor efficiencies. Based on the results obtained, the follow- F oster, G.H., Peart, R.M., 1976. Solar grain drying: progress anding conclusions were drawn. potential. In: Agricultural Information Bulletin No. 401. USDA.1. The mathematical model developed for the covered H arner, J.P., Lambert, A.J., Baker, J.L., Vaughn, D.H., Steele, J.L.,

1981. Improving Peanut Curing Efficiency with Air Recircula-plate attic solar collector was relatively accurate fortion. ASAE, St. Joseph, MI, ASAE paper no. 81-3545.predicting steady state performance of the collector.

H ussein, H.M., Mohamad, M.A., El-Asfouri, A.S., 2001. Theoret-2. Wind speed above the collector and air speed inside theical analysis of laminar-film condensation heat transfer insidecollector affected its efficiency. The lower the windinclined wickless heat pipes flat-plate solar collector. Renew.speed the higher the collector efficiency. The optimumEnergy 23, 525–535.

air speed inside the collector was found to be 4–6 m/s.I MSL Reference Manual, 1980. In: 8th Edition. ZSCNT. IMSL

3. Cost analysis indicated that the attic solar collector Reference manual, vol. 3. International Mathematical anddrying system is cost effective particularly when com- Statistical Libraries.pared to LPG and is expected to be much more M orrison, D.W., Shove, G.C., 1979. Survey of Grain Dryingeffective when other more expensive fuels or electricity Practices in Illinois. ASAE, St. Joseph, MI, ASAE paper no.

79-3018.are used instead.S canlin, D., 1997. The design, construction and use of an indirect,

through-pass, solar food dryer. Home Power 57, 62–72.S canlin, D., 1999. Improving solar food dryers. Home Power 69,

24–34.R eferences S olar Livestock Housing Handbook. Midwest Plan Services, Iowa

State University, Ames, IA.A hmad, N.T., 2001. Agricultural solar air collector made from S oponronnarit, S., Peyre, A., 1982. Low temperature sorghum

low-cost plastic packing film. Renew. Energy 23, 663–671. drying in the south of France. In: Ashworth, J.C. (Ed.),B oonlong, P., 1984. Solar-assisted tobacco curing. In: The Re- Proceedings of the 3rd International Drying Symposium, Bir-

gional Seminar on Solar Drying, Yogyakarta, Indonesia. mingham.B rooker, D.B., Bakker-Arkema, F.W., Hall, C.W., 1974. In: Drying T roeger, J.M., Butler, J.L., 1979. Simulation of solar peanut

Cereal Grains. AVI Publishing, Westport, CT, p. 216. drying. Trans. ASAE 22, 906–911.

simulation study of solar air heater

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