effect of greenhouse on crop drying under natural and forced convection ii. thermal modeling and...

Energy Conversion and Management 45 (2004) 2777–2793www.elsevier.com/locate/enconman

Effect of greenhouse on crop drying under naturaland forced convection II. Thermal modeling

and experimental validation

Dilip Jain a,*, G.N. Tiwari b

a Central Institute of Post Harvest Engineering and Technology, PAU Campus, Ludhiana 141 004, Indiab Center for Energy Studies, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110 016, India

Received 16 April 2002; received in revised form 28 March 2003; accepted 9 December 2003

Available online 24 January 2004

Abstract

In this paper, mathematical models are presented to study the thermal behavior of crops (cabbage and

peas) for open sun drying (natural convection) and inside the greenhouse under both natural and forcedconvection. The predictions of crop temperature, greenhouse room air temperature and rate of moisture

evaporation (crop mass during drying) have been computed in Matlab software on the basis of solar

intensity and ambient temperature. The models have been experimentally validated. The predicted crop

temperature and crop mass during drying showed fair agreement with experimental values within the root

mean square of percent error of 2.98 and 16.55, respectively.

� 2004 Elsevier Ltd. All rights reserved.

Keywords: Solar drying; Greenhouse; Heat and mass transfer; Thermal modeling

1. Introduction

Solar crop drying involves the transport of moisture to the surface of the product and sub-sequent evaporation of the moisture by thermal heating. Thus, solar thermal crop drying is acomplex process of simultaneous heat and mass transfer. Several researchers have reported the-oretical and experimental studies on solar crop drying.Basunia and Abe [1] conducted experiments on thin layer solar drying of rough rice in natural

convection and determined the drying rate by using the Page equation. Manohar and Chandra [2]

* Corresponding author. Tel.: +91-161-2808155.

E-mail address: [email protected] (D. Jain).

0196-8904/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.enconman.2003.12.011

mail to: [email protected]

Nomenclature

A area (m2), coefficients in Eqs. (17) and (19)a derivative of Eq. (17)C specific heat (J/kg �C), coefficient of Eq. (17)Cd coefficient of diffusivityD coefficient of Eq. (17)dm dry mass in crop (kg/kg of crop)e root mean square of percent deviationF fraction of solar radiationf ðtÞ time dependent derivative of Eq. (8)g acceleration due to gravity (m/s2)DH difference in pressure head (m)h total heat transfer coefficient (W/m2 �C)hc convective heat transfer coefficient of crop (W/m2 �C)hca convective heat transfer coefficient of air (W/m2 �C)hr radiative heat transfer coefficient (W/m2 �C)hb convective heat transfer coefficient from crop to air (bottom loss)¼ 5.7 (W/m2 �C)hw convective heat transfer coefficient due to wind ¼ 5:7þ 3:8v (W/m2 �C)IðtÞ solar intensity on horizontal surface (W/m2)Ii solar intensity on greenhouse wall/roof i (W/m2)K thermal conductivity (J/m2 �C)k coefficients in Eq. (19) (h�1)M mass (kg)mev moisture evaporated (kg)N number of air changes per hourPðT Þ partial vapour pressure at temperature T (N/m2)DP difference in partial pressure (N/m2)Qe rate of heat utilized to evaporate moisture (J/m2 s)R coefficient of Eq. (4) for linear expression of partial pressurer coefficient of correlationt time (s)T temperature (�C) and time in Eq. (19) (h)Ti average of crop and humid air temperature (�C)U over all heat loss (W/m2 �C)v wind/air velocity (m/s)V volume of greenhouse (m3)Wm ¼ Xm=Xm0 dimension less water contentXm water content (dry basis) (kg water/kg dry matter)

Greek letters

a absorptivity of crop surfaceb coefficient of volumetric expansion (1/�C)

2778 D. Jain, G.N. Tiwari / Energy Conversion and Management 45 (2004) 2777–2793

c relative humidity of air (dec.)e emissivityr Stefan–Boltzmann constant¼ 5.6696 · 10�8 (W/m2 K4)k latent heat of vaporization (J/kg)l dynamic viscosity of air (kg/m)q density of air (kg/m3)s transmissivity

Subscripts

0 initial valuea ambient or airc crope above the crop surfaceg ground or greenhouse floori greenhouse wall/roof ði ¼ 1; 2; . . . ; 6Þm massn north wallr greenhouse room airv humid air or ventce crop to environmentgr greenhouse floor to roomg1 greenhouse floor to undergroundjx¼0 surface of floor of greenhouse

D. Jain, G.N. Tiwari / Energy Conversion and Management 45 (2004) 2777–2793 2779

studied the drying process in a greenhouse type solar dryer using natural as well as forcedventilation and the drying data were represented with the Page drying equation. Yaldiz et al. [3]presented various mathematical models of thin layer solar drying of sultana grapes on the basis ofregression analysis of the experimental data.Mulet et al. [4] proposed a method of standardizing open sun drying time by defining the

equivalent time based on the average solar radiation input. Sodha et al. [5] presented an analyticalmodel of open sun drying and a cabinet type solar dryer. The model was used to predict thehourly variation of crop temperature and rate of moisture evaporation under constant and fallingrates of drying. Goyal and Tiwari [6] presented a thermal model to predict the crop parameters fora reverse absorber cabinet type solar dryer. Ratti and Majumdar [7] developed a simulation codeto predict the batch drying performance of a packed bed of particles (carrots or apple slices). Themodel was used to predict the crop temperature and moisture ratio with respect to drying time in acabinet solar dryer.Rachmat and Horibe [8] studied the solar heat collection characteristics of a fiber reinforced

plastic drying greenhouse. A mathematical model was presented to predict the air temperatureinside the greenhouse on the basis of ambient conditions. Condor�ı and Saravia [9] presented ananalytical study of the evaporation rate in two types of forced convection greenhouse dryers usingsingle and double chamber systems.


Considering the importance of solar crop drying, in this paper, three simple mathematicalmodels are presented for open sun drying and greenhouse drying under natural and forcedconvection. These models are solved in the Matlab software to predict the hourly crop temper-ature, greenhouse room temperature and rate of moisture evaporation. The predicted values areexperimentally validated. The agreements of predicted and experimental values are presented withthe coefficient of correlation and root mean square of percent deviation.

2. Working principle of solar crop drying

Solar energy for crop drying is a process in which solar radiation is converted to thermalenergy. The working principle of crop drying under open sun is illustrated in Fig. 1a. The solarradiation falling on the crop surface is partly absorbed and partly reflected. The absorbed radi-ation heats the crop surface. A part of this heat is utilized to evaporate the moisture from the crop

hce

crop

I(t)

SUN

hchw

hb

Ta

Fn

Ui

SUN

I(t)

Tr

Tr

Tc

crop

hcFc hgr

hg∞ ∞

SUN

I(t)Ta Ui

Fn

hgrFc

Tr

hcTc

crop

Tr

hg

(a)

(b) (c)

Fig. 1. Principle of solar crop drying under greenhouse effect showing the various heat transfer coefficients. (a) Open

sun drying, (b) Greenhouse drying under natural convection and (c) Greenhouse drying under forced convection.


surface to the surrounding air. The remaining part of this heat is conducted into the interior of thecrop or lost through radiation (long wavelength) to the atmosphere and through the bottom loss(through conduction to the ground if the crop is laid on the ground). The rate of moistureevaporation depends on the vapor pressure difference between the crop and the environment airsurrounding the crop.Placing a plastic cover over the crop produces a greenhouse effect. It traps the solar energy in

the form of thermal heat within the cover ðPIiAisiÞ since the plastic cover acts essentially as

opaque to the thermal heat radiation radiated by the crop and reduces the convective heat loss.The fraction of trapped energy ðFc

PIiAisiÞ will be received partly by the crop and partly

ð1� FnÞPIiAisi by the floor and exposed tray area. Further, the remaining solar radiation

ðð1� FnÞð1� FcÞð1� agÞPIiAisiÞ will heat the enclosed air inside the greenhouse. The principle of

crop drying inside a greenhouse under natural convection is shown in Fig. 1b. The natural drafttakes place due to the temperature difference between the greenhouse air and ambient air. The rateof moisture evaporation depends on the vapor pressure difference between the crop and thegreenhouse air. A greenhouse with the forced mode of drying reduces the relative humidity insidethe greenhouse and increases the vapor pressure difference, resulting in a faster rate of moistureremoval (Fig. 1c).

3. Thermal modeling

Thermal models for prediction of crop temperature and moisture evaporation have beendeveloped using energy balance equations for open sun drying and greenhouse drying under bothnatural and forced modes. The energy balance equations have been written with the followingassumptions:

(i) thin layer (single layer) drying is adopted,(ii) heat capacity of cover and wall material is neglected,(iii) no stratification in greenhouse air temperature,(iv) absorptivity of air is negligible,(v) greenhouse is east–west oriented.

3.1. Thermal modeling of open sun drying (OSD) (Fig. 1a)

(a) Energy balance equation on crop surface for moisture evaporation [10]

acIðtÞAc � hceðTc � TeÞAc � 0:016hc½P ðTcÞ � cePðTeÞAc � hbðTc � TaÞAc ¼ McCcdTcdt

ð1Þ

(b) Energy balance equation of moist air above the crop

hceðTc � TeÞAc þ 0:016hc½PðTcÞ � ceP ðTeÞAc ¼ hwðTe � TaÞAc ð2Þ
(c) Moisture evaporated can be evaluated as [11]
mev ¼ 0:016hck½P ðTcÞ � cePðTeÞAct ð3Þ


3.2. Thermal modeling of greenhouse drying (GHD) under natural mode (Fig. 1b)

(a) Energy balance equation at crop surface,

ð1� FnÞFcacX

IiAisi ¼ McCcdTcdt

þ hcðTc � TrÞAc þ 0:016hc½P ðTcÞ � crP ðTrÞAc ð4Þ

(b) Energy balance equation at ground surface

ð1� FnÞð1� FcÞagX

IiAisi ¼ hg1ðT jx¼0 � T1ÞAg þ hgrðT jx¼0 � TrÞðAg � AcÞ ð5Þ

(c) Energy balance equation at greenhouse chamber, using the coefficient of diffusion and differ-ence in partial pressure due to the temperature difference of the greenhouse chamber air andambient air [12]

ð1� FnÞð1� FcÞð1� agÞX

IiAisi þ hcðTc � TrÞAc þ 0:016hc½PðTcÞ � crPðTrÞAcþ hgrðT jx¼0 � TrÞðAg � AcÞ ¼ CdAv

ffiffiffiffiffiffiffiffiffiffiffiffiffi2gDH

pDP þ

XUiAiðTr � TaÞ ð6Þ

where

DH ¼ DPqrg

ð7Þ

DP ¼ P ðTrÞ � caPðTaÞ ð8Þ

3.3. Thermal modeling of greenhouse drying under forced mode (Fig. 1c)

(a) Energy balance equation at crop surface and ground surface are similar to Eqs. (4) and (5),respectively.

(b) Energy balance at greenhouse chamber

ð1� FnÞð1� FcÞð1� agÞX

IiAisi þ hcðTc � TrÞAc þ 0:016hc½PðTcÞ � crPðTrÞAcþ hgrðT jx¼0 � TrÞðAg � AcÞ ¼ 0:33NV ðTr � TaÞ þ

XUiAiðTr � TaÞ ð9Þ

4. Solution of thermal models

The above mathematical models are solved with the following approximations:

(i) The crop area during the drying process reduces with the moisture reduction due to shrinkagein the crop. Therefore, the crop area ðAcÞ for absorption of solar energy will also change dur-ing drying. The shrinkage ratio is used as a function of moisture ratio [13] to get the approxi-mate value of crop area ðAcÞ for solving the above mathematical models.

(ii) The partial vapor pressure has an exponential relationship with temperature and is too complexto solve the above equations. Therefore, the partial vapor pressure has been linearised for thesmall range of temperature between 25 and 55 �C, which mostly occurs in solar drying, as

P ðT Þ ¼ R1T þ R2 ð10Þ


4.1. Open sun drying

By substituting the linear expression of partial vapor pressure in Eqs. (1) and (2), the newequations become

acIðtÞAc � hceðTc � TeÞAc � 0:016hc½ðR1Tc þ R2Þ � ceðR1Te þ R2ÞAc � hbðTc � TaÞAc ¼ McCcdTcdt

ð11Þ

hceðTc � TeÞ þ 0:016hcðR1Tc þ R2Þ � 0:016hcceðR1Te þ R2Þ ¼ hwðTe � TaÞ ð12Þ

From Eq. (12)

Te ¼ðhce þ 0:016hcR1ÞTc þ R2½0:016hcð1� ceÞ þ hwTa

hce þ 0:016hcceR1 þ hwð13Þ

By combining Eqs. (11) and (13) a form of first order differential equation is produced as

dTcdt

þ aTc ¼ f ðtÞ ð14Þ

where

a ¼½ðhce þ hbÞAc þ 0:016hcR1Ac � Acðhceþ0:016hcR1ceÞðhceþ0:016hcR1Þ

hceþ0:016hcceR1þhwMcCc

and

f ðtÞ ¼acIðtÞAc þ hbAcTa þ hwðhceþ0:016hcR1ceÞAc

hceþ0:016hcceR1þhw

h iTa þ ðhceþ0:016hcR1ceÞAcR20:016hcð1�ceÞ

hceþ0:016hcceR1þhw

McCc

The solution of Eq. (14) for the average f ðtÞ for the time interval 0–1 is

Tc ¼f ðtÞa

ð1� e�atÞ þ Tc0e�at ð15Þ

Once Tc is known, Te can be determined by Eq. (13) and mev by Eq. (3), which can be rewritten as

mev ¼ 0:016hck½ðR1Tc þ R2Þ � ceðR1Te þ R2ÞAct ð16aÞ

4.2. Greenhouse drying under natural mode

The partial pressure of vapor at Tr and Ta has been determined with the help of the linearregression technique as Eq. (10). With the help of Eqs. (5), (7), (8) and (10), Eq. (6) has beensimplified in the form of a third order polynomial equation to determine the greenhouse roomtemperature ðTrÞ for assumed values of crop temperature and ambient temperature as

AT 3r þ BT 2r þ CTr þ D ¼ 0 ð17Þ
where
A ¼ ð2=qrÞðCdAvÞ2R21


B ¼ ð2=qrÞðCdAvÞ23R21½R2 � caðR1Ta þ R2Þ � hcAc

hþ 0:016hcAccrR1 þ ðUAÞg1 þ

XUiAi

i2

C ¼ ð2=qrÞðCdAvÞ23R1½R2 � caðR1Ta þ R2Þ2 þ hcAc

hþ 0:016hcAccrR1 þ ðUAÞg1 þ

XUiAi

i Ieff Rh

þ HgIeff G þ hcAcTc þ 0:016hcAcðR1Tc þ R2 � crR2Þ þ ðUAÞg1Ta þX

UiAiTai

D ¼ ð2=qrÞðCdAvÞ2½R2 � caðR1Ta þ R2Þ3

� Ieff Rh

þ HgIeff G þ hcAcTc þ 0:016hcAcðR1Tc þ R2 � crR2Þ þ ðUAÞg1Ta þX

UiAiTai2

Once the value of room air temperature ðTrÞ is known, with the help of Eq. (4), the crop tem-perature ðTcÞ can be determined, which is in the form of a first order differential equation asEq. (14) where

a ¼ hcAcð1þ 0:016R1ÞMcCc

and

f ðtÞ ¼ Ieff C þ hcAc½Tr � 0:016fR2 � crðR1Tr þ R2ÞgMcCc

Once the temperatures of the crop and greenhouse room air are known, the rate of moistureevaporation can be evaluated with the expression

mev ¼ 0:016hck½ðR1Tc þ R2Þ � crðR1Tr þ R2ÞAct ð16bÞ

4.3. Greenhouse drying under forced mode

With the help of Eqs. (9) and (10), Eq. (9) has been simplified to determine the greenhouseroom temperature under forced mode for assumed values of crop temperature and ambienttemperature as

Tr ¼Ieff R þ hcAcTc þ 0:016ðR1Tc þ R2 � crR2Þ þ HgIeff G þ ½0:33NV þ

PUiAi þ ðUAÞg1Ta

hcAc þ 0:016hccrR1 þ ðUAÞg1 þ 0:33NV þPUiAi

ð18Þ
If the value of room air temperature ðTrÞ is known, with the help of Eq. (4) the crop temperatureðTcÞ can be determined, which is in the form of a first order differential equation as Eq. (14). Thederivatives of a and f ðtÞ are the same as those of the case of greenhouse drying under naturalmode. The rate of moisture evaporation can be evaluated with the help of Eq. (16b).
5. Input values and computational procedure

Computer programs based on Matlab software [14] were used to solve the mathematicalmodels. The hourly average solar intensity and ambient temperature (from 8 AM to 33 h of


continuous drying time) were obtained from the hourly data recorded during the drying experi-ment (Table 1). The hourly variations in convective heat transfer for the different modes of dryingwere obtained from the two term exponential expression.

Table

Ambi

Dry

time

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

hc ¼ A1 expðk1T Þ þ A2 expðk2T Þ ð19Þ

The coefficients of the exponential expression for the different modes of drying for cabbage andpeas have been obtained by Jain and Tiwari [15] and are presented in Table 2. The constant andinput values for cabbage and peas are given in Tables 3 and 4, respectively.

1

ent data used in modeling

ing

(h)

September 2001 October 2001 November 2001 December 2001

IðtÞ (W/m2) Ta (�C) IðtÞ (W/m2) Ta (�C) IðtÞ (W/m2) Ta (�C) IðtÞ (W/m2) Ta (�C)160 30.4 80 24.8 60 18.4 20 15.5

240 31.1 280 29.6 200 18.1 80 17.0

380 34.5 400 31.2 300 21.6 220 19.5

600 34.5 500 32.0 380 24.4 280 21.2

680 35.8 520 33.3 400 25.5 320 22.4

700 35.5 460 34.8 440 29.3 300 24.1

560 36.3 500 37.2 360 29.4 240 23.8

500 39.0 500 35.1 220 28.6 180 23.4

280 34.6 180 34.0 80 25.1 80 22.0

100 35.4 40 30.0 20 21.5 20 20.9

20 33.7 0 29.0 0 20.8 0 19.0

0 34.0 0 29.0 0 20.0 0 18.8

0 34.0 0 28.9 0 19.8 0 18.6

0 34.0 0 28.2 0 19.6 0 18.5

0 34.0 0 28.0 0 19.2 0 18.5

0 34.0 0 27.8 0 17.8 0 16.5

0 33.6 0 27.2 0 17.0 0 14.7

0 33.0 0 26.8 0 16.6 0 13.8

0 32.5 0 26.0 0 16.2 0 13.0

0 32.2 0 25.4 0 15.8 0 12.8

0 32.0 0 25.0 0 14.5 0 12.2

0 31.7 0 24.2 0 13.8 0 12.1

0 31.1 0 22.8 0 14.2 0 13.7

20 29.7 20 23.3 0 15.8 0 14.4

160 31.4 60 24.0 20 16.4 20 15.2

240 33.0 280 29.0 200 20.6 220 17.0

380 35.0 440 31.2 340 22.2 300 17.8

600 35.3 500 32.2 420 25.4 400 19.6

680 35.7 580 34.8 480 27.1 380 21.1

700 38.0 600 33.6 420 28.4 360 22.6

560 39.2 500 37.1 380 28.3 300 23.1

500 39.0 300 36.6 220 27.6 200 23.8

280 36.4 60 32.6 100 25.0 100 23.0

100 35.1 20 30.0 20 22.0 20 20.0

Table 2

Coefficients of two term exponential expression for convective mass transfer coefficient under different mode of drying

[14]

Method of drying Crop Month 2001 Constants

A1 k1 A2 k2

OSD Cabbage September 3.5174 )0.0960 27.2136 )0.1834OSD Peas October 0.1584 )0.0337 24.2968 )0.1612GHD natural mode Cabbage September 10.0664 )0.0968 10.2387 )0.2094GHD natural mode Peas October 11.9934 )0.0855 1.6550 )0.2448GHD forced mode Cabbage November 1.4531 )0.1008 41.6293 )0.1444GHD forced mode Peas December )0.0334 0.0636 38.3583 )0.0905

Table 3

Constant used in modeling

Parameters Values

Ca 1012

Cd 0.425

g 9.81

hb 5.7

hw 5:7þ 3:8vhgr 8.0

Mc 0.300

T 3600

R1 397.52

R2 )7926.90v 0.5

ag 0.6

k 2.26 · 106e 0.9

r 5.67 · 10�8s 0.9


For open sun drying, the average hourly solar radiation on a horizontal surface and ambientair temperature were used for evaluation of the crop temperature from Eq. (15). Then, thetemperatures above the crop surface and the moisture evaporation during the corresponding hourwere computed from Eqs. (3) and (16a), respectively.A roof type even span greenhouse with an effective floor covering of 1.2· 0.8 m2, the central

height of 0.60 m and height of walls of 0.40 m was used for the modeling of greenhouse drying. Theaverage hourly solar radiation on the different walls and roofs of the greenhouse was evaluated fromthe average hourly solar radiation on a horizontal surface with help of the Liu and Jordan formula[16] for Delhi (Latitute-28�350). Then, the average hourly total radiation received by the greenhousewas the sum of the average hourly radiations of the walls and roofs of the greenhouse. Thus, theaverage hourly total radiation received by the greenhouse and the average hourly ambient airtemperature were used as input data to compute the hourly temperature of the crop and greenhouseroom air through simulation. The moisture evaporation was calculated with the help of Eq. (16b).

Table 4

Input values of crops used for modeling

Parameter Cabbage Peas

Ac0 0.32· 0.26 0.20 · 0.20ac 0.4 0.5

Cc 3900 3060

dm 0.070 0.450

Fc (first and second day) 0.25, 0.025 0.15, 0.03

Open sun drying

ce 0.65 0.45

Tc 29.25 26.25

Te 32.5 27.8

GHD natural mode

ca 0.50 0.40

cr 0.65 0.50

Tc 30.0 26.75

Tr 32.0 27.9

GHD forced mode

ca 0.50 0.50

cr 0.45 0.50

Tc 11.25 13.5

Tr 15.9 15.35

m 0.5 0.5

N 30 30


The predicted temperatures of the crop and greenhouse chamber and the moisture evaporationfrom the different drying models have been compared with the experimental data given by Jainand Tiwari [15]. The goodness of agreement has been determined with the help of the coefficientsof correlation and root mean squares of percent deviations [17].

6. Results and discussion

6.1. Open sun drying (OSD)

The mathematical model developed for open sun drying has been solved for the ambient data ofSeptember and October 2001 for cabbage and peas. The predictions of crop temperature, temper-ature above the crop surface and crop mass (rate of moisture evaporation) and their respectiveexperimental values are presented in Fig. 2a and b. The closeness of the predicted and experimentalvalues has been determined with the help of the coefficient of correlation ðrÞ and root mean square ofpercent deviation ðeÞ. The best possible agreement of predicted and experimental values are at valuesof coefficient of correlation and root mean square of percent deviation as one and zero, respectively.The predicted temperatures of the crop and above the crop surface show fair agreement with

the experimental observations within the root mean square of percent deviation ðeÞ range from8.39 to 13.14. The coefficient of correlation ðrÞ ranges from 0.77 to 0.96. The predicted values of

0 5 10 15 20 25 30 350

10

20

30

40

50

60

Drying time in hour

Ambient temp.Predicted crop temp.Exptl crop temp.Predicted temp.above crop surfaceExptl temp. above crop surfacePredicted crop massExptl crop mass

rc = 0.87; ec = 8.39 %

re = 0.77; ee = 9.55 %rm = 0.99; em = 4.49 %

September 2001

Tem

pera

ture

in ˚

C a

nd M

ass

in ×

10-2 k

gT

empe

ratu

re in

˚C

and

Mas

s in

×10

-2 k

g

0 5 10 15 20 25 30 350

10

20

30

40

50

60

Drying time in hour

Ambient temp.Predicted crop temp.Exptl crop temp.Predicted temp.above crop surfaceExptl temp. above crop surface Predicted crop massExptl crop mass

rc = 0.96; e c = 8.85 %

re = 0.94; e e = 13.14 %

rm = 0.98; em = 3.72 %

October 2001

(a)

(b)

Fig. 2. (a) Crop and above the crop temperature and crop mass under open sun drying for cabbage. (b) Crop and above

the crop temperature and crop mass under open sun drying for peas.


crop mass (due to moisture evaporation) also show good agreement with the experimental valueswith the coefficient of correlation as 0.99 and 0.98 and root mean square of percent deviation as4.49 and 3.72 for cabbage and peas, respectively.Under open sun drying, the maximum moisture evaporation took place in 1–10 h of drying time

(Fig. 2a and b). This is due to the higher moisture available in the beginning of drying, and theprocess utilized the solar intensity for evaporation. Therefore, the temperature of the crop did notrise much more than ambient due to the cooling effect by evaporation of the moisture. During thenight hours (11–24 h of drying time), the temperature of the crop remained very close to ambientand less moisture evaporation took place. On the second day of drying (25–30 h of drying time),the crop had very low moisture content, and thus, the crop temperature increased significantlyhigher than ambient due to the absorption of solar radiation. The crop got more drying duringthis period, slightly faster than during the night hours.


6.2. Greenhouse drying (GHD) under natural convection

The mathematical model developed for greenhouse drying under natural convection hasalso been solved for the ambient data of September and October 2001 for cabbage and peas.Fig. 3a and b present the predicted temperature of crop and greenhouse chamber and crop massalong with the experimental values. These figures clearly indicate that the agreement of thepredicted and experimental values is better than with open sun drying due to drying in the en-closed house. The coefficient of correlation ranges from 0.90 to 0.97 and the root mean square ofpercent deviation ranges within 4.36–8.57 for the crop and greenhouse room air temperature,respectively. The coefficient of correlation of the predicted and experimental values of crop massduring drying for cabbage and peas are 0.99 and 0.98, respectively. The agreement of crop masswas within the root mean square of percent deviation as 4.72 and 2.98 for cabbage and peas,respectively.

0 5 10 15 20 25 30 350

10

20

30

40

50

60

Drying time in hour

Ambient temp. Predicted crop temp.Exptl crop temp.Predicted room temp.Exptl room temp.Predicted crop massExptl crop mass

September 2001

rc = 0.96; ec = 4.36 %

rr = 0.90; e r = 8.57 %

rm = 0.99; em = 4.72 %

0 5 10 15 20 25 30 350

10

20

30

40

50

60

Drying time in hour

Ambient temp. Predicted crop temp.Exptl crop temp.Predicted room temp.Exptl room temp.Predicted crop massExptl crop mass

October 2001

rc = 0.97; ec = 5.78 %

rr = 0.97; e r = 4.82 %

rm = 0.98; em = 2.98 %

Tem

pera

ture

in ˚

C a

nd C

rop

mas

s in

×10

-2 k

gT

empe

ratu

re in

˚C

and

Cro

p m

ass

in ×

10-2

kg

(a)

(b)

Fig. 3. (a) Crop and room air temperature and crop mass under greenhouse drying for cabbage (natural convection).

(b) Crop and room air temperature and crop mass under greenhouse drying for peas (natural convection).


The trend of crop temperature and rate of moisture removal in greenhouse drying undernatural mode was similar to that discussed for open sun drying (Fig. 3a and b).

6.3. Greenhouse drying (GHD) under forced convection

The crop temperature, greenhouse room air temperature and crop mass during drying have beenpredicted for the ambient data of November and December 2001 for cabbage and peas with thehelp of the model developed for greenhouse drying under forced convection. The predicted valuesand experimental observations are plotted with drying time in Fig. 4a and b for cabbage and peas.The predicted values were in good agreement with the experimental observations with the coeffi-cient of correlation ranging from 0.92 to 0.97 for the crop and greenhouse room air temperaturesand 0.98–0.99 for the crop mass. The root mean square of percent deviation of the predicted values

0 5 10 15 20 25 30 350

10

20

30

40

50

60

Drying time in hour

Ambient temp.Predicted crop temp.Exptl crop temp. Predicted room temp.Exptl room temp.Predicted crop mass Exptl crop mass

November 2001

rc = 0.92; ec = 13.82 %

rr = 0.97; er = 5.48 %

r m = 0.99; e m = 8.43 %

0 5 10 15 20 25 30 350

10

20

30

40

50

60

Drying time in hour

Ambient temp.Predicted crop temp.Exptl crop temp.Predicted room temp.Exptl room temp.Predicted crop massExptl crop mass

December 2001

r c = 0.94; ec = 16.55 %

rr = 0.94; er = 6.34 %

rm = 0.98; em = 3.88 %

Tem

pera

ture

in ˚

C a

nd C

rop

mas

s in

×10

-2 k

gT

empe

ratu

re in

˚C

and

Cro

p m

ass

in ×

10-2

kg

(a)

(b)

Fig. 4. (a) Crop and room air temperature and crop mass under greenhouse drying for cabbage (forced convection).

(b) Crop and room air temperature and crop mass under greenhouse drying for peas (forced convection).


and experimental observations of crop mass are 8.43 and 3.88 for cabbage and peas, respectively.These results are in harmony with percent uncertainty given by Jain and Tiwari [15].The trends of crop temperature and moisture evaporation in greenhouse drying under the

forced mode were different from those of greenhouse drying under natural mode. The crop driedunder forced mode inside the greenhouse did not attain so high temperature from the ambientbecause of the fast removal of moisture in the greenhouse room, simultaneously cooling the crop(Fig. 4a and b). Therefore, the rate of moisture removal was faster in forced convection dryingwithout raising the crop temperature.

7. Conclusion

Three simple mathematical models were developed to predict the crop temperature, greenhouseroom temperature and moisture evaporation for open sun drying (natural convection) andgreenhouse drying under natural and forced convection. These models were validated withexperimental observations for drying of cabbage and peas with each mode of drying. The pre-dicted values were in good agreement with experimental observations with coefficient of corre-lation ranging between 0.77 and 0.97 for the crop and greenhouse room air temperatures and0.98–0.99 for the crop mass during drying (for rate of moisture evaporation).

Appendix A. Expressions used in thermal modeling

Ieff C ¼ ð1� FnÞFcacX

IiAisi ðA:1Þ

Ieff G ¼ ð1� FnÞð1� FcÞagX

IiAisi ðA:2Þ

Ieff R ¼ ð1� FnÞð1� FcÞð1� agÞX

IiAisi ðA:3Þ

Hg ¼ 1

�þ hg1AghgrðAg � AcÞ

��1ðA:4Þ

ðUAÞg1 ¼ 1

hgrðAg � AcÞ

�þ 1

hg1Ag

��1ðA:5Þ

PðT Þ ¼ exp 25:317

�� 5144

Ti þ 273:15

�ðA:6Þ

hce ¼ hcþ hr ðA:7Þ

hr ¼ er½ðTc þ 273:15Þ4 � ðTe þ 273:15Þ4Tc � Te

ðA:8Þ


Appendix B. Shrinkage ratio

Crop area is a function of the moisture ratio. Ratti [13] studied the shrinkage during drying offoodstuff and established an empirical relationship of the shrinkage ratio to the moisture ratio,which has been used to get the approximate surface area to receive the solar radiation for solvingthe above mathematical models. The expression used is

AcAc0

¼ 0:339þ 1:246Wm � 1:385W 2m þ 0:792W 3

m ðB:1Þ

where Wm ¼ XmXm0.

Appendix C. Procedure of calculation of coefficient of correlation (r) [17]

r ¼ NPXiYi � ð

PXiÞð

PYiÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

NPX 2i � ð

PXiÞ2

q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiNPY 2i � ð

PYiÞ2

q ðC:1Þ

Appendix D. Procedure of calculation of root mean square of percent deviation (e)

e ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiPðeiÞ2

n

sðD:1Þ

where

ei ¼XpreðiÞ � Xexp tlðiÞ

XpreðiÞ

� � 100

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effect of greenhouse on crop drying under natural and forced convection ii. thermal modeling and...

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