and forced convection II. Thermal modeling and experimental validation
Dilip Jain
a,*, G.N. Tiwari
ba Central Institute of Post Harvest Engineering and Technology, PAU Campus, Ludhiana 141 004, India
b 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 forced convection. 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.
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 a complex 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]
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 diffusivity
D coefficient of Eq. (17)
dm dry mass in crop (kg/kg of crop) e root mean square of percent deviation F fraction of solar radiation
fðtÞ 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) = 5.7 (W/m2 °C) hw convective heat transfer coefficient due to wind = 5:7 þ 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 h o u r
PðTÞ 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 pressure r coefficient of correlation
t 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 = Xm=Xm0 dimension less water content
Xm water content (dry basis) (kg water/kg dry matter) Greek letters
a absorptivity of crop surface
P coefficient of volumetric expansion (1/°C)
y e a X
fi
P
T
relative humidity of air (dec.) emissivity
Stefan-Boltzmann constant = 5.6696 x 10"8 (W/m2 K4) latent heat of vaporization (J/kg)
dynamic viscosity of air (kg/m) density of air (kg/m3)
transmissivity Subscripts
0 a c e g i m n r
V
ce gr goo li=0
initial value ambient or air crop
above the crop surface ground or greenhouse floor
greenhouse wall/roof ði = 1; 2;. . .; 6Þ mass
north wall
greenhouse room air humid air or vent crop to environment greenhouse floor to room
greenhouse floor to underground surface of floor of greenhouse
studied the drying process in a greenhouse type solar dryer using natural as well as forced ventilation 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 of regression 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 analytical model of open sun drying and a cabinet type solar dryer. The model was used to predict the hourly variation of crop temperature and rate of moisture evaporation under constant and falling rates of drying. Goyal and Tiwari [6] presented a thermal model to predict the crop parameters for a reverse absorber cabinet type solar dryer. Ratti and Majumdar [7] developed a simulation code to predict the batch drying performance of a packed bed of particles (carrots or apple slices). The model was used to predict the crop temperature and moisture ratio with respect to drying time in a cabinet 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 temperature inside the greenhouse on the basis of ambient conditions. Condon' and Saravia [9] presented an analytical study of the evaporation rate in two types of forced convection greenhouse dryers using single and double chamber systems.
Considering the importance of solar crop drying, in this paper, three simple mathematical models are presented for open sun drying and greenhouse drying under natural and forced convection. 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 are experimentally validated. The agreements of predicted and experimental values are presented with the 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 thermal energy. The working principle of crop drying under open sun is illustrated in Fig. 1a. The solar radiation 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
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 the crop 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 moisture evaporation depends on the vapor pressure difference between the crop and the environment air surrounding 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 ÐFCPIIAISIÞ 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 — agÞ PIiAisiÞ 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 draft takes place due to the temperature difference between the greenhouse air and ambient air. The rate of moisture evaporation depends on the vapor pressure difference between the crop and the greenhouse air. A greenhouse with the forced mode of drying reduces the relative humidity inside the greenhouse and increases the vapor pressure difference, resulting in a faster rate of moisture removal (Fig. 1c).
3. Thermal modeling
Thermal models for prediction of crop temperature and moisture evaporation have been developed using energy balance equations for open sun drying and greenhouse drying under both natural and forced modes. The energy balance equations have been written with the following assumptions:
(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]
1 rw-i
ctJ(t)Ac - hce(Tc - Te)Ac - 0.0l6hc[P(Tc) - yeP(Te)]Ac - hh(Tc - T,)AC = McCc-£- (1) (b) Energy balance equation of moist air above the crop
hUTo - Te)Ac + 0.0\6hc[P{Tc) - yeP{Te)]Ac = hw{Te - T,)AC (2) (c) Moisture evaporated can be evaluated as [11]
mev = 0.0l6-[P(Thc c) - yeP(Te)]Act ð3Þ
3.2. Thermal modeling of greenhouse drying (GHD) under natural mode (Fig. 1b) (a) Energy balance equation at crop surface,
1 rr-i
AiXt = MCCC^ + hc(Tc - Tr)Ac + 0.0\6hc[P(Tc) - yrP{Tx)]Ac (4) (b) Energy balance equation at ground surface
(1 - Fn) ( l -Fc)ag Y.hAtTi = hgQO(T\x=0 - Toa)Ag + hgr(T\x=0 - Tx){Ag - Ac) (5) (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 and ambient air [12]
ð1 - FnÞð1 - FcÞð1 - ag
+ M ^ U - Tx){Ag - Ac) = CdAv^2gAHAP + J] ^ , - ( rr - Ta) (6) where
A « = ^ (7)
PrS
DP = P{Tr) - 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
(1 - Fn) ( l - Fc)(l - <xg) ^hA^ + hc{Tc - Tr)Ac + 0.0\6hc[P{Tc) - y,P{Tt))Ac
+ M ^ U - Tx){Ag - Ac) = 0.33NV{Tr - ra) + J] ^ . - ( ^ - ra) (9)
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 shrinkage in 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 complex to solve the above equations. Therefore, the partial vapor pressure has been linearised for the small range of temperature between 25 and 55 °C, which mostly occurs in solar drying, as
P(T)=RXT þ R2 ð10Þ
4.1. Open sun drying
By substituting the linear expression of partial vapor pressure in Eqs. (1) and (2), the new equations become
1 ry-r
acIðtÞAc - hceðTc - TeÞAc - 0.0\6hc[{R1Tc+R2) - y^T, þ R2)]AC - hbðTc - TaÞAc = McCcd
ð11Þ Mrc - re) +0.0\6hc(RiTc+R2) -0.0\6hcye(RiTe+R2) = hw(Te - Ta) (12) From Eq. (12)
(/ice + 0.016/icfli)rc +R2[0.0\6hc{\ -ye)] + hwTa
£ + 0 0 1 6 ^ 7 ^ + ^
By combining Eqs. (11) and (13) a form of first order differential equation is produced as
-J± + aT =fft\ (14)
where
a= McCc
and
A*) =
McCc
The solution of Eq. (14) for the average fðtÞ for the time interval 0-1 is
^ l - e - a O + r c o e ^ (15)
Once Tc is known, Te can be determined by Eq. (13) and mev by Eq. (3), which can be rewritten as mev = 0.016 — [(Rhc 1Tc þ R2)-ye(R1Te+R2)]Act ð16aÞ
A
4.2. Greenhouse drying under natural mode
The partial pressure of vapor at Tr and Ta has been determined with the help of the linear regression technique as Eq. (10). With the help of Eqs. (5), (7), (8) and (10), Eq. (6) has been simplified in the form of a third order polynomial equation to determine the greenhouse room temperature ðTrÞ for assumed values of crop temperature and ambient temperature as
ATr3 þ BTr2 þ CTrþD = 0 ð17Þ
where
A = {2/Px){CdAv)2R\
B = {2/pr){CdAv)23R2[R2 - ya{RlTa+R2)} - \hcAc + 0.0\6hcAcy,Rx + {UA)goo
C = {2/Px){CAAv)23Rx[R2 - ya(RiT, +R2)}2 + \hcAQ + O.OUhcA^^ + (UA)go
ffjj + ^g/effG + ^ ^crc + 0 . 0 1 6 / ^ ( ^ 7 ; + R2 - 7rR2)
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 as Eq. (14) where
hcAcð1 þ0:016R1Þ
a = McCc
and
IeffC þ hcAc[Tr - 0:016fR2 - crðR1Tr þ R2)}}
McCc
Once the temperatures of the crop and greenhouse room air are known, the rate of moisture evaporation can be evaluated with the expression
hc
mev = 0.016 — [{RXTC +R2) - crðR1Tr þ R2)]Act ð16bÞ 4.3. Greenhouse drying under forced mode
With the help of Eqs. (9) and (10), Eq. (9) has been simplified to determine the greenhouse room temperature under forced mode for assumed values of crop temperature and ambient temperature as
_ effR þ hcAcTc þ 0:016ðR1 Tc þ R2 - crR2Þ þ HgIeffG þ [0.33NV hcAc þ 0:016hccrR1 þ ðUAÞg1 þ 0:33NV þ P
ð18Þ If the value of room air temperature ðTrÞ is known, with the help of Eq. (4) the crop temperature ðTcÞ can be determined, which is in the form of a first order differential equation as Eq. (14). The derivatives of a and fðtÞ are the same as those of the case of greenhouse drying under natural mode. 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 mathematical models. 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 drying were obtained from the two term exponential expression.
hc = A A2 19Þ
The coefficients of the exponential expression for the different modes of drying for cabbage and peas have been obtained by Jain and Tiwari [15] and are presented in Table 2. The constant and input values for cabbage and peas are given in Tables 3 and 4, respectively.
Table 1
Ambient data used in modeling Drying
time (h) 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
September 2001 IðtÞ (W/m2) 160
240 380 600 680 700 560 500 280 100 20 0 0 0 0 0 0 0 0 0 0 0 0 20 160 240 380 600 680 700 560 500 280 100
Ta (°c)
30.4 31.1 34.5 34.5 35.8 35.5 36.3 39.0 34.6 35.4 33.7 34.0 34.0 34.0 34.0 34.0 33.6 33.0 32.5 32.2 32.0 31.7 31.1 29.7 31.4 33.0 35.0 35.3 35.7 38.0 39.2 39.0 36.4 35.1
ovember 2001 IðtÞ ( W / m2)
80 280 400 500 520 460 500 500 180 40 0 0 0 0 0 0 0 0 0 0 0 0 0 20 60 2 0 440 500 580 600 500 300 00 20
Ta (°c)
24.8 29.6 31.2 32.0 33.3 34.8 37.2 35.1 34.0 30.0 29.0 29.0 28.9 28.2 28.0 27.8 27.2 26.8 26.0 25.4 25.0 24.2 22.8 23.3 24.0 29.0 31.2 32.2 34.8 33.6 37.1 36.6 32.6 35.120
November IðtÞ (W/m2)
60 200 300 380 400 440 360 220 80 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 20 200 340 420 480 420 380 220 100 20
2001
Ta (°c)
18.4 18.1 21.6 24.4 25.5 29.3 29.4 28.6 25.1 21.5 20.8 20.0 19.8 19.6 19.2 17.8 17.0 16.6 16.2 15.8 14.5 13.8 14.2 15.8 16.4 20.6 22.2 25.4 27.1 28.4 28.3 27.6 25.0 22.0
December 2001 IðtÞ ( W / m2)
20 80 220 280 320 300 240 180 80 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 20 220 300 400 380 360 300 200 100 20
Ta (°c)
15.5 17.0 19.5 21.2 22.4 24.1 23.8 23.4 22.0 20.9 19.0 18.8 18.6 18.5 18.5 16.5 14.7 13.8 13.0 12.8 12.2 12.1 13.7 14.4 15.2 17.0 17.8 19.6 21.1 22.6 23.1 23.8 23.0 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
OSD OSD
GHD natural mode GHD natural mode GHD forced mode GHD forced mode
Cabbage Peas Cabbage Peas Cabbage Peas
September October September October November December
A1 3.5174 0.1584 10.0664 11.9934 1.4531 )0.0334
h
)0.0960 )0.0337 )0.0968 )0.0855 )0.1008 0.0636
A2
27.2136 24.2968 10.2387 1.6550 41.6293 38.3583
h
)0.1834 )0.1612 )0.2094 )0.2448 )0.1444 )0.0905
Table 3
Constant used in modeling
Parameters Values
Cd g
K
Mc
T
V
ag
1 8 a x
1012 0.425 9.81 5.7 5:7 þ 3:8v 8.0 0.300 3600 397.52 )7926.90 0.5 0.6 2.26 xlO6
0.9 5.67 xl0~s
0.9
For open sun drying, the average hourly solar radiation on a horizontal surface and ambient air temperature were used for evaluation of the crop temperature from Eq. (15). Then, the temperatures above the crop surface and the moisture evaporation during the corresponding hour were computed from Eqs. (3) and (16a), respectively.
A roof type even span greenhouse with an effective floor covering of 1.2x0.8 m2, the central height of 0.60 m and height of walls of 0.40 m was used for the modeling of greenhouse drying. The average hourly solar radiation on the different walls and roofs of the greenhouse was evaluated from the average hourly solar radiation on a horizontal surface with help of the Liu and Jordan formula [16] for Delhi (Latitute-28°35')- Then, the average hourly total radiation received by the greenhouse was the sum of the average hourly radiations of the walls and roofs of the greenhouse. Thus, the average hourly total radiation received by the greenhouse and the average hourly ambient air temperature were used as input data to compute the hourly temperature of the crop and greenhouse room air through simulation. The moisture evaporation was calculated with the help of Eq. (16b).
Table 4
Input values of crops used for modeling
CCC
Cc dm
Fc (first and second day) Open sun drying
ce
Tc Te
GHD natural mode
ca cr
Tc
T
GHD forced mode
ca cr
Tc Tr
V
N
0.32x0.26 0.4 3900 0.070 0.25, 0.025
0.65 29.25 32.5
0.50 0.65 30.0 32.0
0.50 0.45 11.25 15.9 0.5 30
Parameter Cabbage Peas 0.20x0.20 0.5 3060 0.450 0.15,0.03
0.45 26.25 27.8
0.40 0.50 26.75 27.9
0.50 0.50 13.5 15.35 0.5 30
The predicted temperatures of the crop and greenhouse chamber and the moisture evaporation from the different drying models have been compared with the experimental data given by Jain and Tiwari [15]. The goodness of agreement has been determined with the help of the coefficients of 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 of September 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 respective experimental values are presented in Fig. 2a and b. The closeness of the predicted and experimental values has been determined with the help of the coefficient of correlation ðrÞ and root mean square of percent deviation ðeÞ. The best possible agreement of predicted and experimental values are at values of 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 from 8.39 to 13.14. The coefficient of correlation ðrÞ ranges from 0.77 to 0.96. The predicted values of
o 60
50
40
- 20
i
H (a)
10
September 2001 —it— Ambient temp.
- © - Predicted crop temp.
- © - Exptl crop temp.
s— Predicted temp.above crop surface - B - Exptl temp. above crop surface -6— Predicted crop mass
rc = 0.87; ec = 8.39 % re = 0.77; ee = 9.55 % 0.99; e =4.49%
10 15 20 25 Drying time in hour
30
Mftp
O
GO
s
-aCan
c
ure
0
empei
H 50
40
30
20
10
n
October 2001
jzf ©•>
- * -
- e -
- © -
- s -
- B - - * — - * -
Ambient temp.
Predicted crop temp.
Exptl crop temp.
Predicted temp.above crop surface Exptl temp. above crop surface Predicted crop mass Exptl crop mass
'f JjHQi
/yd EJ\^
f>TJ ^ l o
£ , , . . . . . i , ~ , ,
rc = 0.96; ec = 8.85 % re = 0.94; ee =13.14%
rm = 0.98; em =3.72%
(b)
10 15 20 25
Drying time in hour
30 35
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 values with the coefficient of correlation as 0.99 and 0.98 and root mean square of percent deviation as 4.49 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 the process utilized the solar intensity for evaporation. Therefore, the temperature of the crop did not rise much more than ambient due to the cooling effect by evaporation of the moisture. During the night hours (11-24 h of drying time), the temperature of the crop remained very close to ambient and 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 significantly higher than ambient due to the absorption of solar radiation. The crop got more drying during this 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 has also 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 mass along with the experimental values. These figures clearly indicate that the agreement of the predicted 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 of percent 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 mass during drying for cabbage and peas are 0.99 and 0.98, respectively. The agreement of crop mass was within the root mean square of percent deviation as 4.72 and 2.98 for cabbage and peas, respectively.
o
I °
(a)
M 60 o
X 50 c S 40
o2
Ambient temp.
Predicted crop temp.
e- Exptl crop temp.
H— Predicted room temp.
H - Exptl room temp.
3— Predicted crop mass A 0 Exptl crop mass
30 O
1
&
(b) 20
10
10 15 20 25 Drying time in hour
30
—*— Ambient temp.
—01 Predicted crop temp.
- ©- Exptl crop temp.
—B— Predicted room temp.
- B- Exptl room temp.
—*— Predicted crop mass crop mass
35
10 15 20 25 Drying time in hour
30 35
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 under natural 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 been predicted for the ambient data of November and December 2001 for cabbage and peas with the help of the model developed for greenhouse drying under forced convection. The predicted values and 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 temperatures and 0.98-0.99 for the crop mass. The root mean square of percent deviation of the predicted values
60
U 20
10 M O X
c
1
1
ug -a
50
40
30
November
rc = 0.92; ec
rr = 0.97; er
rm = 0.99; e 2001
= 13.82%
= 5.48 %
n = 8.43 %
—+— Ambient temp.
—©— Predicted crop temp.
- 0 - Exptl crop temp.
—B— Predicted room temp.
- B - Exptl room temp.
—*— Predicted crop mass -*- Exptl crop mass
(a)
10 15 20 25 Drying time in hour
30
00 6 0
o X 50
S 40 U
a U c
|
I
H
(b)
30
20
10
December 2001
rc = 0.94; ec = 16.55 % rr = 0.94; er = 6.34 % rm = 0.98; em = 3 . 8 8 %
—*— Ambient temp.
—e- Predicted crop temp.
- 0 - Exptl crop temp.
—B— Predicted room temp.
- B - Exptl room temp.
-^— Predicted crop mass - 4 % Exptl crop mass
10 15 20 25 Drying time in hour
30 35
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 dried under forced mode inside the greenhouse did not attain so high temperature from the ambient because 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 drying without raising the crop temperature.
7. Conclusion
Three simple mathematical models were developed to predict the crop temperature, greenhouse room temperature and moisture evaporation for open sun drying (natural convection) and greenhouse drying under natural and forced convection. These models were validated with experimental 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 and 0.98-0.99 for the crop mass during drying (for rate of moisture evaporation).
Appendix A. Expressions used in thermal modeling
Ieff C = ð1 - FnÞFcac X IiAisi ðA: 1Þ
= ( l - Fn) ( l - Fc) ag^ ^I- TI- (A.2)
hmA' r l ðA:4Þ
(A.5)
hce = hc þ hr ðA:7Þ
Appendix B. Shrinkage ratio
Crop area is a function of the moisture ratio. Ratti [13] studied the shrinkage during drying of foodstuff 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 solving the above mathematical models. The expression used is
— = 0.339 + \.2A6Wm - 1.385^ + 0.792fl£ (B.I)
where Wm = XXm.
Appendix C. Procedure of calculation of coefficient of correlation (r) [17]
r =
Appendix D. Procedure of calculation of root mean square of percent deviation (e)
(D.I)
et = p w p "w x 100
References
[1] Basunia MA, Abe T. Thin layer solar drying characteristics of rough rice under natural convection. J Food Eng 2001;47:295-301.
[2] Manohar KR, Chandra P. Drying of agricultural produce in a greenhouse type dryer. Int Agric Eng J 2000;9(3):
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