effect of greenhouse on crop drying under natural and forced convection i: evaluation of convective...

Energy Conversion and Management 45 (2004) 765–783www.elsevier.com/locate/enconman

Effect of greenhouse on crop drying undernatural and forced convection

I: Evaluation of convective mass transfer coefficient

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 12 April 2002; received in revised form 15 February 2003; accepted 5 July 2003

Abstract

In this paper, a study of convective mass transfer coefficient and rate of moisture removal from cabbage

and peas for open sun drying and inside greenhouse drying has been performed as a function of climatic

parameters. The hourly data for the rate of moisture removal, crop temperature, relative humidity inside

and outside the greenhouse and ambient air temperature for complete drying have been recorded. The

experiments were conducted after the crop harvesting season from September to December 2001. These

data were used for determination of the coefficient of convective mass transfer and then for development ofthe empirical relation of convective mass transfer coefficient with drying time under natural and forced

modes. The empirical relations with convective mass transfer for open and greenhouse drying have been

compared. The convective mass transfer coefficient was lower for drying inside the greenhouse with natural

mode as compared to open sun drying. Its value was doubled under the forced mode inside the greenhouse

drying compared to natural convection in the initial stage of drying.

� 2003 Elsevier Ltd. All rights reserved.

Keywords: Solar energy; Crop drying; Convective mass transfer; Greenhouse

1. Introduction

The most primitive crop drying process is known as open sun drying (OSD), under which solarradiation falls directly on the crop surface and is absorbed. The absorbed radiation heats the crop

* Corresponding author. Tel.: +91-11-2659-1258; fax: +91-11-2659-2208/2686-2037.

E-mail address: [email protected] (G.N. Tiwari).

0196-8904/$ - see front matter � 2003 Elsevier Ltd. All rights reserved.

doi:10.1016/S0196-8904(03)00178-X

mail to: [email protected]

Nomenclature

A area (m2)C constant or specific heat (J/kg �C)d average height of greenhouse (m)g acceleration due to gravity (m/s2)Gr Grashof number ¼ bgX 3q2vDT=l

2v

hc convective heat transfer coefficient (W/m2 �C)IðtÞ solar intensity on horizontal surface (W/m2)K thermal conductivity (J/m2 �C)mev moisture evaporated (kg)n constantNu Nusselt number ¼ hcX=KvPr Prandtl number ¼ lvCv=KvP ðT Þ partial vapour pressure at temperature T (N/m2)Qe rate of heat utilized to evaporate moisture (J/m2 s)Re Reynolds number ¼ qvvd=lvr coefficient of correlationt time (s)T temperature (�C) and time (h)Ti average of crop and humid air temperature (�C)T average temperature (�C)DT effective temperature difference (�C)v air velocity inside greenhouse (m/s)X characteristic dimension (m)

Greek lettersb coefficient of volumetric expansion (1/�C)c relative humidity (dec.)k latent heat of vaporization (J/kg)l dynamic viscosity of air (kg/m)q density of air (kg/m3)v2 mean square deviation

Subscriptsa ambientc crope above crop surfacer greenhouse roomv humid airt tray

766 D. Jain, G.N. Tiwari / Energy Conversion and Management 45 (2004) 765–783

D. Jain, G.N. Tiwari / Energy Conversion and Management 45 (2004) 765–783 767

and evaporates the moisture from the crop. During this process, the amount of solar energyreceived at the crop surface is lost at various stages through reflection, radiation, convectionand conduction. Placing a plastic covering over the crop produces a greenhouse effect to trapthe solar energy in the form of thermal heat radiation and prevents conduction heat loss. Therate of drying (moisture evaporation) depends on a number of external parameters (solar radi-ation, ambient temperature, wind velocity and relative humidity) and internal parameters (ini-tial moisture contents, type of crops, crop absorptivity, mass of product per unit exposed areaetc.).Greenhouse driers have the regular greenhouse structure (when not in use for crop production),

where the product is placed in trays receiving solar radiation through the plastic cover, whilemoisture is removed by natural convection or forced air flow [1,2].Modeling drying of crops under solar energy is a complex problem involving simultaneous heat

and mass transfer in a hygroscopic nature of crop. Convective heat transfer coefficients are one ofthe most critical parameters required for analysis and simulation of the process. Several re-searchers have presented various numerical models for moisture migration, considering diffusionas the primary transport mechanism [3–5].Dincer and Dost [5] presented a method to determine the moisture diffusion coefficient

and moisture transfer coefficient for a solid object by employing the drying coefficient andlag factor. Smith and Sokhansanj [6] have developed a natural convection heat transfermodel in which the density of air was assumed to be a function of temperature and absolutehumidity.Ratti and Crapiste [7] evaluated the heat transfer coefficient under forced convection from the

data on crop drying and heat and mass balances. The experimental heat transfer coefficientswere correlated by dimensionless expressions with Nusselt and Reynolds numbers. The experi-mental heat transfer coefficient values ranged from 25 to 90 W/m2 K for potatoes, apples andcarrots. Anwar and Tiwari [8] evaluated the convective heat transfer coefficients for some cropsunder a simulated condition of forced mode in indoor open and closed conditions. Anwar andTiwari [9] determined the convective heat transfer under open sun drying by using the linearregression technique. Their study was limited to constant rate drying from 11 to 13.30 h of theday. The single value of convective heat transfer was evaluated for each crop for the wholedrying process.Thus, the purpose of this work was to evaluate the heat transfer coefficient at every hour of

drying time for cabbage and peas with the following conditions:

(a) Open sun drying (OSD) under natural convection.(b) Greenhouse drying (GHD) under natural convection.(c) Greenhouse drying (GHD) under forced convection.

The hourly data for rate of moisture removal, crop temperature, relative humidity inside andoutside the greenhouse and ambient air temperature for the complete drying period have beenrecorded. The experiments were conducted after the crop harvesting season from September toDecember 2001. These data were used for determination of the coefficient of convective heattransfer. A suitable empirical model is presented to regress the convective heat and mass transfercoefficients as a function of drying time.


2. Theory

2.1. Determination of convective heat transfer coefficient

The Nusselt number is a function of the Grashof and Prandtl numbers for natural convection.Similarly, for forced convection, it is a function of the Reynolds and Prandtl numbers [10].

Nu ¼ hcXKv

¼ CðGrPrÞn for natural convection ð1aÞ

¼ CðRePrÞn for forced convection ð1bÞ

Thus, the convective heat transfer coefficient under natural convection can be determined as

hc ¼ KvX

CðGrPrÞn ð2Þ

The rate of heat on account of mass transfer (evaporate moisture) is given as [11]

Qe ¼ 0:016hc½PðTcÞ � cPðTeÞ� ð3Þ
The hc in the above expression with moisture evaporation is termed the convective mass transfercoefficient in the case of crop drying.On substituting hc from Eq. (2), Eq. (3) becomes
Qe ¼ 0:016KvX

CðGrPrÞn½PðTcÞ � cP ðTeÞ� ð4Þ

The moisture evaporated is determined by dividing Eq. (4) by the latent heat of vaporization (k)and multiplying by the area of the tray (At) and time interval (t).

mev ¼Qe

kAtt ¼ 0:016

KvXk

CðGrPrÞn½PðTcÞ � cP ðTeÞ�Att ¼ ZCðGrPrÞn ð5Þ

where Z ¼ 0:016 KvXk ½P ðTcÞ � cP ðTeÞ�tAt,

mev

Z¼ CðGrPrÞn ð6Þ

Taking the logarithm of both sides of Eq. (6)

lnmev

Z

h i¼ n lnðGrPrÞ þ lnC ð7Þ

This is the form of a linear equation, Y ¼ mX0 þ C0, where

Y ¼ lnmev

Z

h i; m ¼ n; X0 ¼ ln½GrPr� and C0 ¼ lnC; thus; C ¼ eC0

Similarly, in the case of forced convection,

Y ¼ lnmev

Z

h i; m ¼ n; X0 ¼ ln½RePr�; C0 ¼ lnC and C ¼ eC0

Therefore, once the rate of moisture evaporation, crop temperature and temperature and relativehumidity above the crop surface are known, then the values of Y and X0 can be computed to put


into the linear form to find the m and C0. Now, the m and C0 give the values of n and C, re-spectively, of Eq. (2) for evaluation of the convective mass transfer coefficient.

2.2. Exponential curve fitting

Yaldiz et al. [12] presented regression analyses of various mathematical models betweenmoisture ratio and drying time for thin layer solar drying of sultana grapes. They concluded thatthe two term exponential curve model was most acceptable. Similarly, the regression analysis hasbeen done with exponential curve fitting (two term) as the convective mass transfer coefficient is afunction of drying time.

hc ¼ A1 expðk1T Þ þ A2 expðk2T Þ ð8Þ
The constants A1, A2, k1 and k2 were computed using the technique of Moore [13]. The aboveexpression of the two term exponential curve model was used to present the purely empirical re-lationship between the convective mass transfer coefficient and drying time. This can be employedonly within the limits of drying time (independent variable) where this is corroborated by experi-ments. This is not to be extrapolated for larger or smaller values of the arguments. The goodness offit was ascertained by the coefficient of correlation and the mean square of deviation [14].
3. Materials and methods

3.1. Experimental set up

Wire mesh trays of 0.32· 0.26 m2 and 0.20· 0.20 m2 were used to accommodate 0.300 kgsamples of cabbage and peas as thin layers, respectively. A roof type even span greenhouse withan effective floor covering 1.2· 0.8 m2 has been made of PVC pipe and UV film covering. Thecentral height and height of the walls were 0.60 and 0.40 m, respectively. An air vent was providedat the roof with an effective opening of 0.043 m2 for natural convection. The experimental set upfor open sun drying and greenhouse drying in the natural mode is shown in Fig. 1a. A fan of 225mm sweep diameter with air velocity 5 m/s was provided on the sidewall of the greenhouse duringthe experiments of forced convection (Fig. 1b). The greenhouse had an east–west orientationduring the experiments.

3.2. Instrumentation

A non-contact thermometer (Raytek-MT4), having a least count of 0.5 �C and accuracy of ±2%on a full scale range of )18 to 260 �C was used for measurement of the crop temperature. A digitalhumidity/temperature meter (model Lutron HT-3003) was used to measure the relative humidityand temperature of air in the greenhouse, of ambient and above the crop surface. It had a leastcount of 0.1% relative humidity with accuracy of ±3% on the full scale range of 5–99.9% ofrelative humidity and 0.1 �C temperature with accuracy of ±1% on the full scale range of 10–80�C. A top loading digital balance (Sansui) of 1 kg weighing capacity, having a least count of 0.1 gwith ±2% on the full scale was used to weigh the sample during drying. The difference in weight

Fig. 1. (a) Experimental setup of open sun drying and greenhouse drying under natural convection. (b) Experimental

setup of greenhouse drying under forced convection.


gave the moisture evaporated during that time interval. The solar intensity was measured with acalibrated solarimeter, locally named Suryamapi (Central Electronics Ltd., India). It measuressolar radiation in mW/cm2, having a least count of 2 mW/cm2 with ±2% accuracy of the full scalerange of 0–120 mW/cm2. The air velocity across the greenhouse section during the forced modedrying was measured with an electronic digital anemometer model of Lutron AM-4201. It had aleast count of 0.1 m/s with ±2% on the full scale range of 0.2–40.0 m/s.

3.3. Sample preparation

The fresh cabbage was cut into small slices. The peas were soaked in water for 12 h and thanconditioned in a shed for 2 h after removing the excess water. The same sizes of samples weremaintained simultaneously for open sun drying and inside the greenhouse in all cases.

3.4. Experimentation

Experiments were conducted in the months of September, October, November and December2001 for natural convection and November and December 2001 for forced convection in theclimatic conditions of New Delhi.The 0.300 kg samples were kept in the wire mesh tray for the experiments. Observations were

taken under open sun and inside the greenhouse simultaneously. The observations were recordedfrom 8 AM at every hour interval for the 33 h of continuous drying. All the experiments ofgreenhouse drying (GHD) have been conducted simultaneously with the open sun drying (OSD)for comparative study. The experiments on OSD were always under natural convection. Naturalconvection under GHD was done with the air vent provided at the roof of the greenhouse. Ex-periments in the forced mode under GHD were conducted by providing the ventilating fan on thesidewall of the greenhouse. The air velocity across the greenhouse was measured to be 0.5 m/s withthe help of the anemometer. The sample data for the natural and forced convection modes ofdrying under open sun and inside the greenhouse are presented in Tables 1–4.

Table 1

Observation on open sun drying and greenhouse drying under natural convection for sample cabbage (initial weight of

sample¼ 300 g) (month––September, 2001)Drying

time (h)

IðtÞW/m�2

Ta (�C) Open sun drying Greenhouse drying

Tc (�C) Te (�C) c (%) mev (g) Tc (�C) Tr (�C) c (%) mev (g)

0 160 30.4 28.0 31.1 73.5 – 28.5 31.0 70.1 –

1 240 31.1 30.5 34.0 62.8 38.2 30.5 32.1 72.2 30.3

2 380 34.5 33.0 36.5 67.0 40.6 33.5 36.4 61.0 33.5

3 600 34.5 35.0 35.8 63.8 38.1 37.0 36.3 66.5 34.3

4 680 35.8 39.0 37.5 63.2 31.8 39.5 39.5 67.7 30.0

5 700 35.5 35.0 36.0 69.0 27.0 39.0 37.5 65.2 25.6

6 560 36.3 41.6 36.9 53.1 26.9 44.0 37.8 54.7 26.6

7 500 39.0 41.5 37.6 54.6 19.7 42.9 39.9 53.2 21.2

8 280 34.6 42.5 39.2 51.0 14.4 40.5 37.2 55.0 15.8

9 100 35.4 38.5 36.8 52.3 8.2 39.0 37.2 50.7 11.8

10 20 33.7 34.0 33.8 67.4 4.7 33.5 34.0 61.9 5.9

11 0 34.0 34.0 34.0 63.6 2.8 33.5 34.0 64.0 3.2

12 0 34.0 34.0 33.8 65.2 2.2 33.0 33.8 66.2 2.4

13 0 34.0 34.0 33.2 65.9 1.6 32.8 33.2 67.5 2.2

14 0 34.0 34.0 33.0 68.1 1.4 32.6 33.0 68.2 2.2

15 0 34.0 34.0 32.6 69.5 1.0 32.5 32.7 69.2 1.9

16 0 33.6 33.8 32.2 69.2 1.0 32.2 32.6 69.0 1.6

17 0 33.0 33.4 32.1 69.0 1.0 32.0 32.2 69.6 1.6

18 0 32.5 33.0 30.8 69.9 1.0 31.8 32.0 69.8 1.6

19 0 32.2 32.6 30.6 70.0 1.0 31.5 31.8 70.1 1.6

20 0 32.0 32.1 30.2 70.1 1.0 31.0 31.2 70.4 1.6

21 0 31.7 32.0 30.0 70.6 1.0 30.0 30.5 70.2 1.6

22 0 31.1 29.4 29.5 71.2 1.0 29.1 29.8 69.8 1.6

23 20 29.7 28.5 29.0 71.8 1.0 28.5 29.2 70.5 1.6

24 160 31.4 32.2 31.2 62.9 0.3 34.0 32.5 60.0 1.2

25 240 33.0 36.5 33.3 60.4 2.3 36.0 33.9 57.5 0.5

26 380 35.0 43.0 35.7 54.5 2.1 42.5 37.5 49.7 3.4

27 600 35.3 43.5 36.9 64.1 1.5 43.5 37.7 51.3 1.6

28 680 35.7 42.5 36.6 54.6 1.5 47.5 37.7 51.5 3.1

29 700 38.0 47.5 38.8 47.0 0.9 47.5 42.8 41.0 3.0

30 560 39.2 48.0 41.8 45.8 0.1 48.0 43.8 41.2 2.8

31 500 39.0 50.5 44.2 44.6 0.1 49.5 48.0 40.1 0.1

32 280 36.4 47.5 44.0 38.5 0.1 47.5 46.8 37.8 0.1

33 100 35.1 44.5 43.1 40.1 0.1 44.5 43.2 40.1 0.1


3.5. Computation technique

The average crop temperature (Tc) and temperature above the crop surface (Te or Tr in the casesof crop inside the greenhouse) were calculated at each hour interval with corresponding rate ofmoisture evaporated. The physical properties of humid air were evaluated for the mean tem-perature of Tc and Te, or Tr, by using the expression given in Appendix A [15]. The values of C andn were obtained by a linear regression technique at increments of every hour of observation, andthus, the values of hc were computed at the corresponding hour of drying. The hourly variations

Table 2

Observation on open sun drying and greenhouse drying under natural convection for peas (initial weight of sample ¼300 g) (month––October, 2001)

Drying

time (h)

IðtÞW/m�2



0 80 24.8 23.5 25.5 81.7 – 23.5 25.3 84.0 –

1 280 29.6 29.0 30.1 76.5 9.0 30.0 30.5 78.7 6.1

2 400 31.2 30.5 30.1 67.1 18.9 35.0 31.2 78.8 10.2

3 500 32.0 33.5 32.9 51.3 22.4 35.0 34.4 66.2 17.2

4 520 33.3 32.5 31.2 45.1 25.1 37.0 34.1 52.6 20.9

5 460 34.8 37.5 33.9 42.0 24.7 38.0 35.2 43.2 22.6

6 500 37.2 43.5 36.9 37.5 15.1 38.5 39.8 40.0 18.3

7 500 35.1 41.0 35.6 31.7 9.1 38.0 35.7 40.7 13.5

8 180 34.0 38.0 33.0 40.5 3.8 35.5 34.1 52.1 8.5

9 40 30.0 30.0 31.1 60.7 3.0 32.0 30.8 64.4 4.6

10 0 29.0 30.0 30.3 55.2 1.9 30.5 29.8 60.5 3.4

11 0 29.0 30.0 29.0 57.2 1.5 27.5 29.0 58.0 2.4

12 0 28.9 30.0 28.7 59.0 1.5 27.5 29.0 57.0 1.2

13 0 28.2 30.0 28.5 59.0 0.7 27.5 29.0 59.0 1.2

14 0 28.0 30.0 28.4 59.2 0.4 27.5 28.8 60.0 1.2

15 0 27.8 30.0 28.3 59.3 0.5 27.5 28.5 60.2 1.2

16 0 27.2 29.5 28.1 59.3 0.3 27.0 28.3 60.0 1.0

17 0 26.8 28.0 28.0 59.0 0.2 26.5 28.0 60.0 1.0

18 0 26.0 28.0 27.8 59.0 0.2 26.0 27.7 60.0 1.0

19 0 25.4 27.0 27.0 59.0 0.2 26.0 27.1 60.0 0.9

20 0 25.0 26.0 26.2 59.0 0.2 26.0 26.0 60.0 0.9

21 0 24.2 25.0 25.8 59.0 0.2 25.5 25.4 60.0 0.9

22 0 22.8 24.0 26.0 59.0 0.2 24.0 25.0 60.0 0.8

23 20 23.3 24.5 25.6 58.8 0.2 24.0 25.0 60.9 0.8

24 60 24.0 25.0 25.9 62.0 0.2 24.5 25.2 61.7 0.7

25 280 29.0 35.0 29.5 51.0 0.2 31.5 30.3 64.0 1.2

26 440 31.2 41.0 31.6 48.3 2.2 38.0 31.8 53.8 1.2

27 500 32.2 45.0 31.2 48.4 1.4 45.0 33.4 45.5 1.4

28 580 34.8 49.5 35.4 38.6 1.6 49.5 36.4 45.5 1.4

29 600 33.6 49.5 36.5 37.1 0.8 51.0 36.1 36.3 1.3

30 500 37.1 49.5 36.2 37.7 0.4 51.0 39.9 35.7 1.1

31 300 36.6 45.5 35.8 39.2 0.7 46.0 38.9 35.8 0.6

32 60 32.6 39.5 32.3 46.4 0.1 39.0 32.6 46.9 0.2

33 20 30.0 35.0 27.0 45.0 0.1 33.0 30.0 48.0 0.1


in the experimental convective mass transfer coefficients were fitted to the two term exponentialcurve model. The coefficient of correlation and mean square of deviation were computed for theexperimental hc divided by predicted hc for suitability of the model. The computer program wasprepared in the Matlab-5.3 software [16].The experimental error has been determined in terms of percent uncertainty (internal and ex-

ternal) for the most sensitive parameter, i.e. the rate of moisture evaporation (Appendix B) [17],and presented in Table 5.

Table 3

Observation on open sun drying and greenhouse drying under forced convection for cabbage (initial weight of

sample ¼ 300 g) (month––November, 2001)

Drying

time (h)

IðtÞW/m�2



0 60 18.4 10.5 17.6 65.8 – 9.5 14.7 55.8 –

1 200 18.1 14.5 19.1 58.3 8.4 13.0 17.1 50.6 30.4

2 300 21.6 16.5 20.0 45.4 21.4 17.5 19.6 50.4 34.8

3 380 24.4 20.5 22.2 40.7 33.8 20.0 22.9 53.7 45.9

4 400 25.5 24.5 24.2 40.0 39.5 22.0 25.1 48.5 41.5

5 440 29.3 24.0 28.2 38.0 37.3 27.5 30.1 42.6 32.0

6 360 29.4 24.5 26.2 45.3 37.2 27.5 29.3 42.9 28.3

7 220 28.6 24.5 24.8 45.9 22.0 26.0 27.6 37.2 16.6

8 80 25.1 22.0 24.6 39.7 15.9 24.0 25.5 37.1 11.8

9 20 21.5 19.0 22.8 48.7 15.4 19.5 22.8 52.2 6.1

10 0 20.8 19.0 22.2 49.4 4.6 19.5 22.4 52.0 3.2

11 0 20.0 18.5 22.0 50.1 4.5 19.5 22.2 51.8 2.8

12 0 19.8 18.5 21.8 50.5 3.5 19.5 22.0 51.4 2.5

13 0 19.6 18.5 21.8 51.2 2.6 19.5 21.9 51.2 2.4

14 0 19.2 18.5 21.8 51.4 2.4 19.5 21.8 51.2 2.4

15 0 17.8 17.5 21.0 51.6 2.0 18.5 21.0 51.6 1.2

16 0 17.0 17.0 18.2 51.2 1.5 18.0 18.2 51.4 0.9

17 0 16.6 17.0 16.6 50.8 1.5 17.5 16.8 50.4 0.8

18 0 16.2 15.5 16.3 50.2 1.4 16.0 16.3 50.6 0.7

19 0 15.8 14.0 15.5 52.4 1.4 15.0 15.8 51.6 0.7

20 0 14.5 13.0 14.7 48.6 1.4 13.5 15.0 50.0 0.7

21 0 13.8 11.5 14.3 50.7 1.3 11.5 14.5 50.6 0.7

22 0 14.2 10.5 15.2 52.6 1.3 11.0 15.5 51.7 0.7

23 0 15.8 10.0 15.7 53.2 1.3 11.0 16.0 52.8 0.7

24 20 16.4 10.5 16.3 53.5 1.3 11.5 16.3 52.9 0.6

25 200 20.6 20.0 20.0 44.2 1.0 18.5 20.4 42.6 0.4

26 340 22.2 27.5 21.8 42.8 0.9 24.5 22.1 41.0 0.8

27 420 25.4 32.5 24.5 44.2 2.8 26.5 25.7 59.8 0.8

28 480 27.1 34.5 26.1 43.0 1.7 32.0 28.2 38.0 0.8

29 420 28.4 37.0 27.8 33.1 1.3 32.0 30.3 31.8 0.6

30 380 28.3 34.5 26.8 34.8 0.1 32.5 30.2 28.8 0.2

31 220 27.6 33.5 26.0 32.6 0.1 29.5 27.7 28.9 0.1

32 100 25.0 29.0 25.2 34.1 0.1 26.5 25.0 33.8 0.1

33 20 22.0 24.0 22.0 35.0 0.1 23.0 22.0 35.0 0.1


4. Results and discussion

4.1. Temperature and relative humidity differences

The temperature differences of crop and above the crop with drying time are shown in Fig. 2aand b for cabbage and peas, respectively, for various modes of drying. The higher temperaturedifferences were observed under GHD with natural convection due to trapping of the heat insidethe greenhouse under natural ventilation. The higher temperature difference at the end of OSD

Table 4

Observation on open sun drying and greenhouse drying under forced convection for peas (initial weight of sample ¼300 g) (month––December, 2001)

Drying

time (h)

IðtÞW/m�2



0 20 15.5 12.5 15.5 82.5 – 12.5 15.0 84.8 –

1 80 17.0 14.0 16.4 76.4 2.4 14.5 15.7 80.2 4.2

2 220 19.5 15.5 18.9 72.4 2.8 15.0 19.2 65.2 6.2

3 280 21.2 20.0 19.7 65.1 7.3 18.5 20.1 55.8 13.3

4 320 22.4 20.5 21.1 56.6 13.6 19.0 22.1 48.0 19.1

5 300 24.1 22.0 22.3 51.5 15.8 19.5 23.2 45.7 20.9

6 240 23.8 21.5 22.3 53.3 16.5 20.5 23.6 51.9 20.7

7 180 23.4 20.5 21.8 50.8 14.0 21.0 23.3 52.7 13.1

8 80 22.0 18.5 21.3 50.7 7.2 21.5 21.5 51.4 6.7

9 20 20.9 17.0 20.3 54.8 2.7 18.0 20.1 56.5 4.5

10 0 19.0 17.0 19.8 55.2 2.0 17.5 19.8 54.2 3.4

11 0 18.8 17.0 19.7 57.8 1.8 17.5 19.4 55.6 2.6

12 0 18.6 17.0 19.6 58.7 1.6 17.0 19.2 56.5 2.3

13 0 18.5 17.0 19.5 50.1 1.5 17.0 19.0 50.4 2.0

14 0 18.5 17.0 19.5 53.5 1.5 17.0 18.8 54.9 2.0

15 0 16.5 16.0 18.8 53.1 1.3 16.0 18.6 55.0 1.2

16 0 14.7 14.5 18.4 52.2 1.3 15.5 18.2 51.4 1.0

17 0 13.8 14.0 16.2 58.8 1.3 15.0 16.2 57.8 0.8

18 0 13.0 13.5 15.1 57.2 1.2 14.0 14.8 58.2 0.8

19 0 12.8 13.0 14.2 55.5 1.2 13.5 13.2 56.1 0.8

20 0 12.2 13.0 13.0 50.4 1.2 13.5 12.8 55.8 0.6

21 0 12.1 12.0 13.1 52.1 1.0 13.0 12.4 55.5 0.5

22 0 13.7 12.5 14.8 56.6 1.0 13.0 13.7 56.7 0.5

23 0 14.4 13.5 16.5 58.2 1.1 14.0 16.8 58.4 0.5

24 20 15.2 13.5 17.2 50.1 1.1 15.0 17.0 59.1 0.5

25 220 17.0 14.5 17.5 55.5 1.1 16.5 17.2 58.6 0.8

26 300 17.8 18.5 19.1 59.9 1.4 19.0 19.4 59.9 2.8

27 400 19.6 20.5 20.4 50.0 5.5 19.5 20.2 56.3 1.7

28 380 21.1 23.0 20.5 59.4 7.1 24.5 22.6 49.4 1.6

29 360 22.6 25.0 21.1 55.7 6.3 27.0 22.7 50.1 1.0

30 300 23.1 27.0 23.3 55.6 3.8 27.0 23.8 51.1 1.0

31 200 23.8 26.0 22.6 53.2 2.9 26.0 24.2 48.1 0.4

32 100 23.0 23.5 22.3 45.0 2.0 24.0 22.8 42.0 0.2

33 20 20.0 22.0 20.0 50.0 0.2 22.0 21.0 44.0 0.1


and GHD with natural convection was due to the higher temperature of the dried crop, whereas atthe end of the process with forced convection under GHD, the crop temperature was lowered dueto forced ventilation and resulted in a lower temperature difference.The relative humidity variation with drying time is presented in Fig. 3a and b for cabbage and

peas, respectively, for various modes of drying. The higher relative humidity was observed insidethe GHD with natural convection because of accumulation of water vapour inside the greenhousedue to poor ventilation in the greenhouse. This resulted in a poor rate of drying compared to OSDand GHD under the forced mode.

Tc-Te in OSD (December 01) Tc-Tr in GHD natural convection (October 01)Tc-Tr in GHD forced convection (December 01)

Tem

pera

ture

dif

fere

nce

(o C)

-5

0

5

10

15

20

-10 0 5 10 15 20 25 30 35

Drying time (h)

0 5 10 15 20 25 30 35

-5

0

5

10

15

20

Tem

pera

ture

dif

fere

nce

(o C)

-10

Drying time (h)

Tc-Te in OSD (November 01) Tc-Tr in GHD natural convection (September 01) Tc-Tr in GHD forced convection (November 01)

(a)

(b)

Fig. 2. (a) Drying time vs. temperature difference of crop and above crop during drying of cabbage. (b) Drying time vs.

temperature difference of crop and above crop during drying of peas.

Table 5

Experimental percent uncertainties for cabbage and peas under different modes of drying

Mode of

drying

Cabbage drying Peas drying

Internal

uncertainty

(%)

External

uncertainty

(%)

Total

uncertainty

(%)

Internal

uncertainty

(%)

External

uncertainty

(%)

Total

uncertainty

(%)

Open sun

drying

61.41 0.8 62.21 63.71 0.8 64.51

Greenhouse drying

(natural mode)

53.53 0.8 54.33 58.16 0.8 58.96

Greenhouse drying

(forced mode)

61.48 0.8 62.28 61.48 0.8 62.28


0 5 10 15 20 25 30 35

30

40

50

60

70

80

Drying time (h)

γ in OSD (November 01) γ in GHD natural convection (September 01)γ in GHD forced convection (November 01)

0 5 10 15 20 25 30 35

30

40

50

60

70

80

Drying time (h)

γ in OSD (December 01) γ in GHD natural convection (October 01)γ in GHD forced convection (December 01)

Rel

ativ

e hu

mid

ity

γ (%

)R

elat

ive

hum

idit

y γ

(%)

(a)

(b)

Fig. 3. (a) Drying time vs. relative humidity above crop during drying of cabbage. (b) Drying time vs. relative humidity

above crop during drying of peas.


4.2. Heat transfer in greenhouse drying

4.2.1. Natural convectionTo study the heat transfer under natural convection, the entire drying observations (33) of each

single experiment are considered in three ranges, i.e. 1–11, 1–22 and 1–33. The coefficients C and nof Eq. (1a) were computed for each range of observations with the linear regression analysistechnique. The natural convection heat transfer correlation (GrPr vs. Nu) for drying of peas insidethe greenhouse for the different ranges (1–11, 1–22, 1–33) are shown in Fig. 4a. It was observedfrom these figures that the entire drying falls under the laminar flow regime since GrPr6 107 [19].Changes in coefficients C and n are observed as the number of observations and drying timeincrease. For instance, n values are 0.21 for 1–11, 0.17 for 1–22 and 0.13 for 1–33 observationranges.Accordingly, the values of Nusselt number also varied with the changes in coefficients (C and n)

with increase in drying time. The convective mass transfer coefficient was evaluated in each range

106

107

108

101

102

Gr.Pr

Nu

Nu

Nu

(i)

C=1, n=0.21

106

107

108

101

102

Gr.Pr

(ii)

C=1.11, n=0.17

105

106

107

108

101

102

Gr.Pr

(iii)

C=1.41, n=0.13

0 5 100

5

10

15

20(i)

0 5 10 15 200

5

10

15

20(ii)

0 10 20 300

5

10

15

20(iii)

Number of observations Number of observations Number of observations

(a)

(b)

hc hc hc

Fig. 4. (a) Natural convection heat transfer correlation for heat transfer in GHD of peas for ranges of observations as

(i) 1–11, (ii) 1–22 and (iii) 1–33. (b) Natural convective mass transfer coefficient with number of observations for GHD

of peas for number of observations as (i) 1–11, (ii) 1–22 and (iii) 1–33.


of observations and is shown in Fig. 4b. The variation of hc with number of observations (dryingtime) can be seen in Fig. 4b. The average values of hc, thus, certainly vary for each range ofobservations.

4.2.2. Forced convectionSimilarly, the forced convection heat transfer correlations (RePr vs. Nu) for greenhouse drying

of peas are presented in Fig. 5a for the numbers of observations of 1–11, 1–22 and 1–33. Thenature of heat transfer was under the laminar regime since RePr6 105 [19]. The changes incoefficient n of Eq. (1b) can be observed as 0.36, 0.24 and 0.16 for the 1–11, 1–22 and 1–33ranges of observations. The Nusselt number also decreased as the number of observations(drying time) increased due to the decrease in the rate of moisture evaporation. The convectivemass transfer coefficient under forced mode with these three ranges of observation is presentedin Fig. 5b.With the above observations, it can be seen that there were variations in the convective mass

transfer coefficient with drying time due to the rate of moisture evaporation, temperature andrelative humidity surrounding the crop. Therefore, the dynamic nature of hc has been computedin the further study as the observations start from 1, 2, 3; . . . ; 33. The first regression has beendone with 1 and 2 observations, the second regression with 1, 2 and 3 observations and so on.Thus, the C, n and hc have been computed at 1, 2, 3; . . . ; 33 observations.

104

105

100

101

102

Re.Pr

Nu N

u

Nu

Nu

(i)

C=0.98, n=0.36

104

105

100

101

102

Re.Pr

(ii)

C=1.03, n=0.24

104

105

100

101

102

Re.Pr

(iii)

C=0.95, n=0.16

0 5 100

10

20

30

40

Number of observations

(i)

0 5 10 15 200

10

20

30

40


(ii)

0 10 20 300

10

20

30

40


(iii)

(a)

(b)

hc hc hchc

Fig. 5. (a) Forced convection heat transfer correlation for heat transfer in GHD of peas for ranges of observations as

(i) 1–11, (ii) 1–22 and (iii) 1–33. (b) Forced convective mass transfer coefficient with number of observations for GHD

of peas for number of observations as (i) 1–11, (ii) 1–22 and (iii) 1–33.


4.3. Convective mass transfer coefficient under natural convection

The variation of hc with respect to drying time under natural convection inside the greenhouse(GHD) and open sun drying (OSD) are presented in Fig. 6a and b for cabbage and peas, respec-tively. From these figures, it is clearly indicated that hc is very high in the beginning of drying. This ismainly due to the high initial moisture content of the crop. Thus, the rate of moisture evaporation(mev) is very high in the beginning (Tables 1 and 2), and the crop surface behaves like a wettedsurface. This confirms that hc is a strong function of mev. This also showed that the maximummoisture removal took place in the first 5–6 h of drying (Tables 1 and 2), where the rate of moistureevaporation remained constant. This period falls under the constant rate of drying classification.After 6 h of drying, the mev keeps on decreasing and so does the effect on hc. It also steadily

decreases and then becomes essentially constant after 20 h of drying. This period comes under thefalling rate of drying classification. After 20 h of drying, the surface of the crop behaved like a drysurface, where hc ranged 2.8–0.1 W/m2 �C. This validated the expression of hc for a dry surface,2:8þ 3v at wind velocity (v) equal to zero [18].The behaviors of hc with respect to drying time for cabbage and peas were similar. The values

of hc for cabbage and peas ranged 25–10 and 17–8 W/m2 �C for OSD and GHD, respectively,during the constant rate of drying. During the falling rate of drying, the hc ranged from 8–2.0 W/m2 �C for both cases. These results were within the percent uncertainty of 62.21 and 64.51 forcabbage and peas, respectively, under OSD. Under the GHD, the percent uncertainties were 54.33and 58.96 for cabbage and peas, respectively (Table 5).

Fig. 6. (a) Variation of convective mass transfer coefficient with drying time for cabbage under natural convection in

greenhouse (September 2001). (b) Variation of convective mass transfer coefficient with drying time for peas under

natural convection in greenhouse (October 2001).


Fig. 6a and b also present the effect of the greenhouse on the convective mass transfer coeffi-cient under natural convection. This shows that hc was lower in the initial drying in the case ofGHD relative to OSD in natural convection. This was mainly due to the increase in the relativehumidity inside the greenhouse (Tables 1 and 2), thus the rate of moisture removal decrease. Sincemev depends on the partial pressure difference between the crop surface and the surroundinghumid air (Eq. (5)), higher the relative humidity, the lower is the partial pressure difference, re-sulting in lowering the mev.

4.4. Convective mass transfer coefficient under forced convection

The effect of the greenhouse under forced convection on the change in hc relative to OSD ispresented in Fig. 7a and b. This shows that the values of hc under forced convection in the

0 5 10 15 20 25 30 350

5

10

15

20

25

30

35

40

45

50

Drying time in hour (T)

Coe

ffic

ient

of

conv

ecti

ve m

ass

tran

sfer

(hc

) in

W/m

2 o C

ECF-Exponential Curve Fitting FC-Forced Convection GHD-GreenHouse Drying OSD-Open Sun Drying

hc for FC in GHD ECF of hc for FC in GHD hc for OSD ECF of hc for OSD

November 2001

hc=1.4531*exp(-0.1008*T)+41.6293*exp(-0.1444*T)

hc=554.8568*exp(-0.1491*T)-530.9042*exp(-0.1537*T)( r = 0.9919, χ2 = 0.8142 )

( r = 0.9953, χ2 = 1.0777 )

0 5 10 15 20 25 30 350

5

10

15

20

25

30

35

40

45

50

Drying time in hour (T)

Coe

ffic

ient

of

conv

ecti

ve m

ass

tran

sfer

(hc

) in

W/m

2 o C

ECF-Exponential Curve Fitting FC-Forced Convection GHD-GreenHouse Drying OSD-Open Sun Drying

hc for FC in GHD ECF of hc for FC in GHD hc for OSD ECF of hc for OSD

December 2001

hc=0.9031*exp(0.0200*T)+24.7076*exp(-0.0919*T) ( r = 0.9861, χ2 = 1.2281 )

hc=-0.0334*exp(0.0636*T)+38.3583*exp(-0.0905*T) ( r = 0.9929, χ2 = 1.7929 )

(a)

(b)

Fig. 7. (a) Variation of convective mass transfer coefficient with drying time for cabbage under forced convection in

greenhouse (November 2001). (b) Variation of convective mass transfer coefficient with drying time for peas under

forced convection in greenhouse (December 2001).


greenhouse at the beginning is double that of natural convection in GHD (e.g. comparing Figs. 6aand 7a for cabbage and Figs. 6b and 7b for peas). The values of hc during forced convectionvaried from 38–15 W/m2 �C during the constant rate of drying. These results were within thepercent uncertainty of 61.28 for both the crops. The drying behavior was similar, as discussed inthe earlier Section 4.3. The rate of moisture evaporation under forced convection in the green-house significantly increased (Tables 3 and 4) relative to the OSD. This is due to the decrease inrelative humidity inside the greenhouse.

4.5. Exponential curve fitting

For all the cases, the experimental heat transfer coefficients have been fitted in a two termexponential curve model as a function of drying time in hours, and the equations, and their


coefficient of correlation and mean squares of deviation presented in Figs. 6a–b and 7a–b. Themodel very well fits (e.g. Fig. 6a, r ¼ 0:99) in most cases.

5. Conclusions

The effect of the greenhouse on the convective heat and mass transfer under natural and forcedmodes has been studied for cabbage and peas by using the data of crop drying. The followingconclusions were drawn:

1. The convective mass transfer coefficient inside greenhouse drying under natural mode at initialstage is lower then for open sun drying.

2. The convective mass transfer coefficient in greenhouse drying under forced mode is double thatof natural convection in the initial stage of drying.

3. The maximum rate of moisture evaporation took place in the beginning of the drying time (5–6h). The mass transfer rate became essentially constant after 20 h of drying time.

4. The behavior of the convective mass transfer coefficient in the beginning of drying was like thatof a wetted surface and at the end of the drying like that of a dry surface.

5. The convective mass transfer coefficient as a function of drying time has been established withthe help of a two term exponential curve model.

Appendix A

The following expressions were used for calculating values of the physical properties of air,such as specific heat (Cv), thermal conductivity (Kv), density (qv) and dynamic viscosity (lv) andthe partial vapour pressure (P ) [15]. For obtaining the physical properties of humid air, Ti is takenas the mean of the average crop temperature Tc and the average temperature just above the cropsurface (Te or Tr):

Cv ¼ 999:2þ 0:1434Ti þ 1:101� 10�4T 2i � 6:7581� 10�8T 3i ðA:1Þ

Kv ¼ 0:0244þ 0:6773� 10�4Ti ðA:2Þ

qv ¼353:44

Ti þ 273:15ðA:3Þ

lv ¼ 1:718� 10�5 þ 4:620� 10�8Ti ðA:4Þ

PðT Þ ¼ exp 25:317� 5144

Ti þ 273:15

� �ðA:5Þ


Appendix B

A. Procedure of calculation of coefficient of correlation (r) [14]

r ¼ NP

XiYi � ðP

XiÞðP

YiÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiNP

X 2i � ð

PXiÞ2

q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiNP

Y 2i � ðP

YiÞ2q ðB:1Þ

B. Procedure of calculation of v-square (v2) as the mean square of deviation

v2 ¼PN

i¼1ðXpreðiÞ � Xexp tlðiÞÞ2

N � nðB:2Þ

where N is the number of observations and n the number of constants.C. Procedure for calculation of experimental percent uncertainty (U) [17].

U1 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir21 þ r22 þ þ r2N

pN

ðB:3Þ

where r is the standard deviation expressed as

r ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPðXi � X Þ2

N0

sðB:4Þ

where, Xi � X is the deviation of observation from the mean and N and N0, number of set andnumber of observations in each set, respectively.The percent uncertainty, therefore, could be expressed as

% Internal uncertainty ¼ U1

mean of the total observations� 100 ðB:5Þ

The external uncertainty is taken as the least count of the measuring instruments.

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effect of greenhouse on crop drying under natural and forced convection i: evaluation of convective...

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