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natural 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, India

b 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 of the 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.

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 solar radiation falls directly on the crop surface and is absorbed. The absorbed radiation heats the crop

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Nomenclature

A C d g Gr hc IðtÞ K mev

n Nu Pr PðTÞ Qe Re r t T Ti

T DT

V

X Greek

P

y X

ii

p v2

area (m2)

constant or specific heat (J/kg °C) average height of greenhouse (m) acceleration due to gravity (m/s2) Grashof number = bgX3qv2DT=l

convective heat transfer coefficient (W/m2 °C) solar intensity on horizontal surface (W/m2) thermal conductivity (J/m2 °C)

moisture evaporated (kg) constant

Nusselt number = hcX=Kv

Prandtl number = lvCv=Kv

partial vapour pressure at temperature T (N/m2) rate of heat utilized to evaporate moisture (J/m2 s) Reynolds number = qvvd=lv

coefficient of correlation time (s)

temperature (°C) and time (h)

average of crop and humid air temperature (°C) average temperature (°C)

effective temperature difference (°C) air velocity inside greenhouse (m/s) characteristic dimension (m)

; letters

coefficient of volumetric expansion (1/°C) relative humidity (dec.)

latent heat of vaporization (J/kg) dynamic viscosity of air (kg/m) density of air (kg/m3)

mean square deviation Subscripts

a c e r

V

t

ambient crop

above crop surface greenhouse room humid air

tray

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and evaporates the moisture from the crop. During this process, the amount of solar energy received at the crop surface is lost at various stages through reflection, radiation, convection and conduction. Placing a plastic covering over the crop produces a greenhouse effect to trap the solar energy in the form of thermal heat radiation and prevents conduction heat loss. The rate 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 area etc.).

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, while moisture 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 of the most critical parameters required for analysis and simulation of the process. Several re- searchers have presented various numerical models for moisture migration, considering diffusion as 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 and lag factor. Smith and Sokhansanj [6] have developed a natural convection heat transfer model in which the density of air was assumed to be a function of temperature and absolute humidity.

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 coefficients were 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 and carrots. Anwar and Tiwari [8] evaluated the convective heat transfer coefficients for some crops under a simulated condition of forced mode in indoor open and closed conditions. Anwar and Tiwari [9] determined the convective heat transfer under open sun drying by using the linear regression technique. Their study was limited to constant rate drying from 11 to 13.30 h of the day. The single value of convective heat transfer was evaluated for each crop for the whole drying 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 and outside the greenhouse and ambient air temperature for the complete drying period 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 heat transfer. A suitable empirical model is presented to regress the convective heat and mass transfer coefficients as a function of drying time.

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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 = = CðGrPrÞhcX n for natural convection ð1aÞ

= CðRePrÞn for forced convection ð1bÞ

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

hc = ^C{GrPr)n ð2Þ

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

Qe = 0.0l6hc[P(Tc) - yP(Te)\ (3)

The hc in the above expression with moisture evaporation is termed the convective mass transfer coefficient in the case of crop drying.

On substituting hc from Eq. (2), Eq. (3) becomes

Qe = 0 . 0 1 6 ^ C{GrPrf[P{Tc) - yP(Te)] (4)

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).

W e v = Q-Att = 0.016^-C(GrPr)n[P(Tc) - yP{Te)]Att = ZC(GrPr)n (5)

A JC A

where Z = 0 . 0 1 6 ^ [P(TC) - yP(Te)](Au We

z=C(GrPr)n ð6Þ

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

ln [—1 = n lnðGrPrÞ þ ln C ð7Þ This is the form of a linear equation, Y = mX0 þ C0, where

Y = In [ — 1; m = n; X0 = \n[GrPr\ and C0 = ln C; thus; C = eC° Similarly, in the case of forced convection,

Y = In T—j; m = n; X0 = \n[RePr], C0 = ln C and C = eC°

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

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into the linear form to find the m and Q. Now, the m and Q 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 between moisture ratio and drying time for thin layer solar drying of sultana grapes. They concluded that the two term exponential curve model was most acceptable. Similarly, the regression analysis has been done with exponential curve fitting (two term) as the convective mass transfer coefficient is a function of drying time.

hc = A1 expðk1 TÞ þ A2 expðk2TÞ ð8Þ

The constants A1, A2, k1 and k2 were computed using the technique of Moore [13]. The above expression 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 employed only 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 of fit 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 0.32x0.26 m2 and 0.20x0.20 m2 were used to accommodate 0.300 kg samples of cabbage and peas as thin layers, respectively. A roof type even span greenhouse with an effective floor covering 1.2x0.8 m2 has been made of PVC pipe and UV film covering. The central height and height of the walls were 0.60 and 0.40 m, respectively. An air vent was provided at the roof with an effective opening of 0.043 m2 for natural convection. The experimental set up for open sun drying and greenhouse drying in the natural mode is shown in Fig. 1a. A fan of 225 mm sweep diameter with air velocity 5 m/s was provided on the sidewall of the greenhouse during the experiments of forced convection (Fig. 1b). The greenhouse had an east-west orientation during 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 digital humidity/temperature meter (model Lutron HT-3003) was used to measure the relative humidity and temperature of air in the greenhouse, of ambient and above the crop surface. It had a least count of 0.1% relative humidity with accuracy of ±3% on the full scale range of 5-99.9% of relative 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 g with ±2% on the full scale was used to weigh the sample during drying. The difference in weight

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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 a calibrated solarimeter, locally named Suryamapi (Central Electronics Ltd., India). It measures solar radiation in mW/cm2, having a least count of 2 mW/cm2 with ±2% accuracy of the full scale range of 0-120 mW/cm2. The air velocity across the greenhouse section during the forced mode drying was measured with an electronic digital anemometer model of Lutron AM-4201. It had a least count of 0.1 m/s with ±2% on the full scale range of 0.2^-0.0 m/s.

3.3. Sample preparation

The fresh cabbage was cut into small slices. The peas were soaked in water for 12 h and than conditioned in a shed for 2 h after removing the excess water. The same sizes of samples were maintained 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 December 2001 for natural convection and November and December 2001 for forced convection in the climatic 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 recorded from 8 AM at every hour interval for the 33 h of continuous drying. All the experiments of greenhouse drying (GHD) have been conducted simultaneously with the open sun drying (OSD) for comparative study. The experiments on OSD were always under natural convection. Natural convection 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 the sidewall of the greenhouse. The air velocity across the greenhouse was measured to be 0.5 m/s with the help of the anemometer. The sample data for the natural and forced convection modes of drying under open sun and inside the greenhouse are presented in Tables 1-4.

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Table 1

Observation on open sun drying and greenhouse drying under natural convection for sample cabbage (initial weight of sample = 300 g) (month—September, 2001)

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

w

W/m 2

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 (°Q 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

Open

rc(°c

28.0 30.5 33.0 35.0 39.0 35.0 41.6 41.5 42.5 38.5 34.0 34.0 34.0 34.0 34.0 34.0 33.8 33.4 33.0 32.6 32.1 32.0 29.4 28.5 32.2 36.5 43.0 43.5 42.5 47.5 48.0 50.5 47.5 44.5

s e drying

) Te ( K^J

31.1 34.0 36.5 35.8 37.5 36.0 36.9 37.6 39.2 36.8 33.8 34.0 33.8 33.2 33.0 32.6 32.2 32.1 30.8 30.6 30.2 30.0 29.5 29.0 31.432 33.03 35.7 36.9 36.6 38.8 41.8 44.2 44.0 43.1

y (%) 73.5 62.8 67.0 63.8 63.2 69.0 53.1 54.6 51.0 52.3 67.4 63.6 65.2 65.9 68.1 69.5 69.2 69.0 69.9 70.0 70.1 70.6 71.2 71.8 62.9 60.4 54.5 64.1 54.6 47.0 45.8 44.6 38.5 40.1

mev (g)

38.2 40.6 38.1 31.8 27.0 26.9 19.7 14.4 8.2 4.7 2.8 2.2 1.6 1.4 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.3 2.3 2.1 1.5 1.5 0.9 0.1 0.1 0.1 0.1

Greenhouse drying Tc (°C)

28.5 30.5 33.5 37.0 39.5 39.0 44.0 42.9 40.5 39.0 33.5 33.5 33.0 32.8 32.6 32.5 32.2 32.0 31.8 31.5 31.0 30.0 29.1 28.5 34.0 36.0 42.5 43.5 47.5 47.5 48.0 49.5 47.5 44.5

Tr (°C) 31.0 32.1 36.4 36.3 39.5 37.5 37.8 39.9 37.2 37.2 34.0 34.0 33.8 33.2 33.0 32.7 32.6 32.2 32.0 31.8 31.2 30.5 29.8 29.2 32.5 33.9 37.5 37.7 37.7 42.8 43.8 48.0 46.8 43.2

y (%) 70.1 72.2 61.0 66.5 67.7 65.2 54.7 53.2 55.0 50.7 61.9 64.0 66.2 67.5 68.2 69.2 69.0 69.6 69.8 70.1 70.4 70.2 69.8 70.5 60.0 57.5 49.7 51.3 51.5 41.0 41.2 40.1 37.8 40.1

mev (g)

30.3 33.5 34.3 30.0 25.6 26.6 21.2 15.8 11.8 5.9 3.2 2.4 2.2 2.2 1.9 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.2 0.5 3.4 1.6 3.1 3.0 2.8 0.1 0.1 0.1

3.5. Computation technique

The average crop temperature (Tc) and temperature above the crop surface (Te or Tr in the cases of crop inside the greenhouse) were calculated at each hour interval with corresponding rate of moisture 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 and n were obtained by a linear regression technique at increments of every hour of observation, and thus, the values of hc were computed at the corresponding hour of drying. The hourly variations

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Table 2

Observation on open sun drying and greenhouse drying under natural convection for peas (initial weight of sample 300 g) (month—October, 2001)

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

Hi)

W/m 2

80 280 400 500 520 460 500 500 180 40 0 0 0 0 0 0 0 0 0 0 0 0 0 20 60 280 440 500 580 600 500 300 60 20

Ta (°Q 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 30.0

Open

rc(°c

23.5 29.0 30.5 33.5 32.5 37.5 43.5 41.0 38.0 30.0 30.0 30.0 30.0 30 30.0 30.0 29.5 28.0 28.0 27.160 26.0 25.0 25.060 24.5 25.0 35.0 41.0 45.0 49.5 49.5 49.5 45.5 39.5 35.0

s e drying C) Te (°C)

25.5 30.1 30.1 32.9 31.2 33.9 36.9 35.6 33.0 31.1 30.3 29.0 28.7 28.5 28.4 28.3 28.1 28.0 27.8 27.160 26.02 25.8 060.0 25.6 25.9 29.5 31.6 31.2 35.4 36.5 36.2 35.8 32.3 27.0

y (%) 81.7 76.5 67.1 51.3 45.1 42.0 37.5 31.7 35.5 60.7 55.2 57.2 59.0 59.0 59.2 59.3 59.3 59.0 59.0 59.0 59.0 59.0 59.0 58.8 62.0 51.0 48.3 48.4 38.6 37.1 37.7 39.2 46.4 45.0

mev (g)

9.0 18.9 22.4 25.1 24.7 15.1 9.1 3.8 3.0 1.9 1.5 1.5 0.7 0.4 0.5 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 2.2 1.4 1.6 0.8 0.4 0.7 0.1 0.1

Greenhouse drying Tc (°C)

23.5 30.0 35.0 35.0 37.0 38.0 38.5 38.0 35.5 32.0 30.5 27.5 27.5 27.5 27.5 27.5 28.360 26.5 26.0 26.0 26.0 25.5 25.060 25.0 24.5 31.5 38.0 45.0 49.5 51.0 51.0 46.0 39.0 30.0

Tr (°C) 25.3 30.5 31.2 34.4 34.1 3 . 2 39.8 35.7 34.1 30.8 29.8 29.0 29.0 29.0 28.8 28.5 28.3 28.0 27.7 27.1 26.0 25.4 25.0 25.0 25.2 30.3 31.8 33.4 36.4 36.1 39.9 38.9 32.6 30.0

y (%) 84.0 78.7 78.8 66.2 52.6 43.2 40.0 40.7 52.1 64.4 60.5 58.0 57.0 59.0 60.0 60.2 60.0 60.0 60.0 60.0 60.0 60.0 60.0 60.9 61.7 64.0 53.8 45.5 45.5 36.3 35.7 35.8 46.9 48.0

mev (g)

6.1 10.2 17.2 20.9 22.6 18.3 13.5 8.5 4.6 3.4 2.4 1.2 1.2 1.2 1.2 1.0 1.0 1.0 0.9 0.9 0.9 0.8 0.8 0.7 1.2 1.2 1.4 1.4 1.3 1.1 0.6 0.2 0.1

in the experimental convective mass transfer coefficients were fitted to the two term exponential curve model. The coefficient of correlation and mean square of deviation were computed for the experimental hc divided by predicted hc for suitability of the model. The computer program was prepared 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.

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Table 3

Observation on open sun drying and greenhouse sample = 300 g) (month—November, 2001)

drying under forced convection for cabbage (initial weight of 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

w

W/m 2

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 20.0 340 420 480 420 380 220 100 20

Ta ( ° Q 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

Open

rc(°c

10.5 14.5 16.5 20.5 24.5 24.0 24.5 24.5 22.0 19.0 19.0 18.5 18.5 18.5 18.5 17.5 17.0 17.0 15.5 14.0 13.0 11.5 10.5 10.0 10.5 2.60 27.5 32.5 34.5 37.0 34.5 33.5 29.0 24.0

s e drying

) Te ( K^J

17.6 19.1 20.0 20.52 24 2 28.2 26.2 24.8 24.6 22.8 22 2 22.0 21.8 21.8 21.8 21.0 18.2 16.6 16.3 15.85 14.7 14.3 15.2 15.7 16.3 2.60 21.8 2 . 5 26.1 27.8 26.8 26.0 25.2 22.0

y (%) 65.8 58.3 45.4 40.7 40.0 38.0 45.3 45.9 39.7 48.7 49.4 50.1 50.5 51.2 51.4 51.6 51.2 50.8 50.2 52.4 48.6 50.7 52.6 53.2 53.5 44.2 42.8 44.2 43.0 33.1 34.8 32.6 34.1 35.0

mev (g)

8.4 21.4 33.8 39.5 37.3 37.2 22.0 15.9 15.4 4.6 4.5 3.5 2.6 2.4 2.0 1.5 1.5 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.0 0.9 2.8 1.7 1.3 0.1 0.1 0.1 0.1

Greenhouse drying Tc (°C)

9.5 13.0 17.5 20.0 22.0 27.5 27.5 26.0 24.0 19.5 19.5 19.5 19.5 19.5 19.5 18.5 18.0 17.5 16.0 15.0 13.5 11.5 11.0 11.0 11.5 18.5 24.5 26.5 32.0 32.0 32.5 29.5 26.5 035.0

Tr (°C) 14.7 17.1 19.6 22.9 25.1 30.1 29.3 27.6 25.5 22.8 22.4 22.2 22.0 21.9 21.8 21.0 18.2 16.8 16.3 15.8 15.0 14.5 15.5 16.0 16.3 20.4 22.1 25.7 28.2 30.3 30.2 27.7 25.0 22.0

y (%) 55.8 50.6 50.4 53.7 48.5 42.6 42.9 37.2 37.1 52.2 52.0 51.8 51.4 51.2 51.2 51.6 51.4 50.4 50.6 51.6 50.0 50.6 51.7 52.8 52.9 42.6 41.0 59.8 38.0 31.8 28.8 28.9 33.8 35.0

mev (g)

30.4 34.8 45.9 41.5 32.0 28.3 16.6 11.8 6.1 3.2 2.8 2.5 2.4 2.4 1.2 0.9 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.6 0.4 0.8 0.8 0.8 0.6 0.2 0.1 0.1 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. 2a and b for cabbage and peas, respectively, for various modes of drying. The higher temperature differences were observed under GHD with natural convection due to trapping of the heat inside the greenhouse under natural ventilation. The higher temperature difference at the end of OSD

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Table 4

Observation on open sun drying and greenhouse drying under forced convection for peas (initial weight of sample 300 g) (month—December, 2001)

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

Hi)

W/m 2

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 (°Q 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

Open

rc(°c

12.5 14.0 15.5 20.0 20.5 22.0 21.5 20.5 18.5 17.0 17.0 17.0 17.0 17.0 17.0 16.0 14.5 14.0 13.5 13.0 13.0 12.0 12.5 13.5 13.5 14.5 18.5 20.25 23.0 25.0 27.0 26.0 23.5 20.0

s e drying C) Te (°C)

15.5 16.4 18.9 19.7 21.1 22.3 22.3 21.8 21.3 20.3 19.8 19.7 19.6 19.5 19.5 18.8 18.4 16.2 15.1 14.2 13.0 13.1 14.8 16.5 17.2 17.25 19.1 20.4 20.5 21.1 23.3 22.6 22.3 20.0

y (%) 82.5 42.4 72.4 65.1 56.6 515 53.3 50.8 50.7 54.8 55.2 57.8 58.7 50.1 53.5 53.1 52 2 58.8 57.2 55.5 50.4 52.1 56.6 58.2 50.1 55.5 59.9 50.0 59.4 55.7 55.6 53.2 45.0 50.0

mev (g)

2.4 2.8 7.3 13.6 15.8 16.5 14.0 7.2 2.7 2.0 1.8 1.6 1.5 1.5 1.3 1.3 1.3 1.2 1.2 1.2 1.0 1.0 1.1 1.1 1.1 1.4 5.5 7.1 6.3 3.8 2.9 2.0 0.2

Greenhouse drying Tc (°C)

12.5 14.5 15.0 18.5 19.0 19.5 20.5 21.0 21.5 18.0 17.5 17.5 17.0 17.0 17.0 16.0 15.5 15.0 14.0 13.5 13.5 13.0 13.0 14.0 15.0 16.5 19.0 19.5 24.5 27.0 27.0 26.0 24.0 20.0

Tr (°C) 15.0 15.7 19.2 20.1 22.1 23.2 23.6 23.3 21.5 20.1 19.8 19.4 19.2 19.0 18.8 18.6 18.2 16.2 14.8 13.2 12.8 12.4 13.7 16.8 17.0 17.2 19.4 20.2 22.6 22.7 23.8 24.2 22.8 21.0

y (%) 84.8 80.2 65.2 55.8 48.0 45.7 51.9 52.7 51.4 56.5 54.2 55.6 56.5 50.4 54.9 55.0 51.4 57.8 58.2 56.1 55.8 55.5 56.7 58.4 59.1 58.6 59.9 56.3 49.4 50.1 51.1 48.1 42.0 44.0

mev (g)

4.2 6.2 13.3 19.1 20.9 20.7 13.1 6.7 4.5 3.4 2.6 2.3 2.0 2.0 1.2 1.0 0.8 0.8 0.8 0.6 0.5 0.5 0.5 0.5 0.8 2.8 1.7 1.6 1.0 1.0 0.4 0.2 0.1

and GHD with natural convection was due to the higher temperature of the dried crop, whereas at the end of the process with forced convection under GHD, the crop temperature was lowered due to 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 inside the GHD with natural convection because of accumulation of water vapour inside the greenhouse due to poor ventilation in the greenhouse. This resulted in a poor rate of drying compared to OSD and GHD under the forced mode.

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Table 5

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

drying

Open sun drying

Greenhouse drying (natural mode) Greenhouse drying

(forced mode)

Cabbage drying Internal uncertainty 61.41 53.53 61.48

External uncertainty 0.8 0.8 0.8

Total uncertainty 62.21 54.33 62.28

Peas drying Internal uncertainty 63.71 58.16 61.48

External uncertainty 0.8 0.8 0.8

Total uncertainty 64.51 58.96 62.28

20

15

-10 (a)

Tc-Te in OSD (November 01)

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

10 15 20 25 Drying time (h)

30 35

20 U

-10 (b)

Tc-Te in OSD (December 01)

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

10 15 20 25 Drying time (h)

30 35

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.

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

80

(a)

γinOSD (November 01)

y in GHD natural convection (September 01) y in GHD forced convection (November 01)

10 15 20 25

Drying time (h)

30 35

80 70

H3

ive hi

1

60 50 40 30 (b)

- y in OSD (December 01)

- Y in GHD natural convection (October 01) - Y in GHD forced convection (December 01)

10 15 20 25 Drying time (h)

30 35

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 convection

To 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 n of Eq. (1a) were computed for each range of observations with the linear regression analysis technique. The natural convection heat transfer correlation (GrPr vs. Nu) for drying of peas inside the greenhouse for the different ranges (1-11, 1-22, 1-33) are shown in Fig. 4a. It was observed from these figures that the entire drying falls under the laminar flow regime since GrPr 6 107 [19].

Changes in coefficients C and n are observed as the number of observations and drying time increase. For instance, n values are 0.21 for 1-11, 0.17 for 1-22 and 0.13 for 1-33 observation ranges.

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

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0 5 10 Number of observations

5 10 15 20 Number of observations

10 10 10

Gr.Pr

10 20 30 Number of observations 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 (drying time) can be seen in Fig. 4b. The average values of hc, thus, certainly vary for each range of observations.

4.2.2. Forced convection

Similarly, 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 1 1 , 1-22 and 1-33. The nature of heat transfer was under the laminar regime since RePr6105 [19]. The changes in coefficient n of Eq. (1b) can be observed as 0.36, 0.24 and 0.16 for the 1 1 1 , 1-22 and 1-33 ranges 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 convective mass transfer coefficient under forced mode with these three ranges of observation is presented in 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 and relative humidity surrounding the crop. Therefore, the dynamic nature of hc has been computed in the further study as the observations start from 1, 2, 3;. . .; 33. The first regression has been done 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.

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(a)

10

10

10 (ii)

C=1.03, n=0.24

10

5 101

10 (iii)

C=0.95, n=0.16

10 10 10 10

Re.Pr Re.Pr Re.Pr

Number of observations

5 10 15 20 Number of observations

10 20 30 Number of observations

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 is mainly 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 wetted surface. This confirms that hc is a strong function of mev. This also showed that the maximum moisture removal took place in the first 5-6 h of drying (Tables 1 and 2), where the rate of moisture evaporation 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 the falling rate of drying classification. After 20 h of drying, the surface of the crop behaved like a dry surface, where hc ranged 2.8-0.1 W/m2 °C. This validated the expression of hc for a dry surface, 2:8 þ 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/m2oC 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/

m2oC for both cases. These results were within the percent uncertainty of 62.21 and 64.51 for cabbage and peas, respectively, under OSD. Under the GHD, the percent uncertainties were 54.33 and 58.96 for cabbage and peas, respectively (Table 5).

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-G-- he for NC in GHD ECF of he for NC in GHD - o ~ he for OSD

-*— ECF of he for OSD

ECF-Exponennal Curve Ftttmg GHD-GreenHbuse Drying NC-Natural Convection OSD-Open Sun Drying

hc=3.5174*e>rp(-0.0960*T)+27.2736*exp(-0.1834*T)

(I = 0.9934, X2 = 0.3221)

hc=10.0664*exp(-0.0968*T)+10.2387*exp(-0.2094*T)

(i = 0.9970, X2 = 0.3197)

10 15 20 25 Drying time in hour (I)

Q- he for NC in GHD I - ECF of he for NC in GHD s~ he for OSD

"— ECF of he for OSD

ECF-Exponential Curve Fitting GHD-OreenHouse Drying NC-Natural Convection OSD-Open Sun Drying

15 20 Drying time in hour (I)

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 of GHD relative to OSD in natural convection. This was mainly due to the increase in the relative humidity inside the greenhouse (Tables 1 and 2), thus the rate of moisture removal decrease. Since mev depends on the partial pressure difference between the crop surface and the surrounding humid 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 is presented in Fig. 7a and b. This shows that the values of hc under forced convection in the

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

50

.9 40

g

3 0

I 25

I20 8 15 O

| 10 'oj 5o

o

0 (a)

November 2001 - Q - hc for FC in GHD

- I - ECF of hc for FC in GHD -O-- hc for OSD

- — ECF of hc for OSD ECF-Exponential Curve Fitting FC-Forced Convection GHD-GreenHouse Drying OSD-Open Sun Drying hc=1.4531*exp(-0.1008*T)+41.6293*exp(-0.1444*T)

(r =0.9953, χ2 = 1.0777)

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

15 20 Drying time in hour (T)

g

.9 40 35

1 30

| 25

I20 8 15 O

| 10 1u 53 o

(b)

December 2001 - & - hc for FC in GHD - I — ECF of hc for FC in GHD -«•- hc for OSD

—— ECF of hc for OSD ECF-Exponential Curve Fitting FC-Forced Convection GHD-GreenHouse Drying OSD-Open Sun Drying hc=-0.0334*exp(0.0636*T)+38.3583*exp(-0.0905*T)

(r = 0.9929,χ2= 1.7929)

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

0 15 20

Drying time in hour (T)

25 30 35

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. 6a and 7a for cabbage and Figs. 6b and 7b for peas). The values of hc during forced convection varied from 38-15 W/m2oC during the constant rate of drying. These results were within the percent uncertainty of 61.28 for both the crops. The drying behavior was similar, as discussed in the 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 in relative humidity inside the greenhouse.

4.5. Exponential curve fitting

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

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

5. Conclusions

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

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

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

3. The maximum rate of moisture evaporation took place in the beginning of the drying time (5-6 h). 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 that of 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 with the 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) and the partial vapour pressure (P) [15]. For obtaining the physical properties of humid air, Ti is taken as the mean of the average crop temperature Tc and the average temperature just above the crop surface (Te or Tr):

Cv = 999:2 þ 0:1434Ti þ 1:101 x 10~47f - 6:7581 x 10 87;3 ðA:

Kv = 0:0244 þ 0:6773 x 10~47] ðA:

353:44

qv = 71 + 273:44:15 ð A:3 Þ

lv = 1:718 x 10"5 þ 4:6 2 0 x 10~871 ðA:

25.3,7 - ^ U (A.5)

References

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