Effect of Size on the Convective Heat and Mass Transfer Coefficients during Natural Convection Greenhouse Drying of Khoa-A Heat Desiccated Milk Product

In this research paper, the convective heat and mass transfer coefficients are evaluated for khoa drying under natural convection greenhouse mode for different sizes of khoa samples for a given mass. The khoa pieces of dimensions 0.025 × 0.02 × 0.015 m3, 0.0375 × 0.03 × 0.015 m3, and 0.075 × 0.06 × 0.015 m3 with total quantity of 100 g are dried in the roof type even span greenhouse with a floor area of 1.2 × 0.8 m2. The khoa has been dried at atmospheric pressure till there is almost no variation in its mass is recorded. The experimental data are used to determine the values of the constants in the Nusselt number expression by simple linear regression analysis and, consequently the convective heat transfer coefficients are evaluated. The mass transfer coefficients have also been evaluated. The convective heat and mass transfer coefficients are observed to decrease with the increase in size of the khoa sample and are found more for the khoa pieces having dimension 0.025 × 0.02 × 0.015 m3. The experimental error in terms of percent uncertainty has also been evaluated.


Introduction
Solar energy is abundant, non-pollutant, and renewable form of energy.It can be effectively used for product drying, if harvested properly.The traditional technique for product dehydration is the open sun drying method which has many disadvantages like product pollution and contamination.
An advanced and alternative method to the traditional techniques is greenhouse drying.In greenhouse drying the product is placed in trays which receive solar radiation through the plastic cover and moisture is removed either by natural convection or forced air flow.The use of appropriate greenhouse dryer improves the quality of the product and lead to reduction of drying time interval (Condori et al., 2001).
Khoa is a heat desiccated, partially dehydrated milk product.It forms an important base for preparation of milk _______________ Mahesh Kumar (2014), International Journal of Renewable Energy & Biofuels, DOI: 10.5171/2014.961114sweets which are an integral part of the Indian food heritage.About six lakh tonnes of khoa is being manufactured annually, mostly in private and unorganized sectors of India by utilizing about 7% of the total milk produced (Kumar et al., 2010;Kumar 2013).It contains sufficient amount of moisture which helps in the growth of microorganisms.The shelf-life of khoa is chiefly influenced by the moisture contents among other factors like storage temperature, raw material quality, sanitation conditions, and packaging.The presence of moulds in khoa causes its fast deterioration by producing discoloration defects as well as disagreeable flavors.Solar radiation significantly reduces the counts of these microorganisms (Kumar et al., 1996;Chavan, and Kulkarni, 2006;Rajarajan et al., 2007).
Khoa drying is a continuous heat and mass transfer phenomenon.The heat energy supplied to the khoa surface is utilized in two ways, i.e., to remove the moisture present in the product through the provision of latent heat of vaporization and to increase the product surface temperature in the form of sensible heat which causes evaporation of the moisture to the surrounding air.Removal of moisture occurs from the interior of the khoa due to induced vapor pressure difference between the khoa and the surrounding medium.The convective heat transfer coefficient is an important parameter in drying rate simulation, since the temperature difference between the air and the product varies with this coefficient.The convective mass transfer coefficients for various shapes and sizes of jaggery pieces in a controlled environment were evaluated by Tiwari et al., (2004).It was observed that the convective mass transfer coefficient in forced convection is higher than the natural convection mode.The effect of shape and size of jaggery for a given mass on convective mass transfer coefficient for natural as well as forced convection greenhouse drying was studied Kumar and Tiwari (2006).The convective heat transfer coefficients of khoa were investigated by Kumar et al. (2011a) in an open sun drying and greenhouse drying for natural as well as for forced convection modes for drying a khoa piece of size 0.09 × 0.06 × 0.015 m 3 for three consecutive days.The convective heat transfer coefficients under forced convection were reported higher than the natural convection mode.The convective heat transfer coefficients were observed to decrease with the drying day progression from the first day to the third day and were found to vary in a range of 0.54 to 1.09 W/m 2 o C.
In the present study the effect of size on the convective heat and mass transfer coefficients of khoa for a given mass with greenhouse drying under natural convection mode has been evaluated.This research work would be helpful in the design of an efficient greenhouse for drying khoa to its optimum storage moisture level.

Set-Up and Instrumentation Details
A roof type even span greenhouse of 1.2 × 0.8 m 2 effective floor area was fabricated of PVC pipe and a UV film covering of 200 microns.The central height and the walls were maintained as 0.6 m and 0.4 m respectively.An air vent with an effective opening of 0.043 m 2 was provided at the roof for natural convection.A photograph of the experimental setup for greenhouse drying and khoa sample is shown in

Sample Preparation and Experimental Observations
The khoa sample was prepared by following the traditional khoa making process.The fresh milk was heated over an electric hot plate in an aluminum open pan.The heating was stopped and the product was allowed to cool to room temperature when the desired consistency was obtained.Then cuboids shaped pieces of khoa sample of size 0.025 × 0.02 × 0.015 m 3 , 0.0375 × 0.03 × 0.015 m 3 , and 0.075 × 0.06 × 0.015 m 3 of total quantity of khoa as 100 g were prepared with the help of wooden molds.For each experiment performed fresh sample of khoa of the same shape and mass was prepared by following the above procedure.The observation time interval for khoa drying was taken an hour.Experiments were performed during the month of October 2012 at Guru Jambheshwar University of Science and Technology Hisar (29 o 5'5" N 75 o 45'55" E).

Procedure
For each experiment the initial mass of khoa samples was kept constant as 100 g.The khoa sample was kept in the wire mesh tray directly over the digital weighing balance.The moisture evaporated was calculated by taking the difference of mass of khoa between two consecutive readings.The hourly data for rate of moisture removal, khoa surface temperature, relative humidity inside the greenhouse, temperature just above the khoa surface, and ambient temperature have been recorded.The khoa samples were dried till no variation in its mass was recorded.

Thermal Modeling and Computation Technique
The convective heat transfer coefficient for evaporation under natural convection can be determined by using the following relations (Kumar et al., 2012a): The rate of heat utilized to evaporate moisture is given as (Kumar et al., 2012a) International    7) are obtained by using the simple linear regression method by using the following formulae: The experimental data given in Tables 1-3 for Tk, Te, γ, and mev were used to determine the values of y and

Experimental Error
The experimental error was evaluated in terms of percent uncertainty (internal + external) for the mass of moisture evaporated.The following equation was used for internal uncertainty (Kumar 2013): The percent internal uncertainty was determined by using the following expression: % internal uncertainty = (UI/mean of the total observations) ×100 ( 11) For external uncertainty, the least counts of all the instruments used in measuring the observation data were considered.

Results and Discussion
The experimental data recorded for khoa drying under natural convection greenhouse mode for khoa pieces with dimensions 0.025 × 0.02 × 0.015 m 3 , 0.0375 × 0.03 × 0.015 m 3 , and 0.075 × 0.06 × 0.015 are presented respectively in Tables 1, 2, and 3 given in Appendix-II.
The data given in Tables 1-3  analysis.Then the values of these constants were considered further for determining the values of the convective heat transfer coefficient by Equation (1).After determining the convective heat transfer coefficients, the mass transfer coefficients were evaluated from Equation ( 9).The evaluated values of experimental constants (C & n), the convective heat transfer coefficients (h c ), and the mass transfer coefficients (h m ) during drying all the khoa samples inside the greenhouse under natural convection mode are summarized in Table 4.The range of Grashof number and Prandtl number has also been given.The product of Grashof and Prandtl numbers has been observed as Gr Pr ≤ 10 7 , which indicates that the entire khoa drying falls within a laminar flow (Kumar et al., 2011b).

Appendix-I
The following expressions were used for determining the values of the physical properties of humid air (Kumar et al., 2012a;Kumar 2013): Fig.1._______________ Mahesh Kumar (2014), International Journal of Renewable Energy & Biofuels, DOI: 10.5171/2014.961114

Fig. 1 :
Fig. 1: A Photographs of Experimental UnitExperimental unit was located on the open floor of a three-floor building to have a good exposure to the solar radiation.Due to more availability of sunlight the orientation of the greenhouse was kept east-west.The experiments were carried out with total quantity of khoa as 100 g for each dimension of the khoa pieces, i.e., 0.025 × 0.02 × 0.015 m 3 , 0.0375 × 0.03 × 0.015 m 3 , and 0.075 × 0.06 × 0.015 m 3 .For each experiment, khoa pieces of 1.5 cm thickness for single layer drying were kept in a wire mesh tray of 0.09 m × 0.06 m size directly over the digital weighing balance of 6 kg capacity (TJ-6000, Scaletech, made in India) with a least count of 0.1 g.The khoa and air temperatures at different locations were measured by calibrated copper-constantan thermocouples connected to a ten channel digital

Fig. 2 :
Fig. 2: A Schematic View of Experimental Unit Journal of Renewable Energy & Biofuels _______________ Mahesh Kumar (2014), International Journal of Renewable Energy & Biofuels, DOI: 10.5171/2014.961114 is determined by dividing Equation (3) by the latent heat of vaporization (λ) and multiplying the area of khoa drying tray (At) and time interval (t).
y =In[ mev /z], m = n, = In(Gr Pr) and c = In C, thus, C = e c Values of m and c in Equation ( for different time intervals.Then the constant C and exponent n were obtained from the above equations for natural convection greenhouse drying mode.The experimental constants (C & n) were considered further for evaluating the values of convective heat transfer coefficients from Equation (1).The physical properties of humid air were determined by the expressions given in Appendix-A.The mass transfer coefficient (h m ) were calculated from Equation (9) as given below(Kumar et al., 2012b): (Appendix-II) were used to determine the values of the constant C and exponent n in the Nusselt expression by simple linear regression _______________ Mahesh Kumar (2014), International Journal of Renewable Energy & Biofuels, DOI: 10.5171/2014.961114 m 2 o C) 1 st Sample (0.025 × 0.02 × 0.015 m 3 ) Drying, October 10, (0.0375 × 0.03 × 0.015 m 3 ) Drying, October 11, observed from Table4that the values of convective heat and mass transfer coefficients are more for the khoa piece of dimension 0.025 × 0.02 × 0.015 m 3 .The convective heat and mass transfer coefficients decrease with the increase in size of the khoa pieces which is due to decrease in removal of moisture contents.The hourly variations in the convective heat and mass transfer coefficients for each sample of the given dimensions are illustrated in Figures3 and 4respectively.

Fig. 3 :NQ
Fig. 3: Variations in Convective Heat Transfer Coefficients versus Time