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Effect of size on convective heat and mass transfer coefficients during natural
convection greenhouse drying of khoa-a heat desiccated milk product
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Research Article
Effect of Size on the Convective Heat and
Mass Transfer Coefficients during Natural
Convection Greenhouse Drying of Khoa-A
Heat Desiccated Milk Product
Mahesh Kumar
Copyright © 2014 Mahesh Kumar. Distributed under Creative Commons CC-BY 3.0
Abstract
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.
Keywords: Khoa; Khoa drying; Convective heat transfer coefficient; mass transfer coefficient;
Greenhouse drying; Natural convection.
Cite this Article as: Mahesh Kumar (2014), "Effect of Size on the Convective Heat and Mass Transfer
Coefficients during Natural Convection Greenhouse Drying of Khoa-A Heat Desiccated Milk Product,"
International Journal of Renewable Energy & Biofuels, Vol. 2014 (2014), Article ID 961114, DOI:
10.5171/2014.961114
International Journal of Renewable Energy & Biofuels 2
sweets which are an integral part of the than the natural convection mode. The
Indian food heritage. About six lakh tonnes effect of shape and size of jaggery for a
of khoa is being manufactured annually, given mass on convective mass transfer
mostly in private and unorganized sectors coefficient for natural as well as forced
of India by utilizing about 7% of the total convection greenhouse drying was studied
milk produced (Kumar et al., 2010; Kumar Kumar and Tiwari (2006). The convective
2013). It contains sufficient amount of heat transfer coefficients of khoa were
moisture which helps in the growth of investigated by Kumar et al. (2011a) in an
microorganisms. The shelf-life of khoa is open sun drying and greenhouse drying for
chiefly influenced by the moisture contents natural as well as for forced convection
among other factors like storage modes for drying a khoa piece of size 0.09 ×
temperature, raw material quality, 0.06 × 0.015 m3 for three consecutive days.
sanitation conditions, and packaging. The The convective heat transfer coefficients
presence of moulds in khoa causes its fast under forced convection were reported
deterioration by producing discoloration higher than the natural convection mode.
defects as well as disagreeable flavors. The convective heat transfer coefficients
Solar radiation significantly reduces the were observed to decrease with the drying
counts of these microorganisms (Kumar et day progression from the first day to the
al., 1996; Chavan, and Kulkarni, 2006; third day and were found to vary in a range
Rajarajan et al., 2007). of 0.54 to 1.09 W/m2 oC.
Khoa drying is a continuous heat and mass In the present study the effect of size on the
transfer phenomenon. The heat energy convective heat and mass transfer
supplied to the khoa surface is utilized in coefficients of khoa for a given mass with
two ways, i.e., to remove the moisture greenhouse drying under natural
present in the product through the convection mode has been evaluated. This
provision of latent heat of vaporization and research work would be helpful in the
to increase the product surface design of an efficient greenhouse for drying
temperature in the form of sensible heat khoa to its optimum storage moisture level.
which causes evaporation of the moisture
to the surrounding air. Removal of Materials and Methods
moisture occurs from the interior of the
khoa due to induced vapor pressure Experimental Set-Up and
difference between the khoa and the Instrumentation Details
surrounding medium. The convective heat
transfer coefficient is an important A roof type even span greenhouse of 1.2 ×
parameter in drying rate simulation, since 0.8 m2 effective floor area was fabricated of
the temperature difference between the air PVC pipe and a UV film covering of 200
and the product varies with this coefficient. microns. The central height and the walls
The convective mass transfer coefficients were maintained as 0.6 m and 0.4 m
for various shapes and sizes of jaggery respectively. An air vent with an effective
pieces in a controlled environment were opening of 0.043 m2 was provided at the
evaluated by Tiwari et al., (2004). It was roof for natural convection. A photograph
observed that the convective mass transfer of the experimental setup for greenhouse
coefficient in forced convection is higher drying and khoa sample is shown in Fig.1.
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Mahesh Kumar (2014), International Journal of Renewable Energy & Biofuels, DOI: 10.5171/2014.961114
3 International Journal of Renewable Energy & Biofuels
Experimental unit was located on the open temperature indicator with a least count of
floor of a three-floor building to have a 0.1 oC. For measuring khoa surface
good exposure to the solar radiation. Due temperature four thermocouples were
to more availability of sunlight the placed at the sample surfaces and then
orientation of the greenhouse was kept their average value was considered. To
east-west. The experiments were carried obtain accurate readings of the
out with total quantity of khoa as 100 g for temperatures the thermocouples have been
each dimension of the khoa pieces, i.e., calibrated with respect to the ZEAL
0.025 × 0.02 × 0.015 m3, 0.0375 × 0.03 × thermometer (made in England). The
0.015 m3, and 0.075 × 0.06 × 0.015 m3. For relative humidity (γ or RH) and the
each experiment, khoa pieces of 1.5 cm temperature just above the khoa surface
thickness for single layer drying were kept was measured by a digital
in a wire mesh tray of 0.09 m × 0.06 m size humidity/temperature meter (Lutron-HT
directly over the digital weighing balance 3006, made in Taiwan) with least counts of
of 6 kg capacity (TJ-6000, Scaletech, made 0.1% RH and 0.1 oC. The various
in India) with a least count of 0.1 g. The dimensions and the locations of measured
khoa and air temperatures at different parameters are shown in a schematic of the
locations were measured by calibrated experimental unit in Fig. 2.
copper-constantan thermocouples
connected to a ten channel digital
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Mahesh Kumar (2014), International Journal of Renewable Energy & Biofuels, DOI: 10.5171/2014.961114
International Journal of Renewable Energy & Biofuels 4
For each experiment the initial mass of The rate of heat utilized to evaporate
khoa samples was kept constant as 100 g. moisture is given as (Kumar et al., 2012a)
The khoa sample was kept in the wire mesh
tray directly over the digital weighing
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Mahesh Kumar (2014), International Journal of Renewable Energy & Biofuels, DOI: 10.5171/2014.961114
5 International Journal of Renewable Energy & Biofuels
Let 0.016
Kv
[P(Tk ) − γ P(Te )]At t = Z The experimental error was evaluated in
Xλ terms of percent uncertainty (internal +
external) for the mass of moisture
∴ [mev / Z ] = C (Gr Pr )
n evaporated. The following equation was
(5)
used for internal uncertainty (Kumar
2013):
Taking the logarithm of both sides of
Equation (5),
U I = (σ 1 + σ 2 + Kσ N ) N o
2 2 2
(10)
ln[mev / Z ] = ln C + n ln(Gr Pr ) (6)
The percent internal uncertainty was
This is the form of a linear equation, determined by using the following
y = mx + c (7) expression:
c=
∑ x ∑ y − ∑ x∑ xy
2
dimensions 0.025 × 0.02 × 0.015 m3,
N ∑ x − (∑ x)
2
(8) 0.0375 × 0.03 × 0.015 m3, and 0.075 × 0.06
2
× 0.015 are presented respectively in
Tables 1, 2, and 3 given in Appendix-II.
The experimental data given in Tables 1-3
The data given in Tables 1-3 (Appendix-II)
for Tk, Te, γ, and mev were used to were used to determine the values of the
determine the values of y and for constant C and exponent n in the Nusselt
different time intervals. Then the constant expression by simple linear regression
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Mahesh Kumar (2014), International Journal of Renewable Energy & Biofuels, DOI: 10.5171/2014.961114
International Journal of Renewable Energy & Biofuels 6
analysis. Then the values of these constants coefficients (hm) during drying all the khoa
were considered further for determining samples inside the greenhouse under
the values of the convective heat transfer natural convection mode are summarized
coefficient by Equation (1). After in Table 4. The range of Grashof number
determining the convective heat transfer and Prandtl number has also been given.
coefficients, the mass transfer coefficients The product of Grashof and Prandtl
were evaluated from Equation (9). The numbers has been observed as
evaluated values of experimental constants Gr Pr ≤ 107, which indicates that the
(C & n), the convective heat transfer entire khoa drying falls within a laminar
coefficients (hc), and the mass transfer flow (Kumar et al., 2011b).
Table 4: Results of Evaluated Parameters and the Convective Heat and Mass Transfer
Coefficients for Khoa Pieces
C n Gr × 10 5 Pr hc hm
(W/m2 oC) (W/m2 oC)
st 3
1 Sample (0.025 × 0.02 × 0.015 m ) Drying, October 10, 2012
0.90 0.18 0.815 - 1.667 0.695 - 0.697 2.40 - 2.65 44.50 - 81.51
2nd Sample (0.0375 × 0.03 × 0.015 m3) Drying, October 11, 2012
0.87 0.16 0.810 - 1.656 0.695 - 0.697 1.86 - 2.03 35.84 - 69.64
3rd Sample (0.075 × 0.06 × 0.015 m3) Drying, October 12, 2012
0.89 0.14 0.803 - 1.742 0.695 - 0.697 1.53 - 1.66 29.68 - 52.89
It has been observed from Table 4 that the size of the khoa pieces which is due to
values of convective heat and mass transfer decrease in removal of moisture contents.
coefficients are more for the khoa piece of The hourly variations in the convective
dimension 0.025 × 0.02 × 0.015 m3. The heat and mass transfer coefficients for each
convective heat and mass transfer sample of the given dimensions are
coefficients decrease with the increase in illustrated in Figures 3 and 4 respectively.
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Mahesh Kumar (2014), International Journal of Renewable Energy & Biofuels, DOI: 10.5171/2014.961114
7 International Journal of Renewable Energy & Biofuels
From Figures 3 & 4 it can be seen that the W/m2 oC, and 1.59 W/m2 oC for the khoa
convective heat and mass transfer pieces of size 0.025 × 0.02 × 0.015 m3,
coefficients decrease with the progression 0.0375 × 0.03 × 0.015 m3, and 0.075 × 0.06
of drying time interval for each sample of × 0.015 m3 respectively. The average value
khoa. This is because of decrease in of convective heat transfer coefficients is
moisture removal with the increase in observed to increase by 59.12% by
drying time interval for a particular day. decreasing the khoa sample size from
0.075 × 0.06 × 0.015 m3 to 0.025 × 0.02 ×
In order to make a comparison, the average 0.015 m3. This could be due to increase in
values of convective heat and mass transfer exposure of khoa surface area to solar
coefficients have also been calculated for radiations which causes increased
each dimensions of the khoa sample. The moisture removal rate. The average value
average values of convective heat transfer of the convective heat transfer coefficients
coefficients are found 2.53 W/m2 oC, 1.95 has been plotted in Figure 5.
Fig. 5: Average Value of the Convective Heat Transfer Coefficients for Each Sample
The average values of mass transfer to 0.025 × 0.02 × 0.015 m3. This could be
coefficients are found 60.6 W/m2 oC, 50.25 due to increased moisture removal rate
W/m2 oC, and 39.95 W/m2 oC for the khoa and thus the convective heat transfer
pieces of size 0.025 × 0.02 × 0.015 m3, coefficients values with the decrease in size
0.0375 × 0.03 × 0.015 m3, and 0.075 × 0.06 of the given khoa samples. The average
× 0.015 m3 respectively. The average value value of the mass transfer coefficients for
of mass transfer coefficients is observed to all the khoa samples is illustrated in Figure
increase by 51.69% by decreasing the khoa 6.
sample size from 0.075 × 0.06 × 0.015 m3
Fig. 6: Average Value of the Mass Transfer Coefficients for Each Sample
The average value of percent uncertainty coefficients values from its true value SPSS
(internal + external) is evaluated as software (version 16.0) has been used
33.54%. Thus the different values of the which provided error bars with 95%
convective heat and mass transfer confidence interval. Error bars for the
coefficients were found to be within the convective heat and mass transfer
given range. To show the variability of coefficients are illustrated in Figure 7(a)
convective heat and mass transfer and (b) respectively.
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Mahesh Kumar (2014), International Journal of Renewable Energy & Biofuels, DOI: 10.5171/2014.961114
International Journal of Renewable Energy & Biofuels 8
Fig. 7: Error Bars for the Convective Heat and Mass Transfer Coefficients
Conclusions
Nomenclature
The effect of the size on the convective heat
and mass transfer coefficients for khoa At Area of wire mesh tray, m2
drying under natural convection
greenhouse mode for a given mass has C Experimental constant
been determined. The convective heat and
mass transfer coefficients are more for the
pieces of dimension 0.025 × 0.02 × 0.015
C v Specific heat of humid air, J/kg oC
m3. The convective heat and mass transfer
coefficients decrease with the increase in g Acceleration due to gravity, m/s2
size of the khoa pieces which could be due
to decrease in removal of moisture Gr Grashof number = β g X3 ρv 2 ∆T / µv 2
contents. The average values of convective
heat and mass transfer coefficients are hc Convective heat transfer coefficient,
found to increase from 1.59 W/m2 oC to W/m2 oC
2.53 W/m2 oC and 39.95 W/m2 oC to 60.6
W/m2 oC respectively for decreasing the
hc,av Average convective heat transfer
size of khoa pieces from 0.075 × 0.06 ×
coefficient, W/m2 oC
0.015 m3 to 0.025 × 0.02 × 0.015 m3. The
convective heat and mass transfer
coefficients are also observed to decrease hm Mass transfer coefficient, W/m2 oC
with the progression of drying time
interval during each day of drying. This is hm,av Average mass transfer coefficient,
because of decrease in moisture removal W/m2 oC
with the increase in drying time interval.
Thus from the present research work it is Kv Thermal conductivity of humid air,
inferred that the size of khoa pieces plays a W/m oC
significant role in its drying. This research
work would be highly useful in the design m ev Mass evaporated, kg
of an efficient greenhouse dryer for khoa
drying to its optimum storage moisture n Experimental constant
level.
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Mahesh Kumar (2014), International Journal of Renewable Energy & Biofuels, DOI: 10.5171/2014.961114
9 International Journal of Renewable Energy & Biofuels
N Number of observations in each set of Condori, M., Echazu, R. & Saravia, L. (2001).
tables "Solar Drying of Sweet Pepper and Garlic
Using the Tunnel Greenhouse Drier,"
N o Number of sets Renewable Energy, 22(4), Pp. 447-460.
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Mahesh Kumar (2014), International Journal of Renewable Energy & Biofuels, DOI: 10.5171/2014.961114
International Journal of Renewable Energy & Biofuels 10
(16)
P (T ) = exp 25 . 317 −
5144
( )
T i + 273 . 15
Where Ti = (Tk + Te ) 2
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Mahesh Kumar (2014), International Journal of Renewable Energy & Biofuels, DOI: 10.5171/2014.961114
11 International Journal of Renewable Energy & Biofuels
Appendix-II
Table 1: Khoa Drying Observations for 1st Sample with Dimension 0.025 × 0.02 × 0.015
m3 on October 10, 2012
Table 2: Khoa Drying Observations for 2nd Sample with Dimension 0.0375 × 0.03 × 0.015
m3 on October 11, 2012
Table 3: Khoa Drying Observations for 3rd Sample with Dimension 0.075 × 0.06 × 0.015
m3 on October 12, 2012
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Mahesh Kumar (2014), International Journal of Renewable Energy & Biofuels, DOI: 10.5171/2014.961114