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Determination of convective heat transfer coefficient and specific energy consumption of potato using an ingenious self tracking solar dryer

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Abstract

In the present work, an attempt has been made to experimentally determine the heat transfer properties of potato in terms of convective heat transfer coefficient, specific energy consumption and specific heating rate. Drying experiments with potato cylinders have been performed in an in-house fabricated laboratory scale natural convection indirect solar dryer with self tracking mechanism. The convective heat transfer coefficient of cylindrical potato samples was evaluated by considering the combined effects of heat capacities of food product as well as radiative heat transfer from drying chamber to the food product. This study revealed that the convective heat transfer coefficient for potato cylinders was varying from 11.73 to 16.23 W/m2 °C with an experimental error of 7.86 %. The specific energy consumption was decreasing exponentially with drying time, and the average value was estimated to be 3,491 kJ/kg. It was also observed that the specific heating rate for potato cylinders decrease with dimensionless moisture content.

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Abbreviations

A :

Surface area (m2)

C, n :

Constants in Nusselt Eq. (15)

C p :

Specific heat capacity of the product (J/kg K)

h :

Length of the cylinder (m)

h c :

Convective heat transfer coefficient (W/m2 K)

k :

Thermal conductivity of the product (W/m K)

k a :

Thermal conductivity of air (W/m K)

L :

Characteristic length (m)

M :

Moisture content, dry basis (kg water/kg dry matter)

m d :

Mass of dry matter (kg)

R:

Radius of cylinder (m)

E p :

Specific energy consumption (kJ/kg dry matter)

T :

Temperature of drying air (K)

T p :

Temperature of product (K)

t :

Time (s)

T ch :

Temperature of drying chamber (K)

T f :

Mean fluid temperature (K)

V :

Volume of the sample (m3)

λ :

Latent heat of vaporization (kJ/kg)

ρ :

Density of potato (kg/m3)

β:

Coefficient of volumetric expansion (1/K)

ν:

Kinematic viscosity of air (m2/s)

σ:

Stefan-Boltzmann constant (5.67 × 10−8 W/m2 K4)

ε:

Emissivity of the product

o:

At the beginning of drying

f:

Final value of moisture content

Gr:

Grashof number = \( \frac{{g\beta \varDelta TL^{3} }}{{\nu^{2} }} \)

Nu:

Nusselt number = \( \frac{{h_{c} L}}{{k_{a} }} \)

Pr:

Prandtl number = \( \frac{{C_{p} \upsilon \rho }}{k} \)

Ra:

Rayleigh number = \( Gr \cdot \,\Pr \)

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Acknowledgments

The authors would like to thank Dr. R. Chidambaram, Principal Scientific Adviser, Government of India for providing financial support through RuTAG scheme for carrying out the present work.

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Authors and Affiliations

  1. Department of Agricultural & Food Engineering, Indian Institute of Technology, Kharagpur, 721 302, West Bengal, India

    P. P. Tripathy, S. Abhishek & P. B. S. Bhadoria

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  1. P. P. Tripathy
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  2. S. Abhishek
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  3. P. B. S. Bhadoria
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Correspondence to P. P. Tripathy.

Apendix 1: Uncertainty estimation in experimental heat transfer coefficient

Apendix 1: Uncertainty estimation in experimental heat transfer coefficient

The relation for convective heat transfer coefficient, hc in Eq. (6) can be expressed as:

$$ h_{c} = \frac{{(m_{1} - m_{2} )}}{{(t_{1} - t_{2} )}} \cdot \frac{\lambda }{{A(T - T_{p2} )}} + \frac{V}{A} \cdot \frac{{\rho C_{p} ({{m_{2} } \mathord{\left/ {\vphantom {{m_{2} } {m_{d} }}} \right. \kern-0pt} {m_{d} }})}}{{(T - T_{p2} )}} \cdot \frac{{(T_{p1} - T_{p2} )}}{{(t_{1} - t_{2} )}} - \frac{{\varepsilon \sigma \,\left( {T_{ch}^{4} - T_{p2}^{4} } \right)}}{{\left( {T - T_{p2} } \right)}} $$
(16)

The overall uncertainty in hc can be obtained by partial differentiation of each variable affecting hc in the Eq. (16):

$$ \frac{{\partial h_{c} }}{{\partial m_{1} }}E(m_{1} ) = \frac{1}{{t_{1} - t_{2} }} \cdot \frac{\lambda }{{A(T - T_{p2} )}} \cdot E(m_{1} ) $$
(17)
$$ \frac{{\partial h_{c} }}{{\partial m_{2} }}E(m_{2} ) = - \frac{1}{{(t_{1} - t_{2} )}} \cdot \frac{\lambda }{{A(T - T_{p2} )}} \cdot E(m_{2} ) + \frac{V}{A} \cdot \frac{{\rho C_{p} ({1 \mathord{\left/ {\vphantom {1 {m_{d} }}} \right. \kern-0pt} {m_{d} }})}}{{(T - T_{p2} )}} \cdot \frac{{(T_{p1} - T_{p2} )}}{{(t_{1} - t_{2} )}}E(m_{2} ) $$
(18)
$$ \frac{{\partial h_{c} }}{{\partial t_{1} }}E(t_{1} ) = - \frac{{(m_{1} - m_{2} )}}{{(t_{1} - t_{2} )^{2} }} \cdot \frac{\lambda }{{A(T - T_{p2} )}} \cdot E(t_{1} ) - \frac{V}{A} \cdot \frac{{\rho C_{p} ({{m_{2} } \mathord{\left/ {\vphantom {{m_{2} } {m_{d} }}} \right. \kern-0pt} {m_{d} }})}}{{(T - T_{p2} )}} \cdot \frac{{(T_{p1} - T_{p2} )}}{{(t_{1} - t_{2} )^{2} }}E(t_{1} ) $$
(19)
$$ \frac{{\partial h_{c} }}{{\partial t_{2} }}E(t_{2} ) = \frac{{(m_{1} - m_{2} )}}{{(t_{1} - t_{2} )^{2} }} \cdot \frac{\lambda }{{A(T - T_{p2} )}} \cdot E(t_{2} ) + \frac{V}{A} \cdot \frac{{\rho C_{p} ({{m_{2} } \mathord{\left/ {\vphantom {{m_{2} } {m_{d} }}} \right. \kern-0pt} {m_{d} }})}}{{(T - T_{p2} )}} \cdot \frac{{(T_{p1} - T_{p2} )}}{{(t_{1} - t_{2} )^{2} }}E(t_{2} ) $$
(20)
$$ \frac{{\partial h_{c} }}{{\partial T_{p2} }}E(T_{p2} ) = \frac{{(m_{1} - m_{2} )}}{{(t_{1} - t_{2} )}} \cdot \frac{\lambda }{{A(T - T_{p2} )^{2} }} \cdot E(T_{p2} ) + \frac{V}{A} \cdot \frac{{\rho C_{p} ({{m_{2} } \mathord{\left/ {\vphantom {{m_{2} } {m_{d} }}} \right. \kern-0pt} {m_{d} }})}}{{(T - T_{p2} )^{2} }} \cdot \frac{{(T_{p1} - T)}}{{(t_{1} - t_{2} )}} \cdot E(T_{p2} ) + \frac{{4\varepsilon \sigma T_{p2}^{3} }}{{\left( {T - T_{p2} } \right)}} \cdot E\left( {T_{p2} } \right) $$
(21)
$$ \frac{{\partial h_{c} }}{{\partial T_{p1} }}E(T_{p1} ) = \frac{V}{A} \cdot \frac{{\rho C_{p} ({{m_{2} } \mathord{\left/ {\vphantom {{m_{2} } {m_{d} }}} \right. \kern-0pt} {m_{d} }})}}{{(T - T_{p2} )}} \cdot \frac{1}{{(t_{1} - t_{2} )}} \cdot E(T_{p1} ) $$
(22)
$$ \frac{{\partial h_{c} }}{\partial R}E(R) = - \frac{{(m_{1} - m_{2} )}}{{(t_{1} - t_{2} )}} \cdot \frac{\lambda }{{2\pi R^{2} h(T - T_{p2} )}} \cdot E(R) - \frac{{\rho C_{p} ({{m_{2} } \mathord{\left/ {\vphantom {{m_{2} } {m_{d} }}} \right. \kern-0pt} {m_{d} }})}}{{2(T - T_{p2} )}} \cdot \frac{{(T_{p1} - T_{p2} )}}{{(t_{1} - t_{2} )}} \cdot E(R) $$
(23)
$$ \frac{{\partial h_{c} }}{\partial h}E(h) = - \frac{{(m_{1} - m_{2} )}}{{(t_{1} - t_{2} )}} \cdot \frac{\lambda }{{2\pi Rh^{2} (T - T_{p2} )}} \cdot E(h) $$
(24)

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Tripathy, P.P., Abhishek, S. & Bhadoria, P.B.S. Determination of convective heat transfer coefficient and specific energy consumption of potato using an ingenious self tracking solar dryer. Food Measure 8, 36–45 (2014). https://doi.org/10.1007/s11694-013-9163-2

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