Mathematical model for solar drying of potato cylinders with thermal conductivity radially modulated

Mariana Trujillo Arredondo

doi:10.1117/12.2049771

28 May 2014 Mathematical model for solar drying of potato cylinders with thermal conductivity radially modulated

Mariana Trujillo Arredondo

Proceedings Volume 9108, Sensing for Agriculture and Food Quality and Safety VI; 91080N (2014) https://doi.org/10.1117/12.2049771
Event: SPIE Sensing Technology + Applications, 2014, Baltimore, MD, United States

Abstract

A mathematical model for drying potato cylinders using solar radiation is proposed and solved analytically. The model incorporates the energy balance for the heat capacity of the potato, the radiation heat transfer from the potato toward the drying chamber and the solar radiation absorbed by the potato during the drying process. Potato cylinders are assumed to exhibit a thermal conductivity which is radially modulated. The method of the Laplace transform, with integral Bromwich and residue theorem will be applied and the analytic solutions for the temperature profiles in the potato cylinder will be derived in the form of an infinite series of Bessel functions, when the thermal conductivity is constant; and in the form of an infinite series of Heun functions, when the thermal conductivity has a linear radial modulation. All computations are performed using computer algebra, specifically Maple. It is expected that the analytical results obtained will be useful in food engineering and industry. Our results suggest some lines for future investigations such as the adoption of more general forms of radial modulation for the thermal conductivity of potato cylinders; and possible applications of other computer algebra software such as Maxima and Mathematica.

Citation Download Citation

Mariana Trujillo Arredondo "Mathematical model for solar drying of potato cylinders with thermal conductivity radially modulated ", Proc. SPIE 9108, Sensing for Agriculture and Food Quality and Safety VI, 91080N (28 May 2014); https://doi.org/10.1117/12.2049771

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KEYWORDS

Modulation

Mathematical modeling

Bessel functions

Solar energy

Solar processes

Bismuth

Solar radiation

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