An analytically resolved model of a potato's thermal processing using Heun functions

Agustín Vargas Toro

doi:10.1117/12.2049761

28 May 2014 An analytically resolved model of a potato's thermal processing using Heun functions

Agustín Vargas Toro

Proceedings Volume 9108, Sensing for Agriculture and Food Quality and Safety VI; 91080M (2014) https://doi.org/10.1117/12.2049761
Event: SPIE Sensing Technology + Applications, 2014, Baltimore, MD, United States

Abstract

A potato’s thermal processing model is solved analytically. The model is formulated using the equation of heat diffusion in the case of a spherical potato processed in a furnace, and assuming that the potato’s thermal conductivity is radially modulated. The model is solved using the method of the Laplace transform, applying Bromwich Integral and Residue Theorem. The temperatures’ profile in the potato is presented as an infinite series of Heun functions. All computations are performed with computer algebra software, specifically Maple. Using the numerical values of the thermal parameters of the potato and geometric and thermal parameters of the processing furnace, the time evolution of the temperatures in different regions inside the potato are presented analytically and graphically. The duration of thermal processing in order to achieve a specified effect on the potato is computed. It is expected that the obtained analytical results will be important in food engineering and cooking engineering.

Citation Download Citation

Agustín Vargas Toro "An analytically resolved model of a potato's thermal processing using Heun functions", Proc. SPIE 9108, Sensing for Agriculture and Food Quality and Safety VI, 91080M (28 May 2014); https://doi.org/10.1117/12.2049761

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