A simple method to predict transient diffusion processes in ellipsoids

Abstract

This work is focused on transient diffusion processes inside semi-solid and solid agri-food products presenting ellipsoidal shape, i.e. prolate and oblate spheroids and general ellipsoid. Many typical industrial operations like drying, soaking, rehydration, heating, cooking, and cooling, can be effectively modelled by using Fick's law for mass diffusion and Fourier's law for heat conduction, with constant properties and neglecting volume/shape variations. To predict such processes, there are some methods available in the literature, although they are limited to certain shapes and/or operating conditions and their implementation can be quite complicated. Therefore, our objective was to develop a simple method to predict transient diffusion processes in ellipsoids and spheroids, considering both local and average values of industrial interest. The methodology to obtain such a simple method consisted in first generating numerical data by simulating a wide range of shapes and conditions, and then fitting a simple two-parameter expression, which is based on the analytical solution for regular geometries. The developed method can be easily implemented through the use of tabulated values provided in this article. Finally, the capability of the proposed method was verified by using previously reported data, showing very good results and demonstrating that it is easily implementable. It is expected that the developed simple method can be helpful for industrial applications and to improve calculations in related fields of research, which may not be familiar with transport phenomena modelling.