Some numerical methods of diffusion equation for dic technique

Abstract

Food drying is one of the common techniques for preserving food to decrease the moisture content and minimize the biochemical reactions of degradation. This paper focuses on the mathematical modeling of tropical fruits dehydration using instant controlled pressure drop (Détente Instantanée Controlée or known as DIC) technique. The mathematical model is described based on the Fick’s second type law [1]. Neglecting the effects of shrinkage, the Fick’s law is transformed into one dimensional partial differential equation (PDE) with parabolic type. The discretization of the PDE is based 3 points weighted finite difference approximation. The simulation of the diffusion equation is illustrated through some numerical iterative methods; Jacobi, Gauss Seidel, Red Black Gauss Seidel and Successive Over Relaxation (SOR) methods. The sequential algorithm is developed by using Matlab 7.6.0 software with R2008a version supported by Intel®CoreTM Processor. The numerical analyses of these iterative methods are compared in terms of number of iterations, time execution, maximum error, root mean square error and computational complexity cost.