Modeling of Diffusion in Ellipsoidal Solids: A Comparative Study

Abstract

Most food materials are usually measured in three mutually perpendicular dimensions (length, width, and thickness) and considered approximately as general ellipsoids. In this article, we briefly reviewed the available studies on how to deal with the diffusion problems in ellipsoidal solids. A three-dimensional (3-D) model was proposed to accurately represent the kernel geometry and rigorously interpret the diffusion phenomena. By the finite difference method, the numerical solution of the diffusion equation for kernels of different shape factors was obtained and compared with those predicted by the one-dimensional (sphere) model and two-dimensional (axi-symmetrical body) model. Meanwhile, the effectiveness of the latter two models was evaluated.

Keywords:

• Drying
• Diffusion coefficient
• Finite difference method
• Shape factor
• Three-dimensional model