THEORETICAL ANALYSIS OF THE DIFFUSION PROCESS INSIDE PROLATE SPHEROIDAL SOLIDS

ABSTRACT

A numerical solution of the diffusion equation to describe solute transport inside ellipsoids, assuming a constant difiusion coefficient and a corrective boundary condition, is presented. The difiusion equation in a prolate spheroidal coordinate system was used for a hidimensional case. The finite volume method was employed to discretize the basic equation, utilizing a uniform grid size. The equation was solved irteratively using the Gauss-Seidel method. The effect of Biot number and the aspect ratio of the body on diffusion rate and concentration during the process is presented. Plots are presented for Biot numbers from 0.05 to infinity and aspect ratios of 1.1, 2.0 and 5.0. To investigate the effect of the aspect ratio, different results changing the aspect ratio for Bi= 1.0 are shown. The results show that the model is consistent and it may be used to solve other cases such as those that include cylinder and sphere geometry, and/ or those with variable diffusion coefficients with small modifications.

Key Words and Phrases:

• simulation
• concentration
• drying
• heating
• cooling
• wetting
• ellipsoid
• elliptical geometry