Diffusion in Heterogeneous Media

Abstract

Heat or mass diffusion problems of finite heterogeneous media are characterized by a set of partial differential equations for temperatures or mass concentrations, Tk (x, t), (k = 1, 2, . . . , n), in every point in space, which are coupled through source-sink terms in the equations. In the present analysis, appropriate integral transform pairs are developed for the solution of the n-coupled partial differential equations subject to general linear boundary conditions. Three-dimensional, time-dependent solutions are presented for the distributions of the potentials (i.e., temperatures or mass concentrations), Tk (x, t), (k = 1, 2, . . . , n), as a function of time and position for each of the n-components in the medium. The results of the general analysis are utilized to develop solutions for the specific cases of one-dimensional slab, long solid cylinder, and sphere. Numerical results are presented for the dimensionless potentials (i.e., temperature or mass concentration), Tk (x, t), (k = 1, 2, 3), at the center of the slab, long solid cylinder, or sphere for each of the three components of a three-component system.