Diffusion in Heterogeneous Media

[+] Author and Article Information
M. D. Mikhailov, B. K. Shishedjiev

Applied Mathematics Center, Sofia 1000, Bulgaria

M. N. Ö̧zisik

Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, N. C. 27650

J. Heat Transfer 104(4), 781-787 (Nov 01, 1982) (7 pages) doi:10.1115/1.3245200 History: Received April 24, 1981; Online October 20, 2009


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.

Copyright © 1982 by ASME
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