Heat Transfer in Composite Solids with Heat Generation

[+] Author and Article Information
L. Feijoo, H. T. Davis

Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minn. 55455

D. Ramkrishna

School of Chemical Engineering, Purdue University, West Lafayette, IN 47906

J. Heat Transfer 101(1), 137-143 (Feb 01, 1979) (7 pages) doi:10.1115/1.3450904 History: Received November 30, 1977; Online August 11, 2010


Steady-state heat transfer problems have been considered in a composite solid comprising two materials, one, a slab, which forms the bulk of the interior and the other, a plate, which forms a thin layer around the boundary. Through the use of appropriate Green’s functions, it is shown that the boundary value problem can be converted into a Fredholm integral equation of the second kind. The integral operator in the integral equation is shown to be self-adjoint under an appropriate inner product. Solutions have been obtained for the integral equation by expansion in terms of eigenfunctions of the self-adjoint integral operator, from which the solution to the boundary value problem is constructed. Two problems have been considered, for the first of which the eigenvalues and eigenvectors of the self-adjoint operator were analytically obtained; for the second, the spectral decomposition was obtained numerically by expansion in a convenient basis set. Detailed numerical computations have been made for the second problem using various types of heat source functions. The calculations are relatively easy and inexpensive for the examples considered. These examples, we believe, are sufficiently diverse to constitute a rather stringent test of the numerical merits of the eigenvalue technique used.

Copyright © 1979 by ASME
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