HEAT-TRANSFER IN COMPOSITE SOLIDS WITH HEAT-GENERATION

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. 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, the authors believe, are sufficiently diverse to constitute a rather stringent test of the numerical merits of the eigenvalue technique used.