Three-dimensional heat conduction in laminated anisotropic solids

Abstract

The problem solved in this thesis is one of transient linear heat conduction in a two layer, three-dimensional slab subjected to an arbitrary heat flux on one surface, where each layer is thermally orthotropic. The sides and bottom of the slab are either insulated (Bi = 0) or held at a constant temperature (Bi = infinity). The Biot number of the top surface varies from zero to infinity. The solution is developed by decomposing the problem into a number of simpler problems, each of which is solved using eigenfunction expansions. In the vertical direction, the eigenvalue problem is solved using the Krawczyk algorithm, and an orthogonality relationship is found by Vodicka's method.