The Solution of Three-Dimensional, Composite Media Heat Conduction Problems by Synthesis Methods

A method, known as synthesis, is applied to the task of obtaining approximate solutions to the static heat conduction equation for three-dimensional, composite media problems with mixed boundary conditions. The method is based upon an expansion in terms of known two-dimensional solutions of the problem of interest. These known two-dimensional solutions (trial functions) are blended over the remaining dimension by unknown mixing coefficients which are defined by means of variational techniques. A modified canonical variational principle is derived which permits the use of discontinuous trial functions, which expands the class of problems to which the synthesis method can be applied. The equations defining the mixing coefficients are derived in some detail, and the results of several test problems display the potential of this method for analyzing realistic heat conducting systems.