Generalized Sturm-Liouville Procedure for Composite Domain Anisotropic Transient Conduction Problems

With few exceptions most applications of analytical techniques have been limited to isotropic 1-D laminated domain problems. This is partly due to the added analytical complexity caused by anisotropy as well as the general lack of attention given to such thermal material properties. An attempt is made to extend the relatively simple and straightforward Vodicka-Tittle (1968, 1950, 1965) orthogonal expansion technique to 3-D configurations consisting of finitely many distinct fully anisotropic subdomains. The procedure developed is based on a 3-D piecewise weighted orthogonality principle in which the 1-D isotropic case reduces to the Vodicka-Tittle relation.