Laplace-variational method for transient multidimensional temperature distributions

Abstract

An analytical method has been developed which will provide closed form approximate temperature distributions for two-dimensional transient conduction heat transfer problems. It is referred to a s a Laplace-variational method since it utilizes a Laplace transformation along with methods from the calculus of variations. The Laplace-variational method can be applied to bodies with or without heat generation. Application of the method to both of these types of two-dimensional problems is shown in this paper. Also, some one-dimensional and three-dimensional transient conduction heat transfer problems can be analyzed by the Laplace-variational method even though the method was formally prepared for two-dimensional problems. The procedure used to approach such problems by this method is outlined. Use of the Laplace-variational method in heat transfer problems means that the thermal properties of a material must be constant and also that a radiation boundary condition cannot be considered. Utilization of the technique in this paper has also been restricted to problems involving regular geometry.