Simplified Laplace Transform Inversion for Unsteady Surface Element Method for Transient Conduction

The unsteady surface element method is an analytical procedure for solving certain types of transient heat conduction problems. The method is intended for thermally contacting bodies of similar or dissimilar geometries such as occur in the contact conductance, fin, and temperature measurement problems. The method utilizes Duhamel's integral. The two simplified procedures in this paper utilize an approximate inverse Laplace transform relation given by Schapery to obtain functional forms of the solutions. In certain cases the approximate inverse Laplace relations simplify the solution greatly and produce acceptable accuracy. Tauberian, series, and numerical tests define these successful cases. The results presented are useful for the intrinsic thermocouple problem and as background for more general heat conduction problems.