Influence functions for the unsteady surface element method

The unsteady surface element (USE) method and its variants represent compact analytical and numerical methods for the solution of certain transient heat conduction problems. The USE method is based on Duhamel's theorem and uses two types of convolution integrals, including heat flux-based and temperature-based types. The use of influence functions is required for both types. The present investigation is concerned with some early time influence functions for some basic geometries for the unsteady state surface element method. The functions are developed in terms of simple algebraic expressions. The use of the developed functions is illustrated with the aid of examples.