This paper presents a new procedure for using Green’s functions for transient heat conduction problems. It is developed as part of continuing research on the unsteady surface element (USE) method; the USE method provides a means for combining solutions for two or more different basic geometries. By combining such geometries, problems involving composite media can be solved including problems associated with foil heat flux gages. The new method involves partitioning Green’s function solutions over different time domains for each of which only a few terms are needed to describe the Green’s functions. The method is illustrated for the two-dimensional problem of a circular foil of finite thickness that is uniformly heated over a circular region and otherwise insulated. It is demonstrated that the method has the potential of providing extremely accurate values since six decimal accuracy is provided. Obtaining such accuracy using classical solution procedures is extremely difficult particularly for the extreme aspect ratios covered in this paper.

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