An alternative construction of Green's functions for the two-dimensional heat equation

Abstract An alternative approach is developed for obtaining Green's functions for two-dimensional heat conduction problems that are formulated on thin plates of simple configuration (infinite strip, semi-strip, and rectangle). It is assumed that the plates are made of isotropic homogeneous conductive materials and Newton's law of cooling specifies the heat exchange through the plates’ facial surfaces. An extension is also suggested to make this approach suitable for some compound plates. Various combinations of the classical boundary conditions are imposed on plates’ edges.