Bimaterial Green's function for transient and time harmonic heat transfer revisited

As bimaterial Green's functions for transient problems were often given in implicit or numerical forms, Wang et al. (JAM, 2022) attempted to extend the steady-state bimaterial Green's function to the transient one, but an error was identified recently. This technical brief revisits the derivation of the bimaterial Green's function for transient and time harmonic heat transfer cases. Using the Laplace transform on time and the Fourier transform on every plane parallel to the bimaterial interface, we obtain the explicit Green's function in the transformed space, which can be inversely transformed back to the time-spatial domain numerically for general bimaterials. However, two special cases are introduced with explicit Green's functions for transient and time harmonic heat transfer.