Three-dimensional thermal Green's functions of quasi-steady-state motion in anisotropic bimaterials and some related problems

Three-dimensional thermal Green's functions of quasi-steady-state motion, as well as that of steady-state conduction in anisotropic bimaterials are derived based on two-dimensional Fourier transform, and are separated as a sum of a full-space Green's function and a complementary part. It is worth mentioning that Green's functions of steady-state case can be obtained directly by replacing the moving source by the static one and be expressed in a more concise form. Although the present paper aims to develop Green's functions in anisotropic bimaterials, the derived solutions can be reduced to simple cases, such as in isotropic or orthotropic materials, in half-space or full-space, and on the interface or surface. Numerical examples are presented to verify the validity of present solutions. Moreover, the comparison between steady-state case and quasi-steady-state cases of two different velocities, indicates high correlation with the properties of material and the distortion of thermal fields induced by inertial effect. •Heat conduction of quasi-steady-state motion in general anisotropic media are solved.•Three-dimensional Green's functions of quasi-steady-state motion in bimaterials are derived for the first time.•Solutions can be reduced to simple cases of material properties or structures.•Solutions can be reduced to that of steady-state.•Numerical results show the inertial effect and the anisotropy.