Two-dimensional Green's functions for fluid and thermoelastic two-phase plane

Abstract

The two-dimensional Green's functions for a steady-state line heat source in the interior of fluid and thermoelastic two-phase plane are derived in this paper. By virtue of the compact two-dimensional general solutions which are expressed in harmonic functions, four newly introduced harmonic functions with undetermined constants are constructed. Then, all the thermoelastic components in the fluid and thermoelastic two-phase plane can be derived by substituting these harmonic functions into the corresponding general solutions. And the undetermined constants can be obtained by the corresponding conditions of compatibility, boundary and equilibrium. Numerical results are given graphically by contours.