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.
Highlights
Green’s functions and fundamental solutions play an important role in both applied and theoretical studies on the physics of solids
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
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
Summary
Green’s functions and fundamental solutions play an important role in both applied and theoretical studies on the physics of solids. Melan and Parkus[11] presented the Green’s functions for a point heat source on the surface of a semi-infinite body. This is because the corresponding governing equations and general solutions for the fluid and solid are different Under this background, the Green’s function for fluid and thermoelastic two-phase plane under a line heat source are studied in this paper. Based on the general solutions (1) and (2) for isotropic thermoelastic material and fluid, the corresponding harmonic functions ψ j ( j = 1, 2, 3, 4) will be constructed, and the Green’s functions for a line heat source in the interior of fluid and thermoelastic two-phase plane are presented in following sections. Based on the general solutions (1) and (2), the coupled fields in this two-phase plane is derived
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