Semi-analytical solution for temperature rise in a heterogeneous half plane containing arbitrarily shaped inhomogeneities subjected to surface heating

Temperature rise caused by surface heating is responsible for thermal-related failures of heterogeneous material, such as composites and alloys, in manufacturing processes and tribology. This study presents a semi-analytical method (SAM) for temperature rise in a half plane involving dispersed inhomogeneities of arbitrary shape undergoing external heat load. Green functions and frequency response functions (FRFs) for subsurface heat flux induced by the applied heat load, as well as a set of formulas for influence coefficients correlating disturbed temperature rise and uniform eigen-temperature gradients inside a rectangular inclusion in a full plane, are derived. The rectangular inclusion solution in a full plane is treated as an elementary solution to solve disturbed temperature rise in a heterogeneous half plane involving arbitrarily shaped inhomogeneities, through implementing the equivalent inclusion method (EIM), the method of images and discretizing the total computation area into a good many rectangular elements with the same size. Results obtained by the SAM are consistent with those of the finite element method (FEM). Effects of inhomogeneity numbers, material properties, volume fractions, and velocities of the moving heat load on temperature rise are discussed in detail. HIGHLIGHTS Green functions and frequency response functions for heat flux in a half plane subjected to surface heating are obtained. Influence coefficients relating disturbed temperature rise and uniform rectangular inclusion in a full plane are derived. The elementary rectangular inclusion method is utilized to cope with problems for inhomogeneities of arbitrary shapes and distributions. Effects of inhomogeneity numbers, material properties, volume fractions, and velocities of the moving heat load on temperature rise are discussed.