Scattering of thermal waves by a heterogeneous subsurface spheroid inclusion including non-Fourier effects

Abstract

In this paper, a general solution for the temperature field generated by the modulated heating an opaque, semi-infinite solid containing a heterogeneous subsurface spheroid inclusion was presented. Based on the non-Fourier equation of heat conduction, multiple scattering of the thermal waves from the subsurface spheroid inclusion in the semi-infinite solid was investigated by using the wave function expansion method and the virtual image method. The thermal waves were generated at the surfaces of the semi-infinite solid by modulated, ultra-short laser pulses, and the boundary condition for the inclusion was conductive. The effects of the geometrical and physical parameters on the temperature distribution were analysed. Meanwhile, numerical results for the temperature variation on the frontal surface of the solid were calculated. The analytic method and numerical results can be used for analysis of heat conduction, thermal wave imaging, the physical inverse problem and evaluation of subsurface defects in solid materials.