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

• Based on non-Fourier heat conduction, a general solution of the temperature field produced by the multiple scattering of the thermal waves is presented.
• The position of the maximum surface temperature is determined by the relative thermal diffusion length μ/a.
• Over a certain range, the surface temperature increases as thermal conductivity coefficient ratio λ0/λ increases.
• The thermal relaxation time ratio τ0/τ, primarily influences the fluctuations in the surface temperature.
• When the buried depth is relatively small, the fluctuations in the maximum surface temperature increase due to the increase in the wave number.

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.