Thermal waves scattering by a subsurface sphere in a semi-infinite exponentially graded material using non-Fourier's model

In this study, the multiple scattering of thermal waves and temperature distribution resulting from a subsurface sphere in a semi-infinite exponentially graded material are investigated, and the analytical expression of the temperature at the surface of the graded material is obtained. Non-Fourier heat conduction equation is applied to solve the temperature at the surface, and the image method is used to satisfy the semi-infinite boundary condition of graded material. The thermal wave fields are expressed using wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary condition of the sphere. According to the wave equation of heat conduction, a general solution of scattered thermal waves is presented for the first time. The temperature distribution and phase difference at the surface of the semi-infinite material with different parameters are graphically presented. Analyses show that the hyperbolic heat conduction equation cannot be regarded as a continuation of the parabolic heat conduction equation at very short time scale. The effects of the incident wave number, the structural and physical parameters on the distribution of temperature and phase difference in the semi-infinite material are also examined.