Nondestructive evaluation of a conducting sphere in semi-infinite functionally graded materials using thermal wave method

In this study, a theoretical model is presented to study the multiple scattering of non-homogeneous thermal waves from a conducting sphere buried in a semi-infinite functionally graded material, and the temperature at the semi-infinite surface is presented. The adiabatic boundary condition at the semi-infinite surface is considered. The thermal waves are excited at the surface of semi-infinite functionally graded materials by modulated optical beams. The model includes the multiple scattering effects of spherical thermal waves generated by the heat source. According to non-Fourier heat conduction, a general solution of scattered thermal waves is presented. The effects of subsurface sphere on the temperature and phase at the sample surface under different physical and geometrical parameters are analyzed. It is found that the temperature amplitude above the conducting spherical inclusion decreases because of the existence of the inclusion. The effect of the material properties of the conducting sphere on the temperature amplitude is less than that on the phase difference at the surface. The effect of the inclusion on the temperature at the surface is also related to the non-homogeneous parameter of FGMs, the wave frequency of thermal waves, and the distance between the inclusion and the semi-infinite surface.