Numerical Computation of Transient and Steady-state Periodic Thermal Wave Distribution in Homogeneous Media

Thermal wave inspection techniques utilise controlled heat diffusion to probe the surface and subsurface structure of a component [1-3]. Various techniques have been developed which use localised intensity or spatially modulated laser heating for thermal wave generation [2] and a variety sensors, acoustic, optical, and thermal, for their detection [3,4]. The quantitative application of these techniques rely on the computation of the surface temperature and its relation to the internal or surface thermal structure. Analytical solutions for the surface temperature are available for the inspection of layered structures, for example, a coating on a substrate. For samples containing defects of a finite geometry (spherical, lens, cylindrical, disc void/inclusion etc) analytical solutions are difficult to obtain. In these cases numerical methods are employed to solve the heat diffusion equation for the surface temperature. In this paper we discuss the application and limitations of finite difference method for periodic and transient heat diffusion.