Two-dimensional heat conduction in a rigid thermal conductor within the dual-phase-lag model by one-sided Fourier transform

An exact analytical solution in closed form is obtained for a two-dimensional initial-boundary-value problem of heat wave propagation in a thick slab of an anisotropic rigid thermal conductor within the dual-phase-lag model. One-sided Fourier transform technique is used to obtain a formal solution. The method requires an essential change of the dependent variable in order to guarantee a suitable asymptotic time behavior of the unknown function. The solution satisfies prescribed boundary temperatures and zero initial conditions. Numerical results are presented to put in evidence the effect of the two thermal relaxation times on the behavior of the heat conduction process. In particular, it is shown that the governing equation for temperature includes both characters of wave propagation and diffusion due to the interplay between relaxation times. The influence of anisotropy is investigated. The present results confirm previous findings about heat propagation within dual-phase-lag. The proposed method can treat other geometries, viz. the half-space, quarter-space and the rectangular domain with arbitrary boundary and initial conditions. The obtained exact solution can be used to check approximate solutions arising from other techniques.