Heat Transfer in a Locally Nonequilibrium Anisotropic Half-Space Based on a Generalized Wave Heat Transfer Law

Heat transfer in a thermodynamically nonequilibrium anisotropic half-space with transverse anisotropy is modeled using a generalized wave heat transfer law. The law retains the mathematical structure of the classical Fourier heat conduction equation, but incorporates a time argument delay equal to the relaxation time. The resulting governing equation is of parabolic type with a time delay corresponding to the relaxation time. For the three-dimensional unsteady heat conduction problem with tensorial transport coefficients, a novel analytical solution is derived by applying the double Fourier transform with respect to two spatial coordinates and the Laplace transform with respect to time. The computational results reveal that the isothermal surfaces are approximated by elliptic paraboloids with local inflection lines, while the temporal temperature profiles exhibit propagating fronts of jump discontinuities, thereby confirming the wave-like nature of heat transfer.