2018 Volume 13 Issue 1 Pages JTST0012
In this work, the existing theoretical heat conductive models such as: Cattaneo-Vernotte model, simplified thermomass model, and single-phase-lag two-step model are summarized, and then a general model of hyperbolic heat conduction (HHC) is presented with boundary conditions prescribed as: (1) temperature at the boundary; (2) heat flux (not the temperature gradient) at the boundary. The convective boundary condition is not considered because it is impossible to produce a fluid motion at such time scale, e.g. picoseconds. In the context of HHC, the reciprocity relation of Green's function is systematically proven, based on which Green's function solution equation of the general model is completely derived. Meanwhile, Green's functions are deduced under several different sets of boundary conditions. Thus, solution to HHC based on Green's function is obtained, and it consists of three parts, i.e. boundary conditions, initial conditions and heat generations. The priority of the present solution is that the time-dependent boundary condition and heat generation may be dealt with, and that it is easy to extend the solution to multi-dimensional case. The accuracy of the solution is verified through numerical examples, and Laplace transform method is adopted to avoid the dispersions around the front of temperature wave for jump-type boundary conditions, thus the solution is further perfected.
