Thermodynamically consistent description of heat conduction with finite speed of heat propagation

In this work, governing equations for heat conduction with finite speed of heat propagation are derived directly from classical thermodynamics. For a one-dimensional flow of heat, the developed governing equation is linear and of parabolic type. In a three dimensional case, the system of nonlinear equations is formulated. Analytical solutions of the equations for one-dimensional flow of heat are obtained, and their analysis shows characteristic features of heat propagation with finite speed, being fully consistent with classical thermodynamics.