Thermal shock waves under a Maxwell–Cattaneo model with temperature-dependent conductivity

The propagation of thermal shock waves under the Maxwell–Cattaneo hyperbolic heat conduction theory is considered. In particular, the thermal conductivity is allowed to dependent on the temperature, which makes the model nonlinear. A solution for the evolution of a discontinuity under the linearized version of the governing equations is found via singular surface theory. Then, the Rankine–Hugoniot conditions are established for the nonlinear heat conduction model. The latter two results are used to derive a novel approximate solution to the problem of a Heaviside pulse propagating into a half space. Finally, this approximate analytical expression is compared to the numerically-computed solution of the governing equations, and its range of validity is established.