The problem of non-equilibrium heat conduction in a semi-infinite medium subjected to a step change in
temperature is analyzed thermodynamically using the extended irreversible thermodynamic approach. The
results show clearly the wave nature of the dimensionless temperature distribution, Stanton number and the
dimensionless entropy change profiles. The non-equilibrium profiles approach the equilibrium profiles as
the speed of wave propagation is increased. The results also show that the non-equilibrium temperature is
higher than the equilibrium temperature but the difference decreases as the wave propagation speed increases.