A general analysis is presented of the structure of a steady state, plane-parallel shock wave in which both thermal conduction and radiative cooling are important. The fluid is assumed to have a perfect-gas equation of state, with radiative cooling a function only of its temperature and density. Conduction in both diffusive and saturated regimes is treated. For the case of a strong shock, with conductivity and cooling function varying as power laws in temperature, approximate analytic solutions describing the shock wave are derived. For a plasma of solar composition, conduction is found to have a significant effect on the shock temperature and overall thickness of the postshock layer only for shock velocities greater than about 30,000 km/s, corresponding to shock temperatures greater than about 10 to the 10th K, but it affects the local structure of parts of the shock wave at much lower velocities. The effects of conduction are greatly enhanced if the heavy-element abundance is increased.
Lacey, C. G. (1988). The structure of shocks with thermal conduction and radiative cooling. Astrophysical Journal, 326, 769-778. https://doi.org/10.1086/166136