Similarity solution of a collapsing cylindrical shock wave in a thermal radiating and conducting gas

Cylindrical converging shock waves can produce extremely high temperatures and pressures near the centre. Due to the high temperatures the effects of thermal radiation and heat conduction have a great impact on the motion of such a shock wave. We propose a similarity solution for this problem assuming optically thick gas. The determination of the decay parameter of the shock depends totally on a singularity occurring in the equation system. In our work, we show that the assumed heat transfer effects change this singularity. Solutions for different valves of the mean free path of radiation are shown and compared with the adiabatic solution.