Approximate Analytic Solutions for One-Dimensional Piston Problem with Radiating Transfer

Abstract

We have considered the motion of a spherical, cylindrical or plane piston into a non uniform medium taking into account energy transfer by radiation. We have obtained approximate analytic solutions for the physical situation (i) when the medium is optically thin and (ii)when it is optically thick. We have made use of technique due to Chernyi in which the flow variables are expanded in series of powers of Epsional, the density ratio across the shock. Temperature distribution behind the shock front is depicted graphically for the limiting cases, mentioned above for a large number of cases including the situations when the medium ahead of the shock is homogeneous or otherwise.