Lie group transformations for self‐similar shocks in a gas with dust particles

In this paper, Lie group of transformation method is used to investigate the self‐similar solutions for the system of partial differential equations describing one‐dimensional unsteady plane flow of an inviscid gas with large number of small dust particles. The forms of the drag force D and the heat transfer rate Q experienced by the particle not in equilibrium with the gas have been derived for which the system of equations admits self‐similar solutions. A particular solution to the problem in one case have been found out and is used to study the effect of the dust particles on the similarity exponent. Copyright © 2009 John Wiley & Sons, Ltd.