Approximate analytical solutions for self-similar flows of a dusty gas with variable energy

The study of self-similar flows behind strong shocks propagating in a mixture of a gas and small solid particles with constant initial density is discussed. Using a simple integral method, approximate analytical solutions are obtained for the flow field with both adiabatic and isothermal assumptions. The effect of mass concentration of solid particles in the mixture and the ratio of the density of the solid particles to that of the initial density of the gas on solutions of the flow field are investigated. By taking the parameter characterizing the presence of solid particles as zero, approximate solutions for adiabatic flows of perfect gas with variable energy are obtained. Approximate solutions are compared with numerical solutions and are found to be in close agreement. Graphs and tables are used to illustrate the results.