A self-similar solution for a strong shock wave in a mixture of a non-ideal gas and dust particles with radiation heat-flux

A self-similar solution for the flow behind a strong shock wave propagating in a mixture of a non-ideal gas and small solid particles in which the density remains constant and radiation flux is important, has been obtained. The solid particles are considered as a pseudo-fluid and it is assumed that the equilibrium flow condition is maintained. The radiative flux is calculated from the conservation equations without applying any restriction on optical properties of the medium. The effects of the non-idealness of gas b¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{b}$$\end{document}, the mass concentration of solid particles kp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_p$$\end{document} and the ratio of density of solid particles to the initial density of gas G1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_1$$\end{document} on the shock and on the flow-field behind it are investigated. It is shown that the effects of the non-idealness of the gas on the shock strength and on the flow-profiles in the flow-field behind the shock are reduced by the presence of solid particles in the gas.