Flow behind an exponential shock in a rotational axisymmetric mixture of non-ideal gas and small solid particles with heat conduction and radiation heat flux

Abstract

The propagation of exponential cylindrical shock wave in a rotational axisymmetric dusty gas with heat conduction and radiation heat flux, which has variable azimuthal and axial fluid velocities, is studied. The shock wave is driven out by a piston moving with time according to exponential law. Similarity solutions exist only when the surrounding medium is of constant density and constant angular velocity. The azimuthal and axial components of the fluid velocity in the ambient medium are assumed to be varying and obeying exponential laws. The dusty gas is assumed to be a mixture of small solid particles and non-ideal (or perfect) gas, in which solid particles are continuously distributed. In our model, it is assumed that the small solid particles are pseudo-fluid and the equilibrium flow-conditions are maintained in the flow-field. The heat conduction is expressed in terms of Fourier's law and the radiation is considered to be of the diffusion type for an optically thick grey gas model. The thermal conductivity K and the absorption coefficient αR are assumed to vary with density and temperature. The effects of the variation of the heat transfer parameters, mass concentration of solid particles in the mixture Kp, the ratio of the density of solid particles to the initial density of the gas Ga and the parameter of the non-idealness of the gas b¯ are worked out in detail. It is found that an increase in the ratio of the density of solid particles to the initial density of the gas or the conductive heat transfer parameter Γc or the radiative transfer parameter ΓR increases the compressibility of the mixture in the flow field behind the shock, and hence there is an increase in the shock strength. Also, it is shown that an increase in the parameter of non-idealness of the gas b¯ has decaying effect on the shock wave.