Similarity Solution for a Cylindrical Shock Wave in a Self-gravitating, Rotating Axisymmetric Dusty Gas with Heat Conduction and Radiation Heat Flux

Abstract

Similarity solutions are obtained for unsteady adiabatic propagation of a cylindrical shock wave in a self gravitating, rotating, axisymmetric dusty gas with heat conduction and radiation heat flux in which variable energy input is continuously supplied by the piston. The dusty gas is taken to be a mixture of non-ideal gas and small solid particles. Azimuthal fluid velocity and axial fluid velocity in the ambient medium are taken to be variable. The equilibrium flow conditions are assumed to be maintained. The initial density is assumed to be constant. The heat conduction is expressed in terms of Fourier's law and the radiation is taken to be of the diffusion type for an optically thick grey gas model. The thermal conductivity and the absorption coefficient are assumed to vary with temperature and density. The effects of the variation of the gravitational parameter and the heat transfer parameters on the shock strength and the flow variables such as radial velocity, azimuthal velocity, axial velocity, density, pressure, total heat flux, mass behind the shock front, azimuthal vorticity vector, axial vorticity vector, isothermal speed of sound and adiabatic compressibility are studied. It is found that the presence of gravitation effect in the medium modify the radiation and conduction effect on the flow variables.

Similarity solution for the flow behind a magnetogasdynamic exponential shock wave in a perfect gas with varying density, heat conduction and radiation heat flux

“…We have taken two values of γ, i.e. γ = 5 3 for fully ionized gas and γ = 4 3 for relativistic gas, which are applicable to interstellar medium. The most general range of values of adiabatic exponent seen in real stars are marked by these two values of γ.…”

“…Wang [4] discussed the problems of radiating walls, either moving or stationary, developing shocks at the head of self-similar flow field. Recently, the study of self similar solution of a shock wave in an ideal gas, non-ideal gas or dusty gas with the heat conduction and radiation heat flux has been done by many authors [1], [5], [6], [7], [8], [9], [10], [11].…”

Self similar flow under the action of monochromatic radiation behind a cylindrical shock wave in a self-gravitating, rotating axisymmetric dusty gas

“…The relation ( 53) is analogous to the relations (103) of Rogers [27] and (20) of Singh [29] for the case of a perfect gas with a variable initial density of the medium, equation (3.7) of Patel [28] for the case of a mixture of perfect gas and small solid particles, equation (55) of Bajargaan and Patel [30] for the case of a mixture of non-ideal gas and small solid particles. The quantity G 0 is a gravitation parameter, which is analogous to the parameter l 1 of Rosenau [39].…”

“…The fundamental equations for one-dimensional unsteady adiabatic flow behind a shock wave in a self gravitating, rotating axisymmetric dusty gas (mixture of a non-ideal gas and small solid particles) under the action of monochromatic radiation, neglecting heat-conduction, viscosity, and radiation of the medium, can be presented in the Eulerian coordinates in the following form [1,15,19,30,31,32,33]:…”

“…Patel [28] has obtained self-similar solutions for the one-dimensional unsteady adiabatic flow of a dusty gas behind spherical shock wave under the gravitational field. Recently, the study of self-similar solution of a shock wave in a perfect gas, or non-ideal gas, or dusty gas with the gravitational field has been done by many authors [29,30,31].…”