Flow behind the magnetogasdynamical cylindrical shock wave in rotating non-ideal dusty gas with monochromatic radiation

The proliferation of the cylindrical shock in non-ideal rotating gases accompanying the mixture of crystalline solids with monochromatic radiation as well as magnetic (azimuthal/axial) field is examined. The fluid velocity of ambient media is considered to contain radial, axial, and azimuthal heads. Similarity solutions are achieved. The distribution of flow variables in the medium just behind the shock for the cases of power-law shock paths are analyzed. This is worthy to note, the pressure and density at piston disintegrate in occupancy of an azimuthal magnetic field, therefore suction structures at the axis of symmetry, which is identically in accord with controlled circumstances for trying to produce shock waves.

Similarity solutions for cylindrical shock wave in rotating non-ideal gas using Lie group theoretic method

In this paper, the propagation of cylindrical shock wave in rotating non-ideal gas under adiabatic flow condition using Lie group of transformation method is investigated. The density is assumed to be constant and azimuthal fluid velocity is assumed to be varying in the undisturbed medium. The arbitrary constants appearing in the expressions for the infinitesimals of the Local Lie group of transformations bring about two different cases of solutions i.e. with a power-law and exponential-law shock paths. Numerical solutions are obtained for both the cases. Distribution of gasdynamical quantities is illustrated through figures. It is obtained that the reduced flow variables pressure and azimuthal fluid velocity decrease in general, whereas density and radial fluid velocity increase in case of power-law shock path. The reduced azimuthal fluid velocity decreases, whereas reduced density, pressure and radial fluid velocity increase in case of exponential-law shock path. Also, it is obtained that shock strength decreases with increase in value of adiabatic exponent or gas non-idealness parameter, whereas it increases due to increase in ambient azimuthal fluid velocity exponent.

SIMILARITY SOLUTIONS FOR CYLINDRICAL SHOCK WAVE IN SELF-GRAVITATING NON-IDEAL GAS WITH AXIAL MAGNETIC FIELD: ISOTHERMAL FLOW

The purpose of this study is to obtain the solution using the Lie group of symmetry method for the problem of propagating magnetogasdynamic strong cylindrical shock wave in a self-gravitating non-ideal gas with the magnetic field which is taken to be axial. Here, isothermal flow is considered. In the undisturbed medium, varying magnetic field and density are taken. Out of four different cases, only three cases yield the similarity solutions. Numerical computations have been performed for the cases of power-law and exponential law shock paths, to find out the behavior of flow variables in the flow-field immediately behind the shock. Similarity solutions are carried out by taking arbitrary constants in the expressions of infinitesimals of the Lie group of transformations. Also, the study of the present work provides a clear picture of whether and how the variations in the non-ideal parameter of the gas, Alfven-Mach number, adiabatic exponent, ambient magnetic field variation index and gravitational parameter affect the propagation of shock and the flow behind it. Software package “MATLAB” is used for all the computations.