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The propagation of the blast wave in self-gravitating non-ideal gas under the influence of axial magnetic field is investigated. The magnetic pressure and density are considered to be varying according to the power law. The approximate analytical solutions are obtained by expanding the flow variables in the form of power series using Sakurai’s technique. The zeroth- and first-order approximate solutions of self-gravitating non-ideal gas with magnetic field are discussed in detail. Solutions for zeroth-order approximation are constructed in analytical form. The effect of the flow parameters, namely parameter of non-idealness, adiabatic exponent, ambient density variation exponent and gravitational parameter on the flow variables, is discussed in detail. The results obtained in this work are compared with the results obtained by Sakurai and Nath, which are in good agreement

In this paper, the method of invariance of Lie group is used to find the similarity solutions of the cylindrical shock waves for one-dimensional unsteady flow in magnetogasdynamics in the presence of monochromatic radiation. The density is assumed to be non-uniform ahead of the shock. The radiation flux is assumed to move through the gas. It is also shown that how the radiation parameter, ambient density exponent, ratio of specific heats (adiabatic constant) and the initial magnetic field strength affect the profiles of the flow variables. It is found that the shock wave decays in the presence of strong magnetic field and shows reverse behavior in the case of monochromatic radiation, i.e., the shock wave grows faster in the presence of radiation. To obtain the similarity solutions and the profiles of the flow variables, numerical calculations are performed using the software package MATHEMATICA.