An Exact Solution for the Propagation of Shock Waves in Self-Gravitating Perfect Gas in the Presence of Magnetic Field and Radiative Heat Flux

An Exact Solution for the Propagation of Shock Waves in Self-Gravitating Perfect Gas in the Presence of Magnetic Field and Radiative Heat Flux

G. Nath Mrityunjoy Dutta R. P. Pathak

Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Allahabad - 211004, India.

Department of Mathematics, National Institute of Technology, Raipur G. E. Raipur-492001, India.

Corresponding Author Email:;
5 October 2017
| |
20 November 2017
| | Citation



Propagation of spherical shock wave with azimuthal magnetic field and radiation heat flux in self-gravitating perfect gas is investigated. The azimuthal magnetic field and the initial density are assumed to vary according to power law. An exact similarity solution is reported when loss of energy due to radiation escape is notable and radiation pressure is non-zero. The entire energy of the shock wave is varying and increases with time. The effects of variation of the radiation pressure number, the initial density variation index, the Alfven-Mach number, the gravitational parameter and the adiabatic exponent are workout in detail. The shock strength increases with an increase in the initial density variation index. On the other hand, presence of magnetic field or an increment in the value of the radiation pressure number or the ratio of specific heats or gravitational parameter the shock strength decreases. It is obtained that increase in the radiation pressure number and gravitational parameter has same behavior on the flow variables. Also, it is observed that an increase in the value of gravitational parameter and the adiabatic exponent have same behavior on the fluid velocity, the material pressure, the radiation pressure, the mass and the radiation flux and azimuthal magnetic field.


MHD Shock waves, Similarity solution, Self-gravitating perfect gas, Radiation pressure and radiation energy, Radiation heat flux.

1. Introduction
2. Fundamental Equations of Motions and Boundary Conditions
3. Self-similarity Transformations
4. Results and Discussion

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