EXACT SOLUTION FOR ISOTHERMAL FLOW BEHIND A SHOCK WAVE IN A SELF-GRAVITATING GAS OF VARIABLE DENSITY IN AN AZIMUTHAL MAGNETIC FIELD

Similarity solution for the propagation of a spherical shock wave in a self-gravitating perfect gas with an azimuthal magnetic fi eld in the case of isothermal fl ow is investigated. The density and azimuthal magnetic fi eld strength in the ambient medium are assumed to vary and obey power laws. An exact similarity solution obtained using the McVittie method in the case of isothermal fl ow is reported for the fi rst time. The obtained solutions show that the radial fl uid velocity, density, pressure, magnetic fi eld strength, and the mass tend to zero as the point of symmetry is approached. The effects of the changes in the values of the adiabatic exponent γ and the exponent w in the variation of an initial density are considered in detail. It is shown that the magnetic fi eld strength and mass increase with γ, whereas an increase in w exerts the reverse effect on these fl ow variables.
   
Author:  G. Nath, Mrityunjoy Dutta, and S. Chaurasia
Keywords:  shock waves, similarity solution, gravitation, perfect gas, magnetogasdynamics, exact solution
Page:  1247