EXACT SOLUTION FOR AN UNSTEADY ISOTHERMAL FLOW BEHIND A CYLINDRICAL SHOCK WAVE IN A ROTATING PERFECT GAS WITH AN AXIAL MAGNETIC FIELD AND VARIABLE DENSITY

An exact solution of the problem on the propagation of a cylindrical shock wave in a rotating perfect gas with an axial magnetic fi eld in the case of an isothermal fl ow is obtained. The initial density, magnetic fi eld strength, and the initial angular velocity in the ambient medium are assumed to vary according to the power law. An exact similarity solution obtained by the McVittie method for an isothermal fl ow in a rotating gas is fi rst reported. Similarity transformations are used to transform a system of partial differential equations into a system of ordinary differential equations, and then the product solution of McVittie is used to obtain the exact solution. The effects of the values of the gas specifi c heat ratio, rotational parameter, and of the strength of the initial magnetic fi eld are discussed. It is shown that the shock velocity increases and the shock strength decreases with increase in the values of these parameters. The effect of variation in the value of the initial density index is also studied. The obtained solutions show that the radial fl uid velocity, density, pressure, and the magnetic fi eld strength tend to zero as the axis of symmetry is approached.  
   
Author:  G. Nath
Keywords:  shock waves, exact solution, rotating medium, perfect gas, axial magnetic fi eld
Page:  1538