Magnetogasdynamic shock wave propagation using the method of group invariance in rotating medium with the flux of monochromatic radiation and azimuthal magnetic field

Abstract

Abstract The propagation of a cylindrical shock wave in rotating medium with azimuthal magnetic field under the action of monochromatic radiation using a method of group invariance is investigated. To derive similarity solutions as well as exact solutions, the group invariance technique is used. All classes of the solutions depending on the absorption coefficient are discussed by considering absorption coefficient to be variable or constant. A similarity solution is obtained, when the absorption coefficient is assumed to be variable. Two cases of solutions with a power law shock path are obtained by the different choices of arbitrary constants involving in the infinitesimal generators of the Lie group of transformations. To obtain the similarity solution in the case of the power law shock path, the density, magnetic field, axial and azimuthal velocity components are assumed to be varying and obeying power laws in the undisturbed medium. It is observed that with increase in the values of Alfven Mach number, adiabatic exponent and rotational parameter, shock strength decreases. The effects of variation of magnetic field strength, adiabatic exponent, rotational parameter and initial magnetic field variation index on the flow variables and on shock waves are analyzed graphically. Also, all classes of exact solutions are obtained by considering a constant absorption coefficient.