Similarity solutions for strong magnetogasdynamic cylindrical shock wave in rotating axisymmetric ideal gas with radiation heat flux using Lie group theoretic method

Mathematical model for propagation of cylindrical shock wave under the influence of azimuthal magnetic field in rotating medium with radiation heat flux for adiabatic flow condition, using Lie group of transformation method is formulated and similarity solutions are obtained. The medium ahead of the shock is assumed to be at rest. The density, magnetic field, azimuthal and axial fluid velocities are presumed to be varying in the undisturbed medium. We have obtained two different cases of potential solutions considering different cases for the arbitrary constants appearing in the expressions of infinitesimals. Numerical solutions are obtained in the case of power law shock path. Distributions of magnetogasdynamical quantities are discussed through figures. The effects of increase in ambient azimuthal fluid velocity variation index, strength of magnetic field and ambient density exponent are examined on shock strength and on the flow variables. It is observed that shock strength decreases due to increase in strength of magnetic field. Whereas there is increase in strength of shock due to increase in ambient density or ambient azimuthal fluid velocity variation index. In general, density, azimuthal fluid velocity, pressure, radial fluid velocity, temperature and radiation heat flux decrease as we move inwards from the shock to the axis of symmetry. Magnetic field, axial fluid velocity and non-dimensional azimuthal component of vorticity vector 49 increase as we move inwards from the shock to the axis of symmetry. Non dimensional axial component of vorticity vector l(z) increases, attains the maximum and then decreases as we move inwards from the shock to the axis of symmetry. Numerical calculations are done and graphs are being plot using software Mathematica.