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Similarity solutions are obtained for unsteady adiabatic propagation of a cylindrical shock wave in a self gravitating, rotating, axisymmetric dusty gas with heat conduction and radiation heat flux in which variable energy input is continuously supplied by the piston. The dusty gas is taken to be a mixture of non-ideal gas and small solid particles. Azimuthal fluid velocity and axial fluid velocity in the ambient medium are taken to be variable. The equilibrium flow conditions are assumed to be maintained. The initial density is assumed to be constant. The heat conduction is expressed in terms of Fourier's law and the radiation is taken to be of the diffusion type for an optically thick grey gas model. The thermal conductivity and the absorption coefficient are assumed to vary with temperature and density. The effects of the variation of the gravitational parameter and the heat transfer parameters on the shock strength and the flow variables such as radial velocity, azimuthal velocity, axial velocity, density, pressure, total heat flux, mass behind the shock front, azimuthal vorticity vector, axial vorticity vector, isothermal speed of sound and adiabatic compressibility are studied. It is found that the presence of gravitation effect in the medium modify the radiation and conduction effect on the flow variables.

The system of gas dynamic equations governing the motion of one-dimensional unsteady adiabatic flow of a perfect gas in planer, cylindrical and spherical symmetry is solved successfully by applying the Adomian decomposition method under the exponential initial conditions. The solution of the system of equation is computed up to the five components of the decomposition series. The variation of the approximate velocity, density and pressure of the fluid motion with position and time is studied. It is found that there exists discontinuity or shock wave in the distribution of flow variables. The solution of system of gas dynamic equations by Adomian decomposition method is convergent for a domain of position and time. The decomposition method provides the variation of flow-variables with position and time separately which was not possible in similarity method.

Travelling wave solution of one-dimensional unsteady flow of a perfect gas with the effect of viscosity under Riemann condition is investigated. The system of gas dynamic equations are reduced into a single ordinary differential equation for non-dimensional velocity and Riemann condition is transformed into boundary conditions. The exact solution is obtained for the gas velocity, pressure, temperature and change-in-entropy under the constant boundary conditions taking the origin at inflection point of the gas velocity profile. It is found that the travelling wave is a shock transition zone of the thickness of order 10^(-6) meter. The viscosity of the gas, Mach number, ratio of specific heats, and Riemann condition has significant effects on the shock structure.

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