A self-similar flow of self-gravitating gas behind a shock wave with increasing energy,I

Self-similar flows of self-gravitating gas behind a spherical shock wave which are driven out by a propelling contact surface, propagating in a nonuniform atmosphere at rest, are investigated. The total energy content of the flow between a shock front and contact surface is taken to be time-dependent. In brief, the self-similar homothermal flows of self-gravitating gas behind a shock wave and Roche's model case are also studied in the present paper.     

Self-similar solutions in the theory of flare-ups in novae,II

The self-similar isothermal flow of a gas, moving under the gravitational attraction of a central body of fixed mass behind a spherical shock wave driven out by a propelling contact surface into a non-uniform stationary atmosphere is investigated. The total energy of the wave increases with time obeying a power law.     

Self-similar flows of a self-gravitating gas with increasing energy in uniform atmosphere

Self-similar flows of a gas, moving under the gravitational force of attraction behind a spherical shock wave, which are driven out by a propelling contact surface and propagating into a uniform atmosphere at rest are investigated. The energy of the expanding wave has been assumed to be time-dependent, obeying a power law. In the last section the self-similar homothermal flows of self-gravitating gas has been also discussed. A comparative study has been made between the nature of flow variables for adiabatic and homothermal flows.     

Identification of a blue object with a newly detected X-ray source

An approximate analytical solution for self-similar flow behind a spherically-symmetric magnetogasdynamic strong shock wave is investigated using the method of Laumbach and Probstein (1969). The total energy of flow is taken to be dependent on the shock radius obeying a power law. The shock is propagating into a perfect gas at rest with non-uniform density and magnetic field.     

An isothermal shock wave in a perfectly-conducting and non-homogeneous stellar interior

In the present paper, we have obtained some exact analytic self-similar solutions for a zero-temperature gradient behind a magnetogasdynamic shock wave produced by stellar explosions. The initial density of the medium is taken to vary as some power of the distance from the point of explosion. The solutions are obtained for the cases when the energy of the shocked gas is constant, the energy is varying, and the shock velocity is constant. General solutions are also obtained. We have also analytically obtained the position of the singular surface behind the shock wave.     

Unsteady isothermal flow of a gas behind an exponential shock in magnetogasdynamics

A self-similar flow of a perfect gas behind a strong shock driven out by a propelling contact discontinuity surface moving with time according to an exponential law in the presence of axial component of the magnetic field is investigated. The flow between the shock and the inner-expanding surface is assumed to be isothermal. The infinite electrically conductive and uniform medium has been taken into consideration.     

A self-similar flow behind a spherical shock wave with thermal radiation,I

Similarity solutions, for one-dimensional unsteady flow of a perfect gas behind a spherical shock wave produced on account of a sudden explosion or driven out by an expanding piston including the effects of radiative cooling, are investigated. The shock ahead of the point of explosion or piston is propagating into a transparent medium at rest with non-uniform density. The total energy of the wave is assumed to be time dependent obeying a power law.     

An approximate analytical solution for self-isothermal flow behind a radiation driven shock wave,II

An analytical solution for a self-similar isothermal flow behind a radiation driven shock wave in non-uniform medium at rest is investigated using the method of Laumbach and Probstein (1969).     

Isothermal shock waves in uniform atmospheres

Similarity solutions describing the isothermal flow of a perfect gas behind shock waves are investigated for spherical symmetry. The flow is caused by a propelling contact surface (or expanding piston) and its total energy increases as a power of the time. The shock is propagating in a medium at rest with a uniform density.     

Magneto-radiative shock wave propagation in a conducting plasma

Similarity solutions describing the flow of a perfect gas behind a spherical and cylindrical shock wave in a magnetic field with radiation heat flux have been investigated. The total energy of the expanding wave has been assumed to remain constant. The solutions, however, are only applicable to a gaseous medium where the undisturbed pressure falls as the inverse square of the distance from the line of explosion.     

Self-similar flows behind cylindrical shock waves in magnetogasdynamics

A comparative study has been made between the effects of transverse and axial components of the magnetic field on the self-similar flow variables of the field behind the cylindrical shock waves propagating into a non-uniform atmosphere at rest. The total energy of the wave is constant.     

A self-similar flow of self-gravitating gas behind a shock wave with radiation heat flux,I

Self-similar flows of self-gravitating gas behind the spherical shock wave propagating in a non-uniform atmosphere at rest, taking radiation heat flux into consideration, are investigated. The total energy of the wave is non-constant and can be made to vary slowly with time.     

A self-similar solution for spherically symmetric gravitational collapse

A model of gas-dynamical flow during gravitational collapse is analyzed mathematically by assuming its spherical symmetry and self-similarity. A shock wave diverging from the center emerges in this model. The physical requirements imposed on the post-shock flow at the center for the specified parameters at infinity unambiguously determine the shock front and the flow behind it.     

Shock waves from point-sources in a heat-conducting gas

The shock wave produced by a point source has been studied in a heat-conducting gas medium. The shock is assumed to be strong enough to neglect the ambient gas pressure and the similarity method is used. The distribution of flow quantities behind the shock have been obtained by the numerical integration of a system of ordinary differential equations using the boundary conditions at the shock wave.     

Propagation of a strong cylindrical shock wave in a rotational axisymmetric dusty gas with exponentially varying density

Non-similarity solutions are obtained for one-dimensional isothermal and adiabatic flow behind strong cylindrical shock wave propagation in a rotational axisymmetric dusty gas,which has a variable azimuthal and axial fluid velocity.The dusty gas is assumed to be a mixture of small solid particles and perfect gas.The equilibrium flow conditions are assumed to be maintained,and the density of the mixture is assumed to be varying and obeying an exponential law.The fluid velocities in the ambient medium are assumed to obey exponential laws.The shock wave moves with variable velocity.The effects of variation of the mass concentration of solid particles in the mixture,and the ratio of the density of solid particles to the initial density of the gas on the flow variables in the region behind the shock are investigated at given times.Also,a comparison between the solutions in the cases of isothermal and adiabatic flows is made.     

Self-similar solutions for the blast wave problem in radiative gasdynamics,I

Similarity solutions, describing the flow of a perfect gas behind spherical shock waves, are investigated including the radiation heat flux. The shock is assumed to be propagating in a medium at rest. Shock radius varies exponentially with time and density is inversely proportional to fifth power of the shock radius immediately ahead of the shock front.     

Modelling of self-similar cylindrical shock wave in radiating magnetogasdynamics,I

Self-similar flows of a perfect gas behind a cylindrical blast wave with radiation heat flux in the presence of an azimuthal magnetic field have been investigated. The effects of radiation flux and magnetic field together on the other flow variables have been studied in the region of interest. The magnetic field and density distribution vary as an inverse power of radial distance from the axis of symmetry. The electrical conductivity of the gas is taken to be infinite. The total energy of the flow between the inner expanding surface and the shock is assumed to be constant. We also have supposed the gas to be grey and opaque and the shock to be transparent and isothermal.     

Self-similar problem with increasing energy in radiative magneto-gas dynamics

In the present paper self-similar solutions have been investigated for the propagation of piston driven, radiative gas-dynamic shocks into an inhomogeneous ideal gas permeated by a current free azimuthal magnetic field for spherical symmetry. The effects of radiation flux and magnetic field together have been seen in the region of interest on the other flow variables. The total energy of the flow between the piston and the shock is taken to be dependent on the shock radius obeying a power law. The radiative pressure and energy have been neglected. This problem is more general than the others done so far. The word piston implies some means to drive plasma radially onwards.     

Approximate solutions for isothermal flows behind strong spherical shocks with variable energy

Self-similar unsteady flows with zero temperature gradient behind strong spherical shocks propagating in non-uniform perfect gas at rest are investigated. The total energy of the flow is assumed to be varying with the shock radius obeying a power law. Approximate solutions in a closed analytical form are obtained using the integral method. Also these solutions are shown to be useful to calculate easily and quickly the shock temperature, X-ray surface brightness and luminosity which are important in astrophysical problems. It is found that these approximate solutions are in close agreement with numerical solutions.     

Self-similar magnetogasdynamic cylindrical shock waves,I

Similarity solutions describing the flow of a perfect gas behind a cylindrical shock wave with transverse magnetic field are investigated in an inhomogeneous medium. The total energy of the shock wave is assumed to be constant. A comparative study has been made between the results with and without magnetic field.