Flow behind an attached shock wave in a radiating gas

A simple method is used to determine the curvature of an attached shock wave and the flow variable gradients behind the shock curve at the tip of a straight-edged wedge placed symmetrically in a supersonic flow of a radiating gas near the optically thin limit. The shock curvature and the flow variable gradients along the wedge at the tip are computed for a wide range of upstream flow Mach numbers and wedge angles. Several interesting results are noted; in particular, it is found that the effect of an increase in the upstream flow Mach number or the radiative flux is to enhance the shock wave curvature which, however, decreases with an increase in the specific heat ratio or the wedge angle.     

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.     

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.     

Heat transfer in unsteady MHD couette flow of an electrically conducting,viscous, incompressible rarefied gas

An analytical study is performed to examine the heat transfer characteristics on the flow of a viscous, incompressible rarefied gas in a parallel plate channel under the action of transverse magnetic field when (i) suction velocity normal to the plate is constant, (ii) the second plate oscillates in time about a constant non-zero mean, (iii) fluid is subjected to a constant heat source of absorption type. Apprximate solutions for velocity, temperature, phase, and amplitude of skin-friction and rate of heat transfer are evaluated. Mean temperature profiles, phase and amplitude of rate of heat transfer at both plates are discussed graphically followed by a quantitative discussion. Mean rate of heat transfer is tabulated in Table I.     

Magnetogasdynamic cylindrical shock wave in an isothermal state of a gas,II

Non-self-similar isothermal flows behind weak cylindrical shock waves are investigated. The shock is assumed to be propagating in a medium at rest with uniform density permeated by a uniform transverse magnetic field. The electrical conductivity of the gas is infinite everywhere. The total energy of the disturbance is not constant but can be made to increase at a slow rate. A comparative study has been made between the results with an without a magnetic field.     

Anisotropic propagation of magnetogasdynamic sonic waves in conducting and radiating atmosphere

The propagation of sonic discontinuity in conducting and radiating atmosphere has been discussed under the influence of magnetic field. The velocity of sonic wave and its termination into shock wave has been obtained. We have also obtained the critical time at which sonic wave terminates into shock wave. There is significant effect of magnetic field on sonic velocity and its termination into shock wave.     

The interaction of an obliquely incident plane electromagnetic wave with an anisotropic moving conducting half-space

The interaction of an obliquely incident plane electromagnetic wave with an anisotropic moving conducting medium described by tensor constitutive parameters is studied. Starting from the Maxwell-Minkowski equations the wave solutions in the laboratory frame, the modified law of refraction and the reflecton and the transmission coefficients are obtained both for incidentE- andH-waves, corresponding to the two specific orientations of the plane of incidence relative to the direction of motion of the medium. The reflection and the transmission coefficients for a moving conducting medium do not, in general, add to unity resulting in the possibility of energy transference between the moving medium and the transmitted wave. Further the various reflection and transmission characteristics are modified in an interesting manner due to the finite conductivity, the anisotropy and the motion of the medium. Numerical results for the reflection and the transmission coefficients are presented for a range of the parameters characterizing the anisotropy and the velocity of the moving medium.     

Quasi-similar solution of the strong shock wave problem in non-ideal gas dynamics

The quasisimilar theory is used to investigate the solution of the blast wave problem with generalized geometries in a non-ideal gas satisfying the equation of state of the Van der Waals type. Here it is assumed that the distribution of normalized velocity, pressure and density are nearly similar in the narrow range of the shock strength. A comparison between approximate analytical solution and numerical solution of the problem is presented for the cylindrical geometry. The numerical solutions are presented for the generalized geometry in a non-ideal gas. It is also assessed as to how the non-idealness of the gas affects the behavior of the flow parameters.     

Symmetric flow of a viscous and heat conducting gas following a normal shock of variable strength

This paper makes a comparative study of viscous and heat conducting one dimensional, spherical and cylindrical flows follows a normal shock of variable strength. An exact solution representing progressive waves is applied to the problem of a shock advancing into a viscous and heat conducting region in which the pressure is constant but the density varies according to a simple power law.     

A self-similar flow of self-gravitating gas behind a spherical shock wave in magnetogasdynamics

This paper considers a spherical shock, in a conducting gas, of self-gravitating gas propagating in a non-uniform atmosphere at rest. Similarity principle has been used to reduce the equations governing the flow to ordinary differential equations under the assumption that the density varies as an inverse-power of distance from the point or explosion. The total energy of the wave is variable.Supported by CSIR, New Delhi under grant No. 7/57/287/81/EMR-I.     

Cooling and energy loss of partially ionized hydrogen gas behind a shock wave

We studied the difference in behavior of total energy and its thermal component during the radiative cooling of partially ionized hydrogen gas. Our calculations were fulfilled for the conditions in the atmosphere of a cool star. It is shown that the attenuation of total energy loss does not interfere with the cooling rate.     

The boundary-layer flow of a radiating gas by the integral equation method

The flow in the boundary layer of a very hot two-component plasma is analysed when the radiative heat flux is given by the exact integral equation expression. The basic nonlinear integro-differential equation is solved by perturbing it about the differential approximation for radiation. In this way some light is shed on the order of accuracy of the differential approximation of radiation. In fact an error of about 4% may be incurred by invoking the differential approximation.     

An exact similarity solution for a spherical shock wave in a magneto-radiative gas

An exact similarity solution for a spherical magneto-gas dynamic shock wave is obtained in the case when the loss of energy due to radiation escape is significant. The total energy of the shock wave is not constant but decreases with time. We have shown that due to the magnetic field, the radiation flux changes considerably.     

Magnetogasdynamic cylindrical shock wave model in an optically thin atmosphere

Similarity solutions for one-dimensional unsteady isothermal flow of a perfect gas behind a magnetogasdynamic shock wave including the effects of thermal radiation has been investigated in a uniform thin atmosphere. The flow is caused by an expanding piston and the total energy of the flow is assumed to be constant. Radiation pressure and energy have been neglected in comparison to radiation heat flux and the gas is assumed to be grey and opaque.     

Effects of viscous dissipation and free convection currents on the flow of an electrically conducting fluid past an accelerated vertical porous plate

In the present paper, the effects of free convection currents and the viscous dissipation on the unsteady flow of an electrically conducting and viscous incompressible fluid around an uniformly accelerated vertical porous plate subjected to a suction or injection velocity inversely proportional to the square root of time, in presence of a transverse magnetic field, have been investigated. Analytical solutions for the velocity and the temperature distributions, the skin-friction and the rate of heat transfer are obtained for small magnetic parameterM. During the course of discussion the effects of the Grashof number Gr, the Eckert number Ec, the suction/injection parametera have been considered for unit value of the Prandtl number Pr.Nomenclature a suction/injection parameter - C _p specific heat at constant pressure - B ₀ magnetic induction - g acceleration due to gravity - Gr Grashof number (g(T _w –T )/U ₀ ³ ) - K thermal conductivity - M magnetic field parameter (B ₀ ² /U ₀ ² ) - Pr Prandtl number (C _p/K) - T temperature of the fluid near the plate - T _w temperature of the plate - T temperature of the fluid at infinity - t time - t dimensionless time (tU ₀ ² /) - u velocity of the fluid - u non-dimensional velocity (u/U ₀) - U velocity of the plate - U dimensionless velocity of the plate (U/U ₀) - U ₀ reference velocity - v ₀ suction velocity - v ₀ non-dimensional suction velocity (v ₀/U ₀)=at ^–1/2 - Ec Eckert number ((U ₀)^2/3/C _p(T _w –T )) - T dimensionless temperature of the fluid near the plate ((T–T )/(T _w ^–T )) - x, y coordinates along and normal to the plate - x, y dimensionless coordinates (y=yU ₀/) - kinematic viscosity - coefficient of volume expansion - electric conductivity of the fluid - y/2t ^1/2 - density of the fluid - skin-friction - dimensionless skin-friction - q rate of heat transfer - q non-dimensional rate of heat transfer - coefficient of viscosity - _e magnetic permeability On leave of absence from Department of Mathematics, University of Dhaka, Bangladesh     

Unsteady flow of a relativistic radiating gas in a gravitational field

The unsteady flow of a relativistic radiating neutrino gas is studied in a gravitational field. The curved body is assumed to be a vertical flat plate on which is imposed a time-dependent perturbation on a basic flow. For small perturbations, the ill-posed problem is reduced to a well-posed one and analytical solutions are developed.     

Efficiency of cosmic ray reflections from an ultrarelativistic shock wave

The process of cosmic ray acceleration up to energies in excess of 10²⁰ eV at relativistic shock waves with large Lorentz factors, Γ≫1, requires ∼Γ² particle energy gains at single reflections from the shock (cf. Gallant & Achterberg). In the present Letter , by applying numerical simulations we address an efficiency problem arising for such models. The actual efficiency of the acceleration process is expected to be substantially lower than the estimates of previous authors.     

Effect of overtaking disturbances on a strong cylindrical hydromagnetic shock wave in a self-gravitating gas

The effect of overtaking disturbances upon the free propagation of strong cylindrical hydromagnetic shock through a self-gravitating gas has been studied by an approximating technique developed by Yadav. Assuming an initial density distribution law as ₀=r^–w, where is the density at the axis of symmetry and is a constant, the analytical relation for shock velocity and shock strength modified by overtaking waves has been obtained under two conditions: viz., (i) when the applied axial magnetic field is strong and (ii) when the field is weak. The results obtained here are compared with those for a freely propagating shock. The conclusions arrived at agreed with experimental results.It is shown that the applications of the CCW method and the neglect of overtaking disturbances are equivalent.     

The motion of the cylindrical-symmetrical relativistic shock wave in the presence of an axial magnetic field

Some observed astrophysical phenomena, such as the blast of a supernova, suggest the necessity to study the motion of shock waves in a relativistic fluid flow in the presence of a magnetic field. This paper deals with the motion of a special relativistic shock wave which propagates from the center line outwardly after an explosion with the assumption that the magnetic field which has an axial component only. Similarity solutions which depend on the parameter =r/t are constructed. Two special cases are then studied in detail. In the first case, there is an ultrarelativistic fluid in front of the shock and in the second case, there is a cold fluid in front of the shock.     

Effect of overtaking disturbances on the propagation of spherical shock wave through self-gravitating gas

Effect of overtaking disturbances on the propagation of a spherical shock wave in self gravitating gas has been studied by the technique developed by the first author [Mod. Meas. Cont. B,46(4), 1 (1992)]. The analytical expressions for modified shock velocity and shock strength have been obtained for an initial density distribution0 =r ^–w, where is the density at the axis of symmetry andw is a constant; simultaneously, for the two cases viz.; (i) when the shock is strong and ii) when it is weak. The results accomplished here have been compared with those for freely propagation of shock.It is observed that the conclusions arrived at here agree with experimental observations. Finally, the modified expressions for the pressure, the density and the particle velocity immediately behind the shock have also been derived from, for both cases.