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We construct the solutions to the strong shock wave problem with generalized geometries in nonideal magnetogasdynamics. Here, it is assumed that the density ahead of the shock front varies according to a power of distance from the source of the disturbance. Also, an analytical expression for the total energy carried by the wave motion in nonideal medium under the influence of magnetic field is derived.

The propagation of shock waves, generated by a strong explosion in earth’s atmosphere is of great interest both from mathematical and physical point of view due to its numerous applications in various fields. They result from a sudden release of a relatively large amount of energy; typical examples are lightening and chemical or nuclear explosions. Assume that we have an explosion, following which there may exist for a while a very small region filled with hot matter at high pressure, which starts to expand outwards with its front headed by a strong shock. The process generally takes place in a very short time after which a forward-moving shock wave develops, which continuously assimilates the ambient air into the blast wave. The study of strong shock wave problems has been of long interest for researchers in fields ranging from condensed matter to fluid dynamics due to its theoretical and practical importance. Practically, it is recognized that strong shock waves are excellent means for generating very high-pressure, high temperature plasma at the center of explosion. Many authors, for example, Arora and Sharma [

The study of interaction between gasdynamic motion of an electrically conducting medium and a magnetic field has been of great interest to scientists and engineers due to its application in astrophysics, geophysics, and interstellar gas masses. Taylor [

The present paper aims to construct the closed form solution of the basic equations governing the one dimensional unsteady flows of a nonideal gas involving strong shock waves under the influence of transverse magnetic field. The basic configuration investigated here is that which arises when a transverse magnetic field is generated by a current of finite, constant strength passing along a straight wire of infinite length and either a shock or detonation wave propagates with uniform speed outwards from the wire into the ambient undisturbed gas at rest. Also, an expression for the total energy carried by the wave motion is obtained.

The basic equations for unsteady flow of a one dimensional gasdynamic motion may be written as [

The system of (

The propagation velocity of the shock front

The Rankine-Hugoniot relations, given by the principle of conservation of mass, momentum, and energy across the shock front may be expressed as [

where

In the present problem the density

We construct a relation for the pressure in the flow field satisfying the Rankine-Hugoniot relations (

Plugging the value of

Using the Rankine-Hugoniot relations (

With the help of Rankine-Hugoniot condition (

Consequently, the analytical solution of the blast wave problem described in the prior section is given as

The total energy carried by the wave motion in nonideal medium under the influence of transverse magnetic field is expressed as [

Using solutions (

The constant

The solution (

It may be noted here that the total energy carried by the wave remains constant in planar case of ideal gas, whereas in case of nonideal medium it varies with respect time

In the present paper, a new exact solution is derived for a strong shock wave problem in nonideal magnetogasdynamics with the density ahead of the shock which is varied as a power of the distance from the origin of the shock wave. The effect of coupling between the nonideal effects and magnetogasdynamics phenomena on the flow field is analyzed. The exact solution presented in (

R. Singh acknowledges the financial support from the UGC, New Delhi, India, under the SRF scheme.