An Exact Analytical Solution of the Strong Shock Wave Problem in Nonideal Magnetogasdynamics

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. 1. Introduction 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 [1], Sakurai [2, 3] and Rogers [4] have presented exact solutions for the problem of strong shock wave with spherical geometry, since the study of spherically symmetric motion is important for the theory of explosion in various gasdynamic regimes. Recently, Singh et al. [5, 6] presented an approximate analytical solution to the system of first order quasilinear partial differential equations that govern a one dimensional unsteady planar and nonplanar motion in ideal and nonideal gases, involving discontinuities. 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 [7] obtained exact solution of the equations governing the motion in a gas generated by a point explosion. Singh et al. [8] studied the influence of the magnetic field upon the collapse of the cylindrical shock wave problem. Menon and Sharma [9] investigated the influence of