Distributions of gas dynamical quantities are discussed. The propagation of cylindrical shock wave in rotational axisymmetric perfect gas under isothermal flow condition with azimuthal magnetic field is investigated. The kinetic energy transfer is dominant in interplanetary shock, the plasma β value increases and the normal kinetic energy increment factor decreases with the shock propagating out-ward, which results in the interaction weakened between the shock and solar wind plasma. The energy input into the interaction region between forward-reverse shock through reverse chock while being driven 4. The transfer of magnetic and internal energy are indepedent of the flow speed, while that of kinetic energy shows a linear relation with the flow speed 3. field in interplanetary space, which results in an intensive magnetic region in the west part of a shock wave 2. The energy transfer rates are different in different regions on a shock front, because there are large scale magnetic. They depend on the shock angle, plasma β value in the up-stream and shock strength.1 By analysing these factors, the results demonstrate that: 1. View full-textĮnergy increment factors of MHD shock for magnetic, internal and kinetic energy have been derived from Rankine-Hugoniot relations. Further, these results are found to be in good agreement with those obtained by the Runge‐Kutta method of fourth‐order. Also, it is found that numerical results obtained in the absence of magnetic field recover the existing results in the literature. Increase in the shock Cowling number causes decrease in density and pressure, whereas increase in fluid velocity and magnetic pressure behind the shock. It is observed that an increase in the value of non‐ideal parameter causes fluid velocity to increase, and density, pressure, and magnetic pressure to decrease. Also, the effects of non‐ideal parameter and shock Cowling number on the flow variables are discussed. Distributions of the flow variables such as fluid velocity, density, pressure, and magnetic pressure for the first‐order approximation are analyzed graphically behind the shock front. We construct solutions for the first‐order approximation in closed form. The first‐order and second‐order approximate solutions to the considered problem are discussed with the help of the said method.
#Quasi linear transport equation systems shocks formation series
method, we obtain approximate analytic solutions in the form of a power series in (a0/V )², where a0 and V are the velocities of sound in the undisturbed medium and shock front, respectively. Here, the density is assumed to be uniform and magnetic pressure is assumed to vary according to power law with distance from the symmetry axis in the undisturbed medium. In this paper, we use power series method to study the propagation of cylindrical shock waves produced on account of a strong explosion in a non‐ideal gas under the influence of azimuthal magnetic field. The obtained solutions show that the radial fluid velocity, density, pressure, and the magnetic field strength tend to zero as the axis of symmetry is approached. The effect of variation in the value of the initial density index is also studied. It is shown that the shock velocity increases and the shock strength decreases with increase in the values of these parameters. The effects of the values of the gas specific heat ratio, rotational parameter, and of the strength of the initial magnetic field are discussed. Similarity transformations are used to transform a system of partial differential equations into a system of ordinary differential equations, and then the product solution of McVittie is used to obtain the exact solution. isothermal flow in a rotating gas is first reported. An exact similarity solution obtained by the McVittie method for an. The initial density, magnetic field strength, and the initial angular velocity in the ambient medium are assumed to vary according to the power law. Where \(x \in $$īy imposing certain smoothness and boundedness conditions for the sum of the coefficients.An exact solution of the problem on the propagation of a cylindrical shock wave in a rotating perfect gas with an axial magnetic field in the case of an isothermal flow is obtained.
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