Narrow Results

The propagation of cylindrical shock wave under the influence of axial magnetic field in rotating medium under isothermal flow condition is investigated. The density, magnetic field and azimuthal and axial components of fluid velocity are assumed to be varying in the undisturbed medium. The arbitrary constants appearing in the expressions for infinitesimals of the Local Lie group of transformations bring about three different cases of solutions, i.e. with power law shock path, exponential law shock path and a particular case of power law shock path. Numerical solutions are obtained in the cases of power law and exponential law shock paths. Distribution of gasdynamical quantities are discussed through figures. The effects of variation in values of Alfven-Mach number $M_A^{-2}$, ambient azimuthal velocity index ${\lambda }_1$ and ambient density index $\varphi$ are studied on flow variables and on shock strength. The numerical integration is done using software Mathematica. It is obtained that magnetic field has a decaying effect on shock strength. Also, increase in value of ambient density or ambient azimuthal velocity variation index in the case of power law shock path and increase in value of ambient density variation index in case of exponential law shock path have the decaying effect on shock strength.

In this paper, the propagation of cylindrical shock wave in rotating non-ideal gas under adiabatic flow condition using Lie group of transformation method is investigated. The density is assumed to be constant and azimuthal fluid velocity is assumed to be varying in the undisturbed medium. The arbitrary constants appearing in the expressions for the infinitesimals of the Local Lie group of transformations bring about two different cases of solutions i.e. with a power-law and exponential-law shock paths. Numerical solutions are obtained for both the cases. Distribution of gasdynamical quantities is illustrated through figures. It is obtained that the reduced flow variables pressure and azimuthal fluid velocity decrease in general, whereas density and radial fluid velocity increase in case of power-law shock path. The reduced azimuthal fluid velocity decreases, whereas reduced density, pressure and radial fluid velocity increase in case of exponential-law shock path. Also, it is obtained that shock strength decreases with increase in value of adiabatic exponent or gas non-idealness parameter, whereas it increases due to increase in ambient azimuthal fluid velocity exponent.

This paper concerns with the similarity solutions using Lie group theoretic method for one-dimensional unsteady isothermal flow behind the shock wave in the mixture of non-ideal gas and small solid particles in rotating medium. Group theoretic technique brings the different possible cases of potential solutions with the power law, particular case of power law and exponential law shock paths with the different choices of constants present in the generators of the Lie group of transformations. Similarity solutions for non-ideal dusty gas (a mixture of non-ideal gas and small solid dust particles) exist if the density of the ambient medium is constant. Solutions are obtained for both exponential law and power law shock paths. The effects of the variation of the physical parameters on the flow variables distribution behind the shock wave front, and on the shock are discussed. The shock strength increases with an increase in the ratio of the specific heat of the solid particles to the specific heat of the gas at constant volume ${\beta }^{\prime }$, the initial azimuthal velocity variation index ${𝜃}_1$, and the ratio of the density of solid particles to the initial density of the gas $G_0$. The shock wave decays with an increase in the value of gas non-idealness parameter $\overline{b}$.

The lie group invariance method is used to study a cylindrical shock wave in a self-gravitating, rotating perfect gas in the presence of monochromatic radiation and an azimuthal or axial magnetic field. The density of the ambient medium is taken as variable according as the law of shock path. For the system of equations of motion, the one-dimensional optimal system of subalgebra is determined by using Lie group analysis. We have utilized optimal classes of infinitesimal generators to acquire the flow variable transformation and the similarity variable, which are important prerequisites for obtaining the system of ordinary differential equations from the system of partial differential equations. In detail, we have numerically solved and discussed the results in two cases: with power and exponential laws shock path. The effects of variation of the rotational parameter, gravitational parameter, Alfvén Mach number, adiabatic exponent, and dimensionless parameter that characterize the interaction between incident radiation flux and gas are studied in depth. A comparative study is done between power law and exponential law in respect of the strength of shock wave and the flow variables distribution in the flow-field region behind the shock front. The shock is stronger with an axial magnetic field in a power law case; whereas shock is stronger with an azimuthal magnetic field in an exponential law case. The shock strength is observed to decline when the adiabatic index of the gas or the Alfvén Mach number increases. The shock decay with rotational parameter in case of exponential law, but it strength enhanced in case of power law. Also, the rotational parameter and gravitational parameter have an exact opposite impact on the strength of shock in power law and exponential law cases.

This paper is concerned with the influence of memory-dependent heat transport law on rotating thermoelastic medium with voids via three-phase-lag. The entire pervious medium is rotating with a invariant angular haste, where the bounding airplane is subordinated to a thermal shock and is free of tractions. By employing the normal mode analysis, the exact expressions for the displacement components, stresses, temperature distribution and change in volume fraction field have been depicted graphically in the presence and the absence of gyration and memory-dependent outgrowth. The effect of the voiding is also bandied in the literature review.