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

Verma, B. G.; Vishwakarma, J. P.

doi:10.1007/bf00645381

Cited by 17 publications

(6 citation statements)

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“…This solution is an example of exact solutions (except the solution for the radiation fl ux) for the fl ows of a rotating nonideal gas in radiative magnetogasdynamics. It corresponds to the exact solutions in ordinary gasdynamics by Sedov [1], in radiative gasdynamics by Ashraf and Sachdev [12], in radiative magnetogasdynamics by Verma and Vishwakarma [26], and for fl ows of a nonideal gas in radiative magnetogasdynamics by Vishwakarma and Pandey [17]. Results and Discussion.…”

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confidence: 75%

Magnetogasdynamic Cylindrical Shock Waves in a Rotating Nonideal Gas with Radiation Heat Flux

Vishwakarma

Patel

2015

J Eng Phys Thermophy

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A similarity solution is presented for a cylindrical magnetogasdynamic shock wave in a rotating nonideal gas in the presence of a variable axial magnetic fi eld in the case where the radiation heat fl ux is of importance. The initial angular velocity of the medium is assumed to vary as some power of the distance from the symmetry axis. The radiation heat fl ux is evaluated from the equation of motion without explicit use of the radiation transfer equations. It is shown that the gas nonidealness increases the shock strength but decreases the shock velocity. On the other hand, the presence of a magnetic fi eld decreases the shock strength but increases the shock velocity. Moreover, the shock velocity increases with the ratio of specifi c heats. The total energy of the shock wave increases with time.Keywords: cylindrical shock waves, self-similar fl ow, rotating nonideal gas, radiation heat fl ux, axial magnetic fi eld.Introduction. Formulation of self-similar problems and some examples describing the adiabatic motion in the context of nonrotating gas models of stars are considered by Sedov [1], Zel'dovich and Raizer [2], Lee and Chen [3], and Summers [4]. Experimental studies and astrophysical observations show that the outer atmosphere of planets rotates due to their rotation. Macroscopic motion with a supersonic speed occurs in an interplanetary atmosphere, so that shock waves are generated there. Thus, rotation of planets or stars signifi cantly affects the processes occurring in their outer layers; therefore, questions connected with explosions in a rotating gas atmosphere are of defi nite astrophysical interest. Chaturani [5] studied the propagation of cylindrical shock waves through a gas with solid body rotation and obtained solutions by the similarity method adopted by Sakurai [6]. Nath, Ojha, and Takhar [7] derived similarity solutions for the fl ow behind spherical shock waves propagating in a nonuniform rotating interplanetary atmosphere with increasing energy. Gangualy and Jana [8] studied a theoretical model of propagation of strong spherical shock waves in a self-gravitating atmosphere with a radiation fl ux in the presence of a magnetic fi eld. They also considered that the medium behind the shock rotated, but neglected rotation of the undisturbed medium. In all the works mentioned, the medium is taken to be a gas satisfying the equation of state of a perfect gas.The radiation infl uence on a shock wave and on a fl ow fi eld behind the shock front has always been of great interest, for instance, in nuclear power and space research. Consequently, similarity models for classical blast wave problems have been extended taking into account radiation (see [8][9][10][11][12][13][14][15]). Elliot [9] considered the explosion problem, introducing a radiation fl ux in its diffusion approximation. Wang [10] discussed the piston problem with radiation heat transfer in the thin and thick limits, as well as in the general case with an idealized two-direction approximation. Ashraf and Sachdev [12] did not explicitl...

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confidence: 75%

Magnetogasdynamic Cylindrical Shock Waves in a Rotating Nonideal Gas with Radiation Heat Flux

Vishwakarma

Patel

2015

J Eng Phys Thermophy

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“…We have considered an ideal gas behavior of the medium, so that (Vishwakarma et al [23], Verma and Vishwakarma [19])…”

Section: Fundamental Equations Of Motions and Boundary Conditionsmentioning

confidence: 99%

“…The expressions (34) to (39) identically satisfy equations (15)- (17), and hence they represent a solution of equations (15) - (19) in closed form.…”

Section: Self-similarity Transformationsmentioning

confidence: 99%

“…Their results are more relevant to the shock in the deep interior of stars. Several authors extended the classical selfsimilar approach of Sedov [1] for blast wave problems by taking radiation into account (see, [15][16][17][18][19][20] and many others). The majority of research works on radiation gasdynamics are related to the radiative heat flux only and little research has been done under the consideration of radiation energy and radiation pressure in the presence or absence of gravitational field.…”

Section: Introductionmentioning

confidence: 99%

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An Exact Solution for the Propagation of Shock Waves in Self-Gravitating Perfect Gas in the Presence of Magnetic Field and Radiative Heat Flux

Nath¹,

Dutta²,

Pathak³

2017

MMC_B

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Propagation of spherical shock wave with azimuthal magnetic field and radiation heat flux in self-gravitating perfect gas is investigated. The azimuthal magnetic field and the initial density are assumed to vary according to power law. An exact similarity solution is reported when loss of energy due to radiation escape is notable and radiation pressure is non-zero. The entire energy of the shock wave is varying and increases with time. The effects of variation of the radiation pressure number, the initial density variation index, the Alfven-Mach number, the gravitational parameter and the adiabatic exponent are workout in detail. The shock strength increases with an increase in the initial density variation index. On the other hand, presence of magnetic field or an increment in the value of the radiation pressure number or the ratio of specific heats or gravitational parameter the shock strength decreases. It is obtained that increase in the radiation pressure number and gravitational parameter has same behavior on the flow variables. Also, it is observed that an increase in the value of gravitational parameter and the adiabatic exponent have same behavior on the fluid velocity, the material pressure, the radiation pressure, the mass and the radiation flux and azimuthal magnetic field.

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“…Their solutions, therefore, hold without any restrictions imposed on optical properties of the medium. Verma and Vishwakarma [10] extended the problem treated by Ashraf and Sachdev [9] to take into account the effects of transverse magnetic field.…”

Section: Introductionmentioning

confidence: 99%

An exact solution for the propagation of cylindrical shock waves in a rotational axisymmetric non-ideal gas with axial magnetic field and radiative heat flux

Nath¹,

Sahu²,

Chaurasia³

2018

MMC_B

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Propagation of cylindrical shock wave in a rotational axisymmetric non-ideal gas with axial magnetic field, radiation heat flux and the components of vorticity vectors are investigated. The axial magnetic field and the fluid velocity in the ambient medium are assumed to vary and obey the power laws. An exact similarity solution is obtained. The total energy of the shock wave is not constant but increases with time. The effects of variation of parameter of non-idealness of the gas, the Alfven-Mach number and the adiabatic exponent of the gas are investigated. It is shown that an increase in the non-idealness of the gas or the ratio of specific heats of the gas or strength of initial magnetic field decreases the shock strength but increases the shock velocity. Further it is observed an increase in the value of parameter of non-idealness of the gas and adiabatic exponent of the gas have same behavior on the flow variables and the shock strength.

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

Cited by 17 publications

References 7 publications

Magnetogasdynamic Cylindrical Shock Waves in a Rotating Nonideal Gas with Radiation Heat Flux

Magnetogasdynamic Cylindrical Shock Waves in a Rotating Nonideal Gas with Radiation Heat Flux

An Exact Solution for the Propagation of Shock Waves in Self-Gravitating Perfect Gas in the Presence of Magnetic Field and Radiative Heat Flux

An exact solution for the propagation of cylindrical shock waves in a rotational axisymmetric non-ideal gas with axial magnetic field and radiative heat flux

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