Self similar flow behind an exponential shock wave in a self-gravitating, rotating, axisymmetric dusty gas with heat conduction and radiation heat flux

Bajargaan, Ruchi; Patel, Arvind

doi:10.1007/s12648-018-1199-z

Cited by 6 publications

(5 citation statements)

References 30 publications

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“…These relations show that thermal conductivity K and absorption coefficient α R depends on the ambient density variation index α λ . For the case of constant density, the relation (3.8) is similar to the relations (37) of Nath and Sahu [6] and (84) of Bajargaan and Patel [7].…”

Section: Similarity Transformationssupporting

confidence: 72%

“…Wang [4] discussed the problems of radiating walls, either moving or stationary, developing shocks at the head of self-similar flow field. Recently, the study of self similar solution of a shock wave in an ideal gas, non-ideal gas or dusty gas with the heat conduction and radiation heat flux has been done by many authors [1], [5], [6], [7], [8], [9], [10], [11].…”

Section: Introductionmentioning

confidence: 99%

“…Nath and Singh [22] have obtained self similar solution behind magnetogasdynamic exponential shock wave in a self-gravitating gas. Bajargaan and Patel [7] have obtained the similarity solution for the flow behind an exponential shock wave in a self-gravitating, rotating, axisymmetric dusty gas with heat conduction and radiation heat flux by assuming the variable azimuthal and axial fluid velocities. In all of these works, study of self similar solution of the flow behind a magnetogasdynamic exponential shock wave in a perfect gas under the effect of heat conduction and radiation heat flux together with variable density has not been done.…”

Section: Introductionmentioning

confidence: 99%

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Similarity solution for the flow behind a magnetogasdynamic exponential shock wave in a perfect gas with varying density, heat conduction and radiation heat flux

Bajargaan¹,

Patel²,

Singh³

2018

Preprint

Self Cite

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Similarity solutions are obtained for one dimensional, unsteady, adiabatic propagation of an exponential shock wave in a perfect gas with heat conduction and radiation heat flux, in the presence of azimuthal magnetic field. The shock wave is driven out by a piston moving with time according to an exponential law. The equilibrium flow conditions are maintained. The heat conduction is expressed in terms of Fourier's law and the radiation is considered to be of the diffusion type for an optically thick grey gas model. The thermal conductivity and the absorption coefficient are assumed to vary with temperature and density according to power law. The density and magnetic field ahead of the shock front, are assumed to vary as an exponential law. The effects of the variation of the strength of ambient magnetic field, heat transfer parameters, adiabatic exponent, ambient density variation index on the shock strength, the distance between the piston and the shock front, and on the flow variables are studied out in detail. The similarity solution exists only when the sum of shock radius and ambient magnetic field exponent is equal to the half of the ambient density exponent. It is manifested that the shock strength decreases by increasing the strength of ambient magnetic field but it is independent from the heat transfer parameters. The total energy of the flow field behind the shock front is not constant but varies as power of shock radius. The compressibility of the medium is increased in the non-magnetic field. Also, the presence of the magnetic field have significant effects on the shock wave.

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Section: Similarity Transformationssupporting

confidence: 72%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Similarity solution for the flow behind a magnetogasdynamic exponential shock wave in a perfect gas with varying density, heat conduction and radiation heat flux

Bajargaan¹,

Patel²,

Singh³

2018

Preprint

Self Cite

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“…The fundamental equations for one-dimensional unsteady adiabatic flow behind a shock wave in a self gravitating, rotating axisymmetric dusty gas (mixture of a non-ideal gas and small solid particles) under the action of monochromatic radiation, neglecting heat-conduction, viscosity, and radiation of the medium, can be presented in the Eulerian coordinates in the following form [1,15,19,30,31,32,33]:…”

Section: Equations Of Motion and Boundary Conditionsmentioning

confidence: 99%

“…Patel [28] has obtained self-similar solutions for the one-dimensional unsteady adiabatic flow of a dusty gas behind spherical shock wave under the gravitational field. Recently, the study of self-similar solution of a shock wave in a perfect gas, or non-ideal gas, or dusty gas with the gravitational field has been done by many authors [29,30,31].…”

Section: Introductionmentioning

confidence: 99%

Self similar flow under the action of monochromatic radiation behind a cylindrical shock wave in a self-gravitating, rotating axisymmetric dusty gas

Bajargaan,

Patel

2018

Preprint

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The propagation of a cylindrical shock wave in a self-gravitating, rotating axisymmetric dusty gas under the action of monochromatic radiation with a constant intensity per unit area, which has variable azimuthal and axial components of fluid velocity, is investigated. The gas is assumed to be grey and opaque, and the shock is assumed to be transparent. The dusty gas is considered as a mixture of non-ideal gas and small solid particles, in which solid particles are continuously distributed. To obtain some essential features of shock propagation, small solid particles are considered as a pseudo-fluid, and it is assumed that the equilibrium flow condition is maintained in the entire flow-field. Similarity solutions are obtained as well as the effects of the variation of the radiation parameter, the gravitation parameter, the non-idealness parameter of the gas, the mass concentration of solid particles in the mixture, the ratio of the density of solid particles to the initial density of the gas are worked out in detail. The similarity solution exists under the constant initial angular velocity, and the shock strength is independent from the radiation parameter and the gravitation parameter. It is found that radiation parameter dominates the effect of dusty gas parameters on the variation of radiation heat flux. The total energy of the flow-field behind the shock front is not constant but varies as fourth power of the shock radius.

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Similarity Solution for the Flow Behind a Magnetogasdynamic Exponential Shock Wave in a Perfect Gas with Varying Density, Heat Conduction, and Radiation Heat Flux

Bajargaan

Patel

Singh

2021

J Eng Phys Thermophy

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Self similar flow behind an exponential shock wave in a self-gravitating, rotating, axisymmetric dusty gas with heat conduction and radiation heat flux

Cited by 6 publications

References 30 publications

Similarity solution for the flow behind a magnetogasdynamic exponential shock wave in a perfect gas with varying density, heat conduction and radiation heat flux

Similarity solution for the flow behind a magnetogasdynamic exponential shock wave in a perfect gas with varying density, heat conduction and radiation heat flux

Self similar flow under the action of monochromatic radiation behind a cylindrical shock wave in a self-gravitating, rotating axisymmetric dusty gas

Similarity Solution for the Flow Behind a Magnetogasdynamic Exponential Shock Wave in a Perfect Gas with Varying Density, Heat Conduction, and Radiation Heat Flux

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