Self-Similar Flow under the Action of Monochromatic Radiation Behind a Cylindrical MHD Shock in a Non-Ideal Gas

Vishwakarma, J. P.; Pandey, Vijay Kumar

doi:10.5923/j.am.20120202.06

Cited by 20 publications

(18 citation statements)

References 22 publications

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“…The set of differential Equations to are numerically integrated with the boundary conditions and to obtain the nondimensional variables of the flow‐field W , P , G , and J against the similarity variable η by using the Runge‐Kutta method of order four, for the values (Khudyakov, Nath and Takhar,() and Vishwakarma and Pandey)

γ = \frac{4}{3}, \frac{5}{3}; \bar{b} = 0.0, 0.05, 0.1; λ = - \frac{1}{2}; σ = 0; s = 1; q = - 1; G_{0} = 0.0, 1.0, 2.0, 3.0; ξ = 0.2, 10, 20, 50; n = - \frac{1}{3}; M^{*} = 4, 5 .

For fully ionized gas

γ = \frac{5}{3}

and for relativistic gases

γ = \frac{4}{3}

, which are applicable to interstellar medium. These two values of γ mark the most general range of values seen in real stars.…”

Section: Resultsmentioning

confidence: 99%

“…The dimensions of the constant coefficient K a in Equation are given by (Vishwakarma and Pandey)

false[K_{a} false] = M^{- λ - q - σ} L^{3 λ + q - s - 1} T^{2 q + 3 σ - l} .

…”

Section: Equations Of Motion and Boundary Conditionsmentioning

confidence: 99%

“…The dimensions of the constant coefficient K a in Equation 11 are given by (Vishwakarma and Pandey 19 )…”

Section: Equations Of Motion and Boundary Conditionsmentioning

confidence: 99%

“…Zheltukhin has developed a family of exact solutions of one dimensional motion (plane, cylindrical, or spherical symmetry) of a gas taking into account of the absorption of monochromatic radiation. Nath and Takhar,() Nath,() Vishwakarma and Pandey,() Nath and Sahu, and Sahu have studied the propagation of shock waves in a gas under the action of monochromatic radiation for ideal or non‐ideal gas.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Similarity solution for a spherical shock wave in a non‐ideal gas under the influence of gravitational field and monochromatic radiation with increasing energy

Sahu

2019

Math Methods in App Sciences

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The propagation of a spherical shock wave in a non‐ideal gas with or without gravitational effects is investigated under the action of monochromatic radiation. Similarity solutions are obtained for adiabatic flow between the shock and the piston. The numerical solutions are obtained using the Runge‐Kutta method of the fourth order. The density of the gas is assumed to be constant. The total energy of the shock wave is non‐constant and varies with time. The effects of change in values of non‐idealness parameter, gravitational parameter, shock Mach number, radiation parameter, and adiabatic exponent of the gas on shock strength and flow variables are worked out in detail. It is investigated that the presence of gravitational field increases the compressibility of the medium, due to which it is compressed and, therefore, the distance between the inner contact surface and the shock surface is reduced. A comparison is also made between the solutions in the cases of the gravitating and the non‐gravitating media. It is manifested that the gravitational parameter and the radiation parameter have in general opposite behaviour on the flow variables and the shock strength.

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γ = \frac{4}{3}, \frac{5}{3}; \bar{b} = 0.0, 0.05, 0.1; λ = - \frac{1}{2}; σ = 0; s = 1; q = - 1; G_{0} = 0.0, 1.0, 2.0, 3.0; ξ = 0.2, 10, 20, 50; n = - \frac{1}{3}; M^{*} = 4, 5 .

For fully ionized gas

γ = \frac{5}{3}

and for relativistic gases

γ = \frac{4}{3}

, which are applicable to interstellar medium. These two values of γ mark the most general range of values seen in real stars.…”

Section: Resultsmentioning

confidence: 99%

“…The dimensions of the constant coefficient K a in Equation are given by (Vishwakarma and Pandey)

false[K_{a} false] = M^{- λ - q - σ} L^{3 λ + q - s - 1} T^{2 q + 3 σ - l} .

…”

Section: Equations Of Motion and Boundary Conditionsmentioning

confidence: 99%

“…The dimensions of the constant coefficient K a in Equation 11 are given by (Vishwakarma and Pandey 19 )…”

Section: Equations Of Motion and Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Similarity solution for a spherical shock wave in a non‐ideal gas under the influence of gravitational field and monochromatic radiation with increasing energy

Sahu

2019

Math Methods in App Sciences

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show abstract

“…Shinde [20] obtained the similarity solution of the propagation of magnetogasdynamic cylindrical shock waves in a non-uniform, rotating perfect gas under the action of monochromatic radiation and gravitation. Vishwakarma and pandey [21] obtained the similarity solution for one-dimensional flow under the action of monochromatic radiation behind a cylindrical magnetogasdynamic shock wave propagating in a non-ideal gas. Nath, sahu and Dutta [22] obtained similarity solution of magnetohydrodynamic cylindrical shock wave in a non-uniform rotating nonideal gas under the action of monochromatic radiation.…”

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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Spherical Shock Generated by a Moving Piston in a Nonideal Gas under Gravitation Field with Monochromatic Radiation and Magnetic Field

Nath

2020

J Eng Phys Thermophy

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Self-Similar Flow under the Action of Monochromatic Radiation Behind a Cylindrical MHD Shock in a Non-Ideal Gas

Cited by 20 publications

References 22 publications

Similarity solution for a spherical shock wave in a non‐ideal gas under the influence of gravitational field and monochromatic radiation with increasing energy

Similarity solution for a spherical shock wave in a non‐ideal gas under the influence of gravitational field and monochromatic radiation with increasing energy

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

Spherical Shock Generated by a Moving Piston in a Nonideal Gas under Gravitation Field with Monochromatic Radiation and Magnetic Field

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