Applications of the group of equations of the one-dimensional motion of a gas under the influence of monochromatic radiation

Zedan, Hassan A.

doi:10.1016/s0096-3003(01)00178-3

Cited by 34 publications

(12 citation statements)

References 3 publications

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“…The fundamental equations for cylindrically symmetric motion of a non-ideal gas under the action of monochromatic radiation and axial magnetic field, neglecting heat-conduction, viscosity and radiation of the medium, may be written as (Khudyakov[8], Greifinger and Cole [13], Nath [19], Zedan [23])…”

Section: Basic Equations and Boundary Conditionsmentioning

confidence: 99%

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

Vishwakarma¹,

Pandey²

2012

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Similarity solutions are obtained for one-dimensional flow under the action of monochromatic radiation behind a cylindrical magnetogasdynamic shock wave propagating in a non-ideal gas in presence of an axial magnetic field. The initial density of the medium and initial magnetic field are assumed to be constant. It is investigated that the presence of the magnetic field or the non-idealness of the gas decays the shock wave, and when the initial magnetic field is strong the non-idealness of the gas affects the velocity and pressure profiles significantly. Also, it is observed that the flow-variables behind the shock are affected significantly, by an increase in the parameter of radiation, when the initial magnetic field is strong. It is, therefore, inferred that the effect of the non-idealness of the gas and of the monochromatic radiation on the shock propagation become more significant when the strength of the initial magnetic field is increased.

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Section: Basic Equations and Boundary Conditionsmentioning

confidence: 99%

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

Vishwakarma¹,

Pandey²

2012

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“…In Eulerian coordinate, the governing equations of the unsteady, adiabatic spherically symmetric flow of the non‐ideal gas in the presence of a gravitational field under the action of monochromatic radiation, neglecting viscosity, heat‐conduction, and radiation of the medium may be written as follows (cf Khudyakov, Nath and Takhar,() Zedan, and Nath):

\frac{\partial ρ}{\partial t} + u \frac{\partial ρ}{\partial r} + ρ \frac{\partial u}{\partial r} + \frac{2 u ρ}{r} = 0,

\frac{\partial u}{\partial t} + u \frac{\partial u}{\partial r} + \frac{1}{ρ} \frac{\partial p}{\partial r} + \frac{\overset{G}{true} \overset{m}{true}}{r^{2}} = 0,

\frac{\partial U_{m}}{\partial t} + u \frac{\partial U_{m}}{\partial r} - \frac{p}{ρ^{2}} ((), \frac{\partial ρ}{\partial t} + u \frac{\partial ρ}{\partial r}) = \frac{1}{ρ r^{2}} \frac{\partial}{\partial r} false(F r^{2} false),

\frac{\partial F}{\partial r} = K F,

where r is the radial distance and t is the time, u is the fluid velocity, ρ is the density, p is the pressure, U m is the internal energy per unit mass,

\overset{m}{true}

is the mass of the heavy nucleus at the centre,

\overset{G}{true}

is the gravitational constant, F be monochromatic radiation at radial distance r and time t , and K is the absorption coefficient.…”

Section: Equations Of Motion and Boundary Conditionsmentioning

confidence: 99%

“…Using Equation 26 in Equation 39, we get the expression for the adiabatic compressibility as follows:…”

Section: Self-similarity Transformationsmentioning

confidence: 99%

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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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“…In recent times considerable study for the selfsimilar solutions in the process occurring under the action of monochromatic radiation of gaseous substances in the stellar regions has gained importance. Several problems relating to shock wave propagation in perfect gas and non-ideal gas with radiative and magneto hydrodynamic effects have been studied by Zedan (2002), Leygnac et al (2006), Sampaio (2013), Taylor and Ryan (2013).…”

Section: Introductionmentioning

confidence: 99%

Self-Similar Motion of Strong Converging Cylindrical and Spherical Shock Waves in Non-Ideal Stellar Medium

Dunna

Ramu

Satpathi

2018

JAFM

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A theoretical model for strong converging cylindrical and spherical shock waves in non-ideal gas characterized by the equation of state (EOS) of the Mie-Gruneisen type is investigated. The governing equations of unsteady one dimensional compressible flow including monochromatic radiation in Eulerian hydrodynamics are considered. These equations are reduced to a system of ordinary differential equations (ODEs) using similarity transformations. Shock is assumed to be strong and propagating into a medium according to a power law. In the present work, two different equations of state (EOS) of Mie-Gruneisen type have been considered and the cylindrical and spherical cases are worked out in detail. The complete set of governing equations is formulated as finite difference problem and solved numerically using MATLAB. The numerical technique applied in this paper provides a global solution to the problem for the flow variables, the similarity exponent for different Gruneisen parameters. It is observed that increase in measure of shock strength has effect on the shock front. The velocity and pressure behind the shock front increases quickly in the presence of the monochromatic radiation and decreases gradually. A comparison between the results obtained for non-ideal and perfect gas in the presence of monochromatic radiation has been illustrated graphically.

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Applications of the group of equations of the one-dimensional motion of a gas under the influence of monochromatic radiation

Cited by 34 publications

References 3 publications

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

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

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 Motion of Strong Converging Cylindrical and Spherical Shock Waves in Non-Ideal Stellar Medium

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