A self-similar solution of exponential shock waves in non-ideal magnetogasdynamics

Singh, L. P.; Husain, Akmal; Singh, Madhav

doi:10.1007/s11012-010-9325-9

Cited by 34 publications

(10 citation statements)

References 18 publications

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“…The set of differential equations (3.12)-(3.16) are numerically integrated with the boundary conditions (3.17)-(3.21) to obtain the non-dimensional variables of the flow-field V, R, H, P and J against the similarity variable l by using the Runge-Kutta method of order four, for the values (Khudyakov[8], Nath [19], Nath and Takhar [10], Ranga Rao and Purohit [24], Singh et. al [25], Vishwakarma and Singh [26] 0.05, 0.1. The case = b 0 corresponds to the perfect gas case (Nath[19]).…”

Section: Resultsmentioning

confidence: 95%

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: Resultsmentioning

confidence: 95%

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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“…18,19 Many researchers have worked to better understand the dynamics of shock waves with the magnetic field effects. The works of Arora et al, 20 Jena, 21 Menon and Sharma, 22 Nath and Singh, 23,24 Pandey and Pathak, 25 Pandey et al, 26 Ram et al, 27 Singh and Arora, 28 Singh et al, 29 Siddiqui et al, 30 Singh et al, 31,32 and Vishwakarma and Yadav 33 are worth mentioning in this context.…”

Section: Introductionmentioning

confidence: 95%

Propagation of shock waves in a non‐ideal gas under the action of magnetic field

Singh

Arora

2020

Math Methods in App Sciences

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In this paper, we use power series method to study the propagation of cylindrical shock waves produced on account of a strong explosion in a non-ideal gas under the influence of azimuthal magnetic field. Here, the density is assumed to be uniform and magnetic pressure is assumed to vary according to power law with distance from the symmetry axis in the undisturbed medium. Using power series method, we obtain approximate analytic solutions in the form of a power series in (a 0 /V) 2 , where a 0 and V are the velocities of sound in the undisturbed medium and shock front, respectively. The first-order and second-order approximate solutions to the considered problem are discussed with the help of the said method. We construct solutions for the first-order approximation in closed form. Distributions of the flow variables such as fluid velocity, density, pressure, and magnetic pressure for the first-order approximation are analyzed graphically behind the shock front. Also, the effects of non-ideal parameter and shock Cowling number on the flow variables are discussed. It is observed that an increase in the value of non-ideal parameter causes fluid velocity to increase, and density, pressure, and magnetic pressure to decrease. Increase in the shock Cowling number causes decrease in density and pressure, whereas increase in fluid velocity and magnetic pressure behind the shock. Also, it is found that numerical results obtained in the absence of magnetic field recover the existing results in the literature. Further, these results are found to be in good agreement with those obtained by the Runge-Kutta method of fourth-order. KEYWORDS magnetic field, non-ideal gas, power series method, Rankine-Hugoniot conditions, shock waves MSC CLASSIFICATION 35L67; 58J45

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“…The field variables describing the flow pattern can then be written in terms of the dimensionless functions of such that (Vishwakarma and Nath 2007 ; Singh et al. 2011 ; Nath 2014 ) where U , , W , P , G and H are function of only.…”

Section: Self-similarity Transformationsmentioning

confidence: 99%

“…Singh et al. ( 2011 ) have considered same problem by taking initial magnetic field and initial density constant with the assumption that the gas to be non-ideal and medium to be non-rotating, whereas we have considered the medium to be rotating and the initial magnetic field and initial density decreasing exponentially. Shock waves through a variable-density medium have been treated by Sakurai ( 1956 ), Rogers ( 1957 ), Sedov ( 1959 ), Rosenau and Frankenthal ( 1976 ), Nath et al.…”

Section: Introductionmentioning

confidence: 99%

Flow behind an exponential shock wave in a rotational axisymmetric perfect gas with magnetic field and variable density

Nath

Sahu

2016

SpringerPlus

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A self-similar model for one-dimensional unsteady isothermal and adiabatic flows behind a strong exponential shock wave driven out by a cylindrical piston moving with time according to an exponential law in an ideal gas in the presence of azimuthal magnetic field and variable density is discussed in a rotating atmosphere. The ambient medium is assumed to possess radial, axial and azimuthal component of fluid velocities. The initial density, the fluid velocities and magnetic field of the ambient medium are assumed to be varying with time according to an exponential law. The gas is taken to be non-viscous having infinite electrical conductivity. Solutions are obtained, in both the cases, when the flow between the shock and the piston is isothermal or adiabatic by taking into account the components of vorticity vector. The effects of the variation of the initial density index, adiabatic exponent of the gas and the Alfven-Mach number on the flow-field behind the shock wave are investigated. It is found that the presence of the magnetic field have decaying effects on the shock wave. Also, it is observed that the effect of an increase in the magnetic field strength is more impressive in the case of adiabatic flow than in the case of isothermal flow. The assumption of zero temperature gradient brings a profound change in the density, non-dimensional azimuthal and axial components of vorticity vector distributions in comparison to those in the case of adiabatic flow. A comparison is made between isothermal and adiabatic flows. It is obtained that an increase in the initial density variation index, adiabatic exponent and strength of the magnetic field decrease the shock strength.

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A self-similar solution of exponential shock waves in non-ideal magnetogasdynamics

Cited by 34 publications

References 18 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

Propagation of shock waves in a non‐ideal gas under the action of magnetic field

Flow behind an exponential shock wave in a rotational axisymmetric perfect gas with magnetic field and variable density

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