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

Singh, Deepak Kumar; Arora, Rajan

doi:10.1002/mma.6848

Cited by 12 publications

(6 citation statements)

References 36 publications

(74 reference statements)

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“…Because of several advantages, many non‐linear problems have been solved using the power series method recently. For the latest research work based on the power series method, one may follow the literature available in other works 34–41 . In their study, 34 Siddiqui et al.…”

Section: Introductionmentioning

confidence: 99%

“…For the latest research work based on the power series method, one may follow the literature available in other works. [34][35][36][37][38][39][40][41] In their study, 34 Siddiqui et al analyzed the propagation of magnetogasdynamic shock waves and found the first-order approximate analytic solutions. Singh and Arora 35 extended the work presented in Siddiqui et al 34 by considering the gas to be non-ideal.…”

Section: Introductionmentioning

confidence: 99%

“…[34][35][36][37][38][39][40][41] In their study, 34 Siddiqui et al analyzed the propagation of magnetogasdynamic shock waves and found the first-order approximate analytic solutions. Singh and Arora 35 extended the work presented in Siddiqui et al 34 by considering the gas to be non-ideal. Nath et al 36 investigated the cylindrical shock wave in a rotating ideal gas and found approximate analytic solutions.…”

Section: Introductionmentioning

confidence: 99%

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An analysis of shock wave propagation in a dusty gas

Singh

Arora

2022

Math Methods in App Sciences

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The present work uses a power series method to investigate the propagation of shock waves with generalized geometries generated by an intense explosion in a dusty gas. A mathematical model using a system of partial differential equations (PDEs) is presented for the considered problem. The density of the undisturbed medium is assumed to be constant. Approximate analytic solutions to the considered problem are obtained using the power series method by extending the power series of the flow variables. This work discusses the first‐order and second‐order approximate solutions and provides closed‐form solutions for the first‐order approximation. The behavior of the flow variables is depicted via figures behind the shock front for the first‐order approximation. Furthermore, the effects of geometry factor α, adiabatic exponent γ, and various dusty gas parameters such as Kp (the mass fraction of the dust particles), G0 (the ratio of the density of the dust particles to the initial density of the gas), and σ (the relative specific heat) are analyzed on the flow variables and total energy of disturbance J0 for the first‐order approximation. It is observed that an increase in any of the parameters Kp or σ causes the fluid velocity to increase and density and pressure to decrease. Increase in the parameter G0 causes the density and pressure to increase, whereas the fluid velocity does not get affected. An increase in the value of α results in a decrease in the density and pressure, while the fluid velocity remains the same. An increase in the value of γ results in a decrease in the fluid velocity; however, it has opposite effect on the pressure. The density decreases near the shock front and increases as we move towards the axis/center of symmetry with an increase in γ. Also, it is observed that J0 increases on increasing the value of G0 or σ, while it decreases on increasing the value of Kp, γ or α.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An analysis of shock wave propagation in a dusty gas

Singh

Arora

2022

Math Methods in App Sciences

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“…They obtained both analytical and numerical solutions in their work. Singh and Arora [15] used the power series method to investigate the problem of cylindrical shock wave propagation in non-ideal magnetogasdynamics. By expanding the flow parameters in powers of time, a problem of converging cylindrical shock waves in a non-ideal gas with the effect of azimuthal magnetic field has been solved by Singh and Arora [16].…”

Section: Introductionmentioning

confidence: 99%

Similarity solutions for cylindrical shock waves in a non-ideal gas under the action of monochromatic radiation

Devi¹,

Singh²,

Arora³

2021

J. Phys. A: Math. Theor.

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A theoretical model for the propagation of cylindrical shock waves in the adiabatic flow of a non-ideal gas with the effect of monochromatic radiation into the stellar interiors is studied. We obtain some special class of self-similar solutions to the considered problem using the Lie group of transformations. Here, we assume that the density is uniform in the undisturbed medium. The radiation flux is considered to be moving through the non-ideal gas. The flow variables behind the shock front are discussed through graphs. Also, the effects of variation in the non-ideal parameter, radiation parameter and adiabatic exponent on the flow variables are explained. The obtained results are quite similar to the results obtained by Vishwakarma and Pandey (2012 Int. J. Phys. Math. Sci. 2 27–37). The software package ‘MATLAB’ has performed all the computational work.

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“…Nath and Singh [18] have studied the cylindrical ionizing shock waves in a self-gravitating gas with a magnetic field. The propagation of strong shock waves in a non-ideal gas under the effect of magnetic field is studied by Singh and Arora [19]. Nath [20] obtained the approximate analytical solution for the blast waves in a self-gravitating perfect gas.…”

Section: Introductionmentioning

confidence: 99%

Ionizing blast waves in a non-ideal gas under isothermal flow condition: Power Series Method

Sharma¹,

Chauhan²,

Arora³

2020

Phys. Scr.

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In this work, the propagation of blast waves in a non-ideal gas for isothermal flow with the effect of the azimuthal magnetic field is investigated. It is supposed that the magnetic field is directed orthogonally to the motion of the gas particles having zero electrical resistance. Approximate solutions are obtained analytically by expanding the flow parameters in the form of power series for the cylindrically symmetric motion using Sakurai’s technique. The flow variables are determined behind the shock. The effects of the parameter of non-idealness and the magnetic field strength on the flow density, velocity, pressure and magnetic pressure of the flow are discussed in detail and shown graphically. It is observed that an increase in the value of the parameter of non-idealness causes a decrease in the flow velocity, density and magnetic pressure, while pressure behaves reversely. The magnetic pressure and flow velocity increase with the magnetic field, while the flow density and pressure decrease with an increase in the magnetic field. Some of the applications of the present work include experiments on pinch effect, an explosion of long thin wire, and certain axially symmetric hypersonic problems.

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

Cited by 12 publications

References 36 publications

An analysis of shock wave propagation in a dusty gas

An analysis of shock wave propagation in a dusty gas

Similarity solutions for cylindrical shock waves in a non-ideal gas under the action of monochromatic radiation

Ionizing blast waves in a non-ideal gas under isothermal flow condition: Power Series Method

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