Approximate analytical solution for the propagation of shock waves in self-gravitating perfect gas via power series method: isothermal flow

Nath, G.

doi:10.1007/s12036-020-09638-7

Cited by 16 publications

(7 citation statements)

References 73 publications

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“…Nath et al 36 investigated the cylindrical shock wave in a rotating ideal gas and found approximate analytic solutions. For the problem of non‐planar (cylindrical or spherical) shock wave propagation in a self‐gravitating ideal gas, an approximate analytic solution was obtained by Nath 37 . Nath and Singh 38 extended the work presented in Nath 37 for adiabatic flow in the presence of magnetic field.…”

Section: Introductionmentioning

confidence: 99%

“…For the problem of non‐planar (cylindrical or spherical) shock wave propagation in a self‐gravitating ideal gas, an approximate analytic solution was obtained by Nath 37 . Nath and Singh 38 extended the work presented in Nath 37 for adiabatic flow in the presence of magnetic field. For an isothermal flow condition, the cylindrically symmetric shock waves in an axisymmetric rotating ideal gas with azimuthal magnetic field were investigated by Nath and Singh 39 .…”

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%

“…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%

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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%

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 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. Recently, Sharma and Arora [21] extended the work of Nath [20] and obtained the self-similar solutions for blast waves in non-ideal 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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Optimal system of Lie sub-algebras and numerical solution for shock wave in rotating non-ideal dusty gas with monochromatic radiation

Nath,

Maurya

2024

J Eng Math

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Approximate analytical solution for the propagation of shock waves in self-gravitating perfect gas via power series method: isothermal flow

Cited by 16 publications

References 73 publications

An analysis of shock wave propagation in a dusty gas

An analysis of shock wave propagation in a dusty gas

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

Optimal system of Lie sub-algebras and numerical solution for shock wave in rotating non-ideal dusty gas with monochromatic radiation

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