Similarity solutions for the strong shock waves in magnetogasdynamics with the effect of monochromatic radiation
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Similarity solutions for the strong shock waves in magnetogasdynamics with the effect of monochromatic radiation Astha Chauhana , Kajal Sharmab , Rajan Arorac , Deepika Singhd Department of Applied Science and Engineering, Indian Institute of Technology, Roorkee, Roorkee, India Received: 8 August 2020 / Accepted: 12 September 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, the method of invariance of Lie group is used to find the similarity solutions of the cylindrical shock waves for one-dimensional unsteady flow in magnetogasdynamics in the presence of monochromatic radiation. The density is assumed to be non-uniform ahead of the shock. The radiation flux is assumed to move through the gas. It is also shown that how the radiation parameter, ambient density exponent, ratio of specific heats (adiabatic constant) and the initial magnetic field strength affect the profiles of the flow variables. It is found that the shock wave decays in the presence of strong magnetic field and shows reverse behavior in the case of monochromatic radiation, i.e., the shock wave grows faster in the presence of radiation. To obtain the similarity solutions and the profiles of the flow variables, numerical calculations are performed using the software package MATHEMATICA.
1 Introduction Most of the physical phenomena in our world are essentially nonlinear and can be described by the mathematical models in the form of partial differential equations (PDEs). These PDEs play an important role in many areas of physics: astrophysics, gas dynamics, combustion theory, cosmology, etc. With the help of the basic laws of mechanics and thermodynamics, the theoretical foundation of gas dynamics is formed. Study of propagation of the shock wave in the presence of monochromatic radiation is a topic of great importance as these phenomena are well marked in disassembled nature of the absorption of the energy. “At rest, when a gas occupies a half space bounded by a fixed plane wall, and the radiation flux moves through the gas in the direction of the wall with constant intensity on unit area, then from the instant of arrival of the radiation at the wall, a shock wave propagates out from the latter in the opposite direction of the radiation flux energy which is absorbed in the zone between the wall and the shock wave. Also, the radiation is not absorbed into the undisturbed medium. In this case, the gas does not radiate itself and part of the incident radiation flux reaches the wall without interacting with it. This phenomenon is called monochromatic radiation [1].” The
a e-mail: [email protected] b e-mail: [email protected] c e-mail: [email protected] (corresponding author) d e-mail: [email protected]
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problem concerning radiation in gas dynamics is studied by many researchers using different methodologies in the literature. Marshak [2] and Sedov [3] developed certain cla
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