Exact Similarity Solution for the Propagation of Spherical Shock Wave in a van der Waals Gas with Azimuthal Magnetic Fie
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RESEARCH ARTICLE
Exact Similarity Solution for the Propagation of Spherical Shock Wave in a van der Waals Gas with Azimuthal Magnetic Field, Radiation Heat Flux, Radiation Pressure and Radiation Energy Under Gravitational Field G. Nath1
•
Mrityunjoy Dutta2 • R. P. Pathak2
Received: 5 March 2017 / Revised: 8 March 2019 / Accepted: 29 May 2019 The National Academy of Sciences, India 2019
Abstract We investigated the exact similarity solutions for shock wave propagation in non-ideal gas with radiation heat flux under gravitational field by taking radiation pressure and radiation energy into account in the presence of azimuthal magnetic field for spherical geometry. The solutions are in terms of analytical expressions. Similarity method is used to transform the basic equation from a system of partial differential equation into a system of ordinary differential equations. The system of ODE yields exact solutions for initial magnetic field distributions as power law. Consideration of isothermal approximations, radiation pressure, radiation energy and adiabatic compressibility in gravitating medium into accounts leads to new insights into explosion problem in contrast to earlier model. Finally, the product solution of progressive wave
given by Mc. Vittie is used to obtain the exact similarity solution under the consideration that the radiation pressure is not equal to zero and the energy loss due to radiation escape is significant. The Alfven–Mach number effect, the parameter of gravitational effect, the parameter of nonidealness of the gas, the radiation pressure number and the adiabatic exponent gamma of the gas are discussed in detail. Keywords Shock waves Exact self-similar solution Medium under gravitational field Radiation heat flux Azimuthal magnetic field van der Waals gas Radiation pressure
1 Introduction Significance statement Exact similarity solution for magnetogasdynamic shock waves in non-ideal gas with radiation flux under gravitational field with radiation pressure and radiation energy is studied. The product solution of progressive wave given by Mc. Vittie is used to obtain the exact solution. The radiation pressure is taken into consideration. The radiation pressure is used for cooling such as radiation-pressure cooling of bound resonant absorbers which is elastically bound to laboratory fixed equipment in optical levitation of liquid drops. Other major application of radiation pressure is in the study of the light scattering. & G. Nath [email protected]; [email protected] Mrityunjoy Dutta [email protected] 1
Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Allahabad, Uttar Pradesh 211004, India
2
Department of Mathematics, National Institute of Technology, Raipur, G. E. Road, Raipur, Chhattisgarh 492001, India
Point-like strong explosions for one-dimensional case have been investigated in detail since the pioneering works by Sedov [1] and Taylor [2]. Noh [3] has studied the shock waves arising from the reflections of a fluid
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