Similarity solution using group theoretic method for unsteady flow behind shock wave in a self-gravitating dusty gas. (January 2023)

• Record Type: Journal Article
• Authors: Nath, G.; Devi, Arti
• Is Part Of: International journal of non-linear mechanics. Volume 148(2023)
• Publication Date: 2023-01
• Subjects: Adiabatic and isothermal flows -- Shock wave -- Similarity solution -- Lie group theoretic method -- Self-gravitating non-ideal dusty gas; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2022.104254
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: In this article, the similarity solution using the Lie group theoretic method for unsteady isothermal and adiabatic flows behind cylindrical or spherical shock wave in a mixture of self-gravitating real gas and small solid particles is discussed. The Lie group theoretic method gives out different cases, i.e., exponential law and power-law shock paths. The similarity solution exists only when the shock path varies according to an exponential law. The dispersal of the flow variables with the variations of the solid particles' mass concentration in the mixture k p, gravitational parameter g 0, the ratio of the density of solid particles to the initial density of the gas μ 1, non-idealness parameter b ¯ and the geometry index ν are discussed graphically. It is found that an increase in the value of μ 1 or g 0 or ν leads to an increase in the shock strength, but the shock wave decay with an increase in b ¯ . A comparison between the solutions for cylindrical and spherical symmetry, and for adiabatic and isothermal flows is also made. Highlights: We model shock waves in self-gravitating dusty gas using Lie group theoretic method. The assumption of isothermal flow instead of adiabatic flow reduces shock strength. Shock strength increases with particles mass concentration and gravitational field. Shock is more impressive in spherical case in comparison to that in cylindrical case. Shock wave decay with an increase in the non-idealness of the gas in the mixture.