Abstract
We examine a quasilinear system of PDEs governing the one-dimensional unsteady flow of a radiating van der Waals fluid in radial, cylindrical and spherical geometry. The local value of the fundamental derivative (Γ) associated with the medium is of order O(𝜖) and changes sign about the reference state (Γ = 0); the undisturbed medium is assumed to be spatially variable. An asymptotic method is employed to obtain a transport equation for the system of Navier Stokes equations; the impact of radiation and the van der Waals parameters on the evolution of the initial pulse is studied.
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References
Bethe, H.A.: On the theory of shock waves for an arbitrary equation of state. Tehnical Report No. 545, Office of Scientific Research and Development (1942)
Clarke, J.F., McChesney, M.: Dynamicss of Relaxing gases. Butterworth, London (1976)
Fan, H., Slemrod, M.: Dynamic flows with liquid/vapor phase transitions. In: Handbook of Mathematical Fluid Dynamics, 1, pp. 373–420, North Holland, Amsterdam (2002)
Fusco, D.: Some comments on wave motions described by nonhomogeneous quasilinear first order hyperbolic systems. Meccanica 17, 128–137 (1982)
Kluwick, A., Cox, E.A.: Nonlinear waves in materials with mixed nonlinearity. Wave Motion 27, 23–41 (1998)
Pai, S.I.: Radiation Gasdynamics. Springer, New York (1966)
Penner, S.S., Olfe, D.B.: Radiation and Reentry. Academic Press, New York (1968)
Radha, Ch., Sharma, V.D.: High and low frequency small amplitude disturbances in a perfectly conducting and radiating gas. Int.J.Engng Sci. 33, 2001–2010 (1995)
Sharma, V.D., Madhumita G.: Nonlinear wave propagation through a stratified atmosphere. J. Math. Anal. Appl. 311, 13–22 (2005)
Shukla, T.P., Sharma, V.D.: Weakly nonlinear waves in nonlinear fluids. Studies in Applied Mathematics 00, 1–22 (2016)
Shukla, T.P., Madhumita G., Sharma, V.D.: Evolution of planar and cylindrically symmetric magneto-acoustic waves in a van der waals fluid. Int.J.Nonlinear Mechanics 91, 58–68 (2017)
Thompson, P.A.: A fundamental derivative in gas dynamics. Phys. Fluids 14, 1843–1849 (1971)
Thompson, P.A., Lambrakis, K.S.: Negative shock waves. J.Fluid Mech. 60, 187–207 (1973)
Varley, E., Cumberbatch, E., Nonlinear high frequency sound waves. J. Inst. Math. Appl. 2, 133–143 (1966)
Vincenti, W.G., Kruger, C.H.: Introduction to Physical Gasdynamics. Wiley. New York (1965)
Zhao, N., Mentrelli, A., Ruggeri, T., Sugiyama, M.: Admissible shock waves and shock induced phase transitions in a van der waals fluid. Phys. Fluids 23, 086101 (2011)
Zeldovich, Y.B.: On the possibility of rarefaction shock waves. Zh. Eksp. Teor. Fiz. 4, 363–364 (1946)
Acknowledgements
The author wishes to sincerely thank the University Grants Commission, India, for its support through a Major Research Project No. F/788/2012/SR.
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Gangopadhyay, M. (2019). Nonlinear Wave Propagation Through a Radiating van der Waals Fluid with Variable Density. In: Rushi Kumar, B., Sivaraj, R., Prasad, B., Nalliah, M., Reddy, A. (eds) Applied Mathematics and Scientific Computing. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-01123-9_34
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DOI: https://doi.org/10.1007/978-3-030-01123-9_34
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