Nonlinear Wave Propagation Through a Radiating van der Waals Fluid with Variable Density
- 379 Downloads
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.
KeywordsHyperbolic system Mixed nonlinearity van der Waals fluid Radiation
The author wishes to sincerely thank the University Grants Commission, India, for its support through a Major Research Project No. F/788/2012/SR.
- 1.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)Google Scholar
- 2.Clarke, J.F., McChesney, M.: Dynamicss of Relaxing gases. Butterworth, London (1976)Google Scholar
- 7.Penner, S.S., Olfe, D.B.: Radiation and Reentry. Academic Press, New York (1968)Google Scholar
- 10.Shukla, T.P., Sharma, V.D.: Weakly nonlinear waves in nonlinear fluids. Studies in Applied Mathematics 00, 1–22 (2016)Google Scholar
- 15.Vincenti, W.G., Kruger, C.H.: Introduction to Physical Gasdynamics. Wiley. New York (1965)Google Scholar
- 17.Zeldovich, Y.B.: On the possibility of rarefaction shock waves. Zh. Eksp. Teor. Fiz. 4, 363–364 (1946)Google Scholar