Spherical Shock Waves of Variable Energy in A Radiating Atmosphere

  • R K Anand University of Allahabad
  • H C Yadav CMP College
Keywords: Shock Waves, Variable Energy, Radiation Heat Flux, Power Series Similarity Solutions

Abstract

This paper presents power series similarity solutions for spherical shock waves of variable energy propagating in a radiating gas, taking into consideration the Rosseland’s radiative diffusion model. These similarity solutions are obtained for an energy input , where  is the energy released up to time t and  is a functional constant. The effects of radiation-parameter are explored on the pressure, the density, the particle velocity and the heat flux of radiation just behind the spherical shock front. The results provided a clear picture of whether and how the radiation flux affects the distribution of the flow variables in the region behind the spherical shock waves.

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Author Biographies

R K Anand, University of Allahabad

Department of Physics, UGC Centre of Advanced Studies, University of Allahabad, Allahabad 211002, India

H C Yadav, CMP College

Department of Physics, CMP College, Allahabad 211002, India

References

Shull J M and McKee C F 1979 Theoretical Models of Interstellar Shocks. I. Radiative Transfer and Ultraviolet Precursors J. Astrophys. 227 131-49

Blondin J M, Wright E B, Borkowski K J and Reynolds S P 1998 Transition to the radiative phase in supernova remnants J. Astrophys. 500 342-54

Stokes G 1851 An examination of the possible effect of the radiation of heat on the propagation of sound Phil. Mag. 1, 305-17

Sachs R G 1946 Some properties of very intense shock waves Phys. Rev. 69 514 - 22

Guess A W and Sen H K 1958 Radiation effects on Rankine Hugoniot Shock conditions, Conference on Extremely high temperatures (New York: John Wiley)

Sen H K and Guess A W 1957 Radiation effects in shock-wave structure Phys. Rev. 108 (3) 560 - 4

Zeldovich Ya B and Raizer Yu P 2002 Physics of Shock Waves and High Temperature Hydrodynamics Phenomena (New York: Dover)

Mihalas D and Mihalas B W 1999 Foundations of Radiation Hydrodynamics (New York: Dover)

Marshak R E 1958 Effect of radiation on shock wave behaviour Phys. Fluids 1(1) 24–9

Elliott L A 1960 Similarity methods in radiation hydrodynamics Proc. R. Soc. Lond. A 258(3) 287–301

Wang K C 1964 The piston problem with thermal radiation Fluid Mech. 20(3) 447–55

Helliwell J B 1969 Self-similar piston problem with radiative heat transfer Fluid Mech. 37(3) 497–512

Laumbach D and Probstein R F 1970 A point explosion in a cold exponential atmosphere- Part 2, Radiating flow Fluid Mech. 40(4) 833–58

Laumbach D and Probstein R F 1970 Self-similar strong shocks with radiation in a decreasing exponential atmosphere Phys. Fluids 13 1178-83

Bhowmick J B 1981 An exact analytical solution in radiation gas dynamics Astrophys. Space Sci. 74 (2) 481-5

Singh J B and Srivastava S K 1982 Propagation of spherical shock waves in an exponential medium with radiation heat flux Astrophys. Space Sci, 88 (2) 277-82

Ghoniem A F, Kamel M M, Berger S A and Oppenheim A K 1982 Effects of internal heat transfer on the structure of self-similar blast waves Fluid Mech. 117 473–91

Gretler W and Wehle P 1993 Propagation of blast waves with exponential heat release and internal heat conduction and thermal radiation Shock Waves 3(2) 95–104

Anand R K 2018 On the strong spherical shock waves in a two-phase gas-particle medium Int. J. Appl. Comput. Math. 4 (1) 49 14pp

Pomraning G C 1973 The Equations of Radiation Hydrodynamics, Int. Ser. Monographs in natural philosophy 54 (New York: Pergamon)

Freeman R A 1968 Variable energy blast wave J. Phys. D: Appl. Phys. 1 1697-1710.

Wang K C 1966 Approximate solution of a plane radiating piston problem Phys. Fluids 9 (10) 1922-8.

Sakurai A 1953 On the Propagation and Structure of the Blast Wave I J. Phys. Soc. Japan 8 (5) 662-9.

Published
2019-04-30
How to Cite
Anand, R. K., & Yadav, H. C. (2019). Spherical Shock Waves of Variable Energy in A Radiating Atmosphere. To Physics Journal, 2, 22-39. Retrieved from http://purkh.com/index.php/tophy/article/view/267
Section
Research Articles