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


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.


Download data is not yet available.

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


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.

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
Research Articles