Self-Similar Solution of Spherical Shock Wave Propagation in a Mixture of a Gas and Small Solid Particles with Increasing Energy under the Influence of Gravitational Field and Monochromatic Radiation

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Communications in Theoretical Physics ›› 2018, Vol. 70 ›› Issue (02) : 197-208.

Gravitation Theory, Astrophysics and Cosmology

Self-Similar Solution of Spherical Shock Wave Propagation in a Mixture of a Gas and Small Solid Particles with Increasing Energy under the Influence of Gravitational Field and Monochromatic Radiation

P. K. Sahu

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Abstract

Similarity solution for a spherical shock wave with or without gravitational field in a dusty gas is studied under the action of monochromatic radiation. It is supposed that dusty gas be a mixture of perfect gas and micro solid particles. Equilibrium flow condition is supposed to be maintained and energy is varying which is continuously supplied by inner expanding surface. It is found that similarity solution exists under the constant initial density. The comparison between the solutions obtained in gravitating and non-gravitating medium is done. It is found that the shock strength increases with an increase in gravitational parameter or ratio of the density of solid particles to the initial density of the gas, whereas an increase in the radiation parameter has decaying effect on the shock waves.

Key words

spherical shock wave / dusty gas / similarity solution / gravitational medium / Roche model / monochromatic radiation

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P. K. Sahu. Self-Similar Solution of Spherical Shock Wave Propagation in a Mixture of a Gas and Small Solid Particles with Increasing Energy under the Influence of Gravitational Field and Monochromatic Radiation[J]. Communications in Theoretical Physics, 2018, 70(02): 197-208

References

[1] L. I. Sedov, Similarity and Dimensional Methods in Mechanics, Academic Press, New York (1959).

[2] R. E. Marshak, Phys. Fluids 1 (1958) 24.

[3] L. A. Elliott, Proc. R. Soc. London. Ser. A Math. Phys. Sci. 258 (1960) 287.

[4] K. C. Wang, J. Fluid Mech. 20 (1964) 447.

[5] J. B. Helliwell, J. Fluid Mech. 37 (1969) 497.

[6] J. R. NiCastro, Phys. Fluids 13 (1970) 2000.

[7] G. Deb Ray and J. B. Bhowmick, Ind. J. Pure Appl. Math. 7 (1976) 96.

[8] V. M. Khudyakov, Sovit Phys. Dokl. (Trans. American Institute of Physics) 28 (1983) 853.

[9] A. N. Zheltukhin, Geophys. Astrophys. J. Appl. Math. Mech. 52 (1988) 262.

[10] O. Nath and H. S. Takhar, Astrophys. Space Sci. 166 (1990) 35.

[11] O. Nath and H. S. Takhar, Astrophys. Space Sci. 202 (1993) 355.

[12] O. Nath, IL Nuovo Cimento D 20 (1998) 1845.

[13] J. P. Vishwakarma and V. K. Pandey, Appl. Math. 2 (2012) 28.

[14] G. Nath and P. K. Sahu, Ain Shams Eng. J. (2016), DOI 10.1016/j.asej.2016.06.009.

[15] K. K. Singh, Int. J. Appl. Math. Mech. 9 (2013) 37.

[16] G. Nath and P. K. Sahu, Commun. Theor. Phys. 67 (2017) 327.

[17] P. K. Sahu, Phys. Fluids 29 (2017) 086102.

[18] S. I. Pai, S. Menon, and Z. Q. Fan, Int. J. Eng. Sci. 18 (1980) 1365.

[19] F. Higashino and T. Suzuki, Z. Naturforsch. 35a (1980) 1330.

[20] W. Gretler and R. Regenfelder, Eur. J. Mech. B/Fluids 24 (2005) 205.

[21] S. I. Popel and A. A. Gisko, Nonlin. Process. Geophys. 13 (2006) 223.

[22] O. Igra, G. Hu, J. Falcovitz, et al., Int. J. Mult. Flow 30 (2004) 1139.

[23] M. Sommerfeld, Exper. Fluids 3 (1985) 197.

[24] T. Elperin, G. Ben-Dor, and O. Igra, Int. J. heat Fluid Flow 8 (1987) 303.

[25] H. Miura, Fluid Dyna. Res. 6 (1990) 251.

[26] H. Miura and I. I. Glass, Proc. Roy. Soc. Lond. 397 (1985) 295.

[27] G. Nath, Indian J. Phys. 90 (2016) 1055, DOI 10.1007/s12648-016-0842-9.

[28] G. Nath and J. P. Vishwakarma, Acta Astronaut. 128 (2016) 377.

[29] G. Nath, Astrophys. Space Sci. 361 (2016) 31.

[30] V. P. Korobeinikov, Problems in the Theory of Point Explosion in Gases, Proceedings of the Steklov Institute of Mathematics, American Mathematical Society 119 (1976).

[31] S. I. Pai, Two Phase Flows (Vieweg Tracts in Pure and Applied Physics, vol. 3, Vieweg-Verlag, Braunschweig (1977).

[32] H. Steiner and T. Hirschler, Eur. J. Mech. B/Fluids 21 (2002) 371.

[33] J. P. Vishwakarma and G. Nath, Phys. Scri. 74 (2006) 493.

[34] K. Shibasaki, S. Shibasaki, G. Jagadeesh,et al., Development of a High-Speed Cylindrical Rotor Device for Industrial Applications of Shock Waves, in Proc. 23rd., Int. Symposium on Shock Waves (2001).

[35] J. S. Park and S. W. Baek, Int. J. Heat Mass Transf. 46 (2003) 4717.

[36] P. A. Carrus, P. A. Fox, Fa. Hass, and Z. Kopal, Astrophys. J. 113 (1951) 193.

[37] M. H. Rogers, Astrophys. J. 125 (1957) 478.

[38] H. A. Zedan, Appl. Math. Compu. 132 (2002) 63.

[39] G. Nath, Astrophys. Space Sci. 361 (2016) 31.

[40] Y. B. Zel'dovich and Y. P. Raizer, Physics of Shock Waves and High Temperature Hydrodynamic Phenomena, vol. Ⅱ. Academic Press, New York (1967).

[41] E. A. Moelwyn-Hughes, Physical Chemistry, Pergamon, London (1961).

[42] A. V. Fedorov and Y. V. Kratova, Heat Transf. Res. 43 (2012) 123.

[43] H. Miura and I. I. Glass, Proc. R. Soc. Lond. A 385 (1983) 85.

[44] A. S. Korolev and E. A. Pushkar, Fluid Dyn. 49 (2014) 270.

[45] S. I. Popel, V. N. Tsytovich, and M. Y. Yu, Astrophys. Space Sci. 256 (1997) 107.