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Exact Solution for a Magnetogasdynamical Cylindrical Shock Wave in a Self-Gravitating Rotating Perfect Gas with Radiation Heat Flux and Variable Density

  • HYDROGASDYNAMICS IN TECHNOLOGICAL PROCESSES
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Journal of Engineering Physics and Thermophysics Aims and scope

An exact similarity solution for a magnetoradiative cylindrical shock wave in a self-gravitating rotating perfect gas is obtained. The density, azimuthal velocity, and magnetic field strength are assumed to vary in an undisturbed medium. It is shown that the flow variables, namely, the radial velocity, pressure, magnetic field strength, azimuthal velocity, mass, and the radiation flux, decrease from the highest values at the shock front to zero; however, the density tends to infinity as the symmetry axis is approached. The effects of variation in the magnetic field strength, gravitational parameter, rotational parameter, and in the adiabatic exponent on the flow variables and shock strength are discussed. The solutions obtained for self-gravitating and nongravitating media are compared. The total energy of the shock wave is shown to be not constant.

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References

  1. R. E. Marshak, Effect of radiation on shock wave behavior, Phys. Fluids, 1, No. 1, 24–29 (1958).

    Article  MathSciNet  Google Scholar 

  2. L. A. Elliot, Similarity methods in radiation hydrodynamics, Proc. R. Soc. Lond., 258, 287–301 (1960).

    Article  MathSciNet  Google Scholar 

  3. K. C. Wang, The "piston problem" with thermal radiation, J. Fluid Mech., 20, 447–455 (1964).

    Article  MathSciNet  Google Scholar 

  4. S. Ashraf and P. L. Sachdev, An exact similarity solution in radiation-gas-dynamics, Proc. Indian Acad. Sci., Sect. A, 71, No. 6, 275–281 (1970).

    Google Scholar 

  5. D. D. Laumbach and R. F. Probstein, Self-similar strong shocks with radiation in a decreasing exponential atmosphere, Phys. Fluids, 13, No. 5, 1178–1183 (1970).

    Article  Google Scholar 

  6. S. N. Ojha, A solution to the radiative blast wave in stellar interiors, Acta Phys. Hung., 31, No. 4, 375–383 (1972).

    Article  Google Scholar 

  7. G. C. McVittie, Spherically symmetric solutions of the equations of gas dynamics, Proc. R. Soc. Lond., A220, No. 1142, 339–355 (1953).

    Article  MathSciNet  Google Scholar 

  8. Onkar Nath, S. Ojha, and H. S. Thakar, A study of stellar point explosion in a self-gravitating radiative magnetohydrodynamic medium, Astrophys. Space Sci., 183, 135–145 (1991).

    Article  Google Scholar 

  9. S. K. Srivastava and R. K. Singh, An exact similarity solution for a spherical shock wave in a self-gravitating system, Astrophys. Space Sci., 92, 365–372 (1983).

    Article  Google Scholar 

  10. J. P. Vishwakarma and Nanhey Patel, Magnetogasdynamic cylindrical shock waves in a rotating nonideal gas with radiation heat flux, J. Eng. Phys. Thermophys., 88, No. 2, 521–530 (2015).

    Article  Google Scholar 

  11. J. P. Vishwakarma, R. C. Srivastava, and Arun Kumar, An exact similarity solution in radiation magneto-gas-dynamics for the flows behind a spherical shock wave, Astrophys. Space Sci., 129, 45–52 (1987).

    Article  Google Scholar 

  12. P. Chaturani, Strong cylindrical shocks in a rotating gas, Appl. Sci. Res., 23, 197–211 (1970).

    Article  MathSciNet  Google Scholar 

  13. A. Sakurai, Propagation of spherical shock waves in stars, J. Fluid Mech., 1, 436–453 (1956).

    Article  MathSciNet  Google Scholar 

  14. L. I. Sedov, Similarity and Dimensional Methods in Mechanics [in Russian], Mir, Moscow (1982).

    MATH  Google Scholar 

  15. P. Carrus, P. Fox, F. Hass, and Z. Kopal, The propagation of shock waves in a stellar model with continuous density distribution, Astrophys. J., 113, 496 (1951).

    Article  MathSciNet  Google Scholar 

  16. B. Balick and A. Frank, Shapes and shaping of planetary nebulae, Annu. Rev. Astron. Astrophys., 40, No. 1, 439–486 (2002).

    Article  Google Scholar 

  17. L. Hartmann, Accretion Processes in Star Formation, Cambridge Univ. Press, Cambridge (1998).

    Google Scholar 

  18. G. Nath, Magnetogasdynamic shock wave generated by a moving piston in a rotational axisymmetric isothermal flow of perfect gas with variable density, Adv. Space Res., 47, 1463–1471 (2011).

    Article  Google Scholar 

  19. P. Rosenau and S. Frankenthal, Equatorial propagation of axisymmetric magnetohydrodynamic shocks, Phys. Fluids, 19, 1889–1899 (1976).

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Allahabad, Uttar Pradesh, 211004, India

    G. Nath, Sumeeta Singh & Pankaj Srivastava

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  1. G. Nath
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  2. Sumeeta Singh
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  3. Pankaj Srivastava
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Correspondence to G. Nath.

Additional information

Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 91, No. 5, pp. 1372–1382, September–October, 2018.

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Nath, G., Singh, S. & Srivastava, P. Exact Solution for a Magnetogasdynamical Cylindrical Shock Wave in a Self-Gravitating Rotating Perfect Gas with Radiation Heat Flux and Variable Density. J Eng Phys Thermophy 91, 1302–1312 (2018). https://doi.org/10.1007/s10891-018-1862-4

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  • DOI: https://doi.org/10.1007/s10891-018-1862-4

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