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     Research Journal of Applied Sciences, Engineering and Technology


Transport Equations of Three-point Distribution Functions in MHD Turbulent Flow for Velocity, Magnetic Temperature and Concentration

M.A.K. Azad, M. Nazmul Islam and Mst. Mumtahinah
Department of Applied Mathematics, University of Rajshahi, Bangladesh
Research Journal of Applied Sciences, Engineering and Technology  2014  24:5184-5220
http://dx.doi.org/10.19026/rjaset.7.916  |  © The Author(s) 2014
Received: February 11, 2014  |  Accepted: March ‎24, ‎2014  |  Published: June 25, 2014

Abstract

In this study, the statistical theory of certain distribution functions for simultaneous velocity, magnetic temperature and concentration fields in MHD turbulent flow have been studied. The various properties of the constructed joint distribution functions such as, reduction property, separation property, coincidence and symmetric properties have been discussed. We have made an attempt to derive the transport equations for two and three point distribution functions. Lastly, the transport equation for evaluation of three point distribution functions has been derived.

Keywords:

Concentration, magnetic temperature, MHD turbulent flow, three-point distribution functions, transport equation,


References

  1. Azad, M.A.K. and M.S.A. Sarker, 2003. Decay of MHD turbulence before the final period for the case of multi-point and multi-time in presence of dust particle. Bangladesh J. Sci. Ind. Res., 38(3-4): 151-164.
  2. Azad, M.A.K. and M.S.A. Sarker, 2004. Statistical theory of certain distribution functions in MHD turbulence in a rotating system in presence of dust particles. Rajshahi Univ., Stud. Part-B. J. Sci., 32: 193-210.
  3. Azad, M.A.K. and M.S.A. Sarker, 2009. Decay of temperature fluctuations in MHD turbulence before the final period in a rotating system. Bangladesh J. Sci. Ind. Res., 44(4): 407-414.
  4. Azad, M.A.K., M.A. Aziz and M.S.A. Sarker, 2011. Statistical theory of certain distribution functions in MHD turbulent flow for velocity and concentration undergoing a first order reaction in a rotating system. Bangladesh J. Sci. Ind. Res., 46(1): 59-68.
    CrossRef    
  5. Azad, M.A.K., M.H.U. Molla and M.Z. Rahman, 2012. Transport equatoin for the joint distribution function of velocity, temperature and concentration in convective tubulent flow in presence of dust particles. Res. J. Appl. Sci. Eng. Tech., 4(20): 4150-4159.
  6. Azad, M.A.K., M.H.U. Molla and M.Z. Rahman, 2013. Transport equatoin for the joint distribution functions in convective tubulent flow in presence of dust particles undergoing a first order reaction. Rajshahi Univ., J. Sci. Eng., Accepted for Publication, Vol. 41.
  7. Aziz, M.A., M.A.K. Azad and M.S. Alam Sarker, 2010a. Statistical theory of certain distribution functions in MHD turbulent flow undergoing a first order reaction in presence of dust particles. J. Mod. Math. Stat., 4(1): 11-21.
    CrossRef    
  8. Aziz, M.A., M.A.K. Azad and M.S.A. Sarker, 2010b. Statistical theory of distribution functions in magneto-hydrodynamic turbulence in a rotating system undergoing a first order reaction in presence of dust particles. Res. J. Math. Stat., 2(2): 37-55.
  9. Bigler, R.W., 1976. The structure of diffusion flames. Combust. Sci. Technol., 13: 155.
    CrossRef    
  10. Dixit, T. and B.N. Upadhyay, 1989. Distribution functions in the statistical theory of MHD turbulence of an incompressible fluid in the presence of the coriolis force. Astrophys. Space Sci., 153: 297-309.
  11. Edward, S., 1964. The statistical dynamics of homogeneous turbulence. J. Fluid Mech., 18(2): 239-273.
    CrossRef    
  12. Herring, J.R., 1965. Self-consistent field approach to turbulence theory. Phys. Fluids, 8: 2219-2225.
    CrossRef    
  13. Hopf, E., 1952. Statistical hydrodynamics and functional calculus. J. Rotational Mech. Anal., 1: 87-123.
  14. Islam, M.A. and M.S.A. Sarker, 2007. Distribution functions in the statistical theory of MHD turbulence for velocity and concentration undergoing a first order reaction. Rajshahi Univ., Stud. Part-B. J. Sci., Vol. 35.
  15. Kishore, N., 1978. Distribution functions in the statistical theory of MHD turbulence of an incompressible fluid. J. Sci. Res., 28(2): 163.
  16. Kishore, N. and S.R. Singh, 1984. Transport equation for the bivariate joint distribution function of velocity and temperature in turbulent flow. Bull. Tech. Univ., Istambul, 37: 91-100.
  17. Kishore, N. and S.R. Singh, 1985. Transport equation for the joint distribution function of velocity, temperature and concentration in convective turbulent flow. Prog. Math., 19(1/2): 13-22.
  18. Kollman, W. and J. Janica, 1982. The transport equation for the probability density function of a scalar in turbulent shear flow. Phys. Fluids, 25: 1955.
    CrossRef    
  19. Kraichanan, R.H., 1959. Distribution functions in the statistical theory of convective MHD turbulent flow. J. Fluid Mech., 5: 497.
  20. Lundgren, T.S., 1967. Hierarchy of coupled equations for multi-point turbulence velocity distribution functions. Phys. Fluids, 10: 967.
    CrossRef    
  21. Pope, S.B., 1979. The statistical theory of turbulence flames. Philos. T. Roy. Soc. A, 291: 529.
    CrossRef    
  22. Pope, S.B., 1981. The transport equation for the joint probability density function of velocity and scalars in turbulent flow. Phys. Fluids, 24: 588.
    CrossRef    
  23. Sarker, M.S.A. and N. Kishore, 1991. Distribution functions in the statistical theory of convective MHD turbulence of an incompressible fluid. Astrophys. Space Sci., 181: 29.
    CrossRef    
  24. Sarker, M.S.A. and N. Kishore, 1999. Distribution functions in the statistical theory of convective MHD turbulence of mixture of a miscible incompressible fluid. Prog. Math., 33(1-2): 83.
  25. Sarker, M.S.A. and M.A. Islam, 2002. Distribution functions in the statistical theory of convective MHD turbulence of an incompressible fluid in a rotating system. Rajshahi Univ., Stud. Part-B. J. Sci., Vol. 30.
  26. Ta-You, W., 1966. Kinetic Theory of Gases and Plasma. Addision-Wesley Pub. Co.

Competing interests

The authors have no competing interests.

Open Access Policy

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Copyright

The authors have no competing interests.

ISSN (Online):  2040-7467
ISSN (Print):   2040-7459
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