American Journal of Applied Mathematics

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Temperature Fluctuations in Dusty Fluid Homogeneous Turbulence at Four Point Correlations

Received: 08 May 2017    Accepted: 25 May 2017    Published: 30 September 2017
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Abstract

In this study the temperature fluctuations in dusty fluid homogeneous turbulence prior to the final period is considered by using the four point correlation equations for fluctuating quantities in the flow field. The correlation equations are converted into spectral form by their Fourier-transform. The set of equations are made to determinate by neglecting the quintuple correlations in comparison to the fourth- order correlation terms. Finally by integration of the energy spectrum over all wave numbers and have obtained the energy equation of decaying of temperature fluctuations in dusty fluid homogeneous turbulence for four point correlations. The obtained results have been shown by graphically at different Prandtl no. and at the different state of temperature. It is also determined the values of the constant appear at the energy equation by using the values of the parameters which exist in it for different fluids. It has also been shown the effects of the parameters by graphically.

DOI 10.11648/j.ajam.20170505.12
Published in American Journal of Applied Mathematics (Volume 5, Issue 5, October 2017)
Page(s) 132-144
Creative Commons

This is an Open Access article, 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 or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Four-Point Correlation, Decay, Temperature Fluctuations, Final Period, Dust Particles, Prandtl No

References
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[2] ] R. G. Deissler, on the decay of homogeneous turbulence before the final period, Phys. Fluids, Vol.1, pp 111-121, 1958.
[3] R. G. Deissler, A theory of decaying homogeneous turbulence, Phys. Fluids, Vol. 3, pp176-187.1960.
[4] A. L. Loeffler and R. G. Deissler, Decay of temperature fluctuations in homogeneous turbulence before the final period, Int. J. Heat Mass Transfer,Vol.1, pp 312-324,1961.
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[6] N. Kishore and S. R. Singh, Statistical theory of decay process of homogeneous hydromagnetic turbulance,Astrophysics and Space Scie. Vol.104, pp121-125,1984.
[7] Kishor, N. And Y. T. Golsefied, Effect of coriolis force on acceleration covariance in MHD turbulent flow of a dusty incompressible fluid. Astrophys. Space Sci., Vol.150(1), pp89-101,1988.
[8] N. Kishore and M. S. A. Sarker, Rate of change of vorticity covariance in MHD turbulent flow of dusty incompressible fluid. I. J. Energy Res. m 14, Vol. 5, pp 573-57.1990.
[9] M. A. K. Azad and M. S. AlamSarker, 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. Vol. 38(3-4), pp151-164,2003.
[10] . M. A. K. Azad and M. S. Alam Sarker, Decay of temperature fluctuations in homogeneous turbulence before the final period for the case of multi-point and multi-time in presence of dust particle, Rajshahi University Studies, Part-B, Journal of Science, Vol. 34, pp 37-50, 2006.
[11] M. A. K. Azad, M. S. Alam Sarker and N. I. Mondal, Decay of temperature fluctuations in dusty fluid MHD turbulence before the final period in a rotating system, Journal of Engng. and Applied Siences, Vol. 1(2), pp187-194, 2006.
[12] M. A. K. Azad and M. S. Alam Sarker, Decay of temperature fluctuations in homogeneous turbulence before the final period for the case of multi-point and multi-time in a rotating system in presence of dust particle, Journal of Applied Sciences Research, Vol.4(7), pp793-802,2008.
[13] M. A. K. Azad, M. A. Aziz and M. S. Alam Sarker, First Order Reactant in Magneto-hydrodynamic Turbulence before the Final Period of Decay in presence of dust particles in a Rotating System, Journal of Physical Sciences, vol.13, pp 175-190, 2009.
[14] M. S. Alam Sarker, M. A. K. Azad and M. A. Aziz, First Order Reactant in MHD Turbulence before the Final Period of Decay for the Case of Multi-Point and Multi-Time in Presence of Dust Particles. J. Phy, Sci, Vol. 13, pp21-38, 2009.
[15] . M. A. K. Azad, M. S. Alam Sarker and M. A. Aziz, Decay Law of temperature fluctuations in dusty fluid MHD Turbulence before the final Period, J. Math. Forum, Vol. XX, pp 32-48, 2007-7008-2009.
[16] M. A. K. Azad, M. H. U. Molla and M. Z. Rahman,Transport Equatoin for the Joint Distribution Function of Velocity, Temperature and Concentration in Convective Tubulent Flow in Presence of Dust Particles, Research Journal of Applied Sciences, Engineering and Technology( RJASET) Vol.4(20), pp4150-4159, 2012.
[17] M. A. K. Azad and Mist. Mumtahinah, Decay of Temperature fluctuations in dusty fluid homogeneous turbulence prior to final period, Research Journal of Applied Sciences, Engineering and Technology Vol. 6(8), pp 1490-1496, 2013.
[18] M. A. K. Azad and Mist. Mumtahinah, Decay of Temperature fluctuations in dusty fluid homogeneous turbulence prior to the ultimate period in presence of coriolis force, Res. J. Appl. Sci. Engng. and Tech. Vol.7(10), pp1932-1939, 2014.
[19] M. A. BkarPk, A. Malek and M. A. K. Azad, 4-point correlations of dusty fluid MHD turbulent flow in a 1st order reaction, Global J. of Science Frontier Research: F Mathematics & Decision Sciences Vol.15(2), version 1.0, pp53-69, 2015.
[20] M. A. K. Azad, Abdul Malek& M. A. BkarPk, 3-Point Distribution Functions in the Statistical Theory in MHD Turbulent flow for Velocity, MagneticTemperature and Concentration undergoing a First Order Reaction, Global J. of Science Frontier Research: A Physics and Space Science, Vol.15(2) Version 1.0, pp 13-45, 2015.
[21] M. A. K. Azad, M. Abu BkarPk, & Abdul Malek, Effect of Chemical Reaction on Statistical Theory of Dusty Fluid MHD Turbulent Flow for Certain Variables at Three- Point Distribution Functions, Science Journal of Applied Mathematics and Statistics, Vol.3(3), pp 75-98, 2015
[22] M. A. K. Azad, Mst. Mumtahinah & M. Abu BkarPk, Statistical Theory of Three- Point Distribution Functions in MHD Turbulent flow for Velocity, Magnetic Temperature and Concentration in a Rotating System in presence of Dust Particles, Int. J. Scholarly Res. Gate, Vol.3(3), pp 91-142, 2015.
[23] M. A. K. Azad,., M. H. U. Molla & M. Z. Rahman, 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. and Engng (accepted for publication), Vol.40-42, pp31-43, 2012- 2014.
[24] M. S. Alom,M. Ali. M. A. Alim, Study the Effect of Chemical Reaction and Magnetic Field on Free Convection Boundeary Layer Flow of Heat and MassTransfer with Variable Prandtl Number. J. Sci. Res. Vol.8(1), pp41-18,2016.
[25] M. Mamun Miah, M. A. K. Azad, M. Masidur Rahman, The Effect of 1st Order Chemical Reaction in Convective Dusty Fluids Turbulent Flow for Three-Point Joint Distribution Functions, IOSR Journal of Mathematics (IOSR-JM), Vol. 12, pp 12-35, I(Jan. - Feb. 2016), 17-35, 2016.
Author Information
  • Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh

  • Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh

  • Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh

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  • APA Style

    Abdul Malek, Md. Abul Kalam Azad, Md. Abu Bkar Pk. (2017). Temperature Fluctuations in Dusty Fluid Homogeneous Turbulence at Four Point Correlations. American Journal of Applied Mathematics, 5(5), 132-144. https://doi.org/10.11648/j.ajam.20170505.12

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    ACS Style

    Abdul Malek; Md. Abul Kalam Azad; Md. Abu Bkar Pk. Temperature Fluctuations in Dusty Fluid Homogeneous Turbulence at Four Point Correlations. Am. J. Appl. Math. 2017, 5(5), 132-144. doi: 10.11648/j.ajam.20170505.12

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    AMA Style

    Abdul Malek, Md. Abul Kalam Azad, Md. Abu Bkar Pk. Temperature Fluctuations in Dusty Fluid Homogeneous Turbulence at Four Point Correlations. Am J Appl Math. 2017;5(5):132-144. doi: 10.11648/j.ajam.20170505.12

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  • @article{10.11648/j.ajam.20170505.12,
      author = {Abdul Malek and Md. Abul Kalam Azad and Md. Abu Bkar Pk},
      title = {Temperature Fluctuations in Dusty Fluid Homogeneous Turbulence at Four Point Correlations},
      journal = {American Journal of Applied Mathematics},
      volume = {5},
      number = {5},
      pages = {132-144},
      doi = {10.11648/j.ajam.20170505.12},
      url = {https://doi.org/10.11648/j.ajam.20170505.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajam.20170505.12},
      abstract = {In this study the temperature fluctuations in dusty fluid homogeneous turbulence prior to the final period is considered by using the four point correlation equations for fluctuating quantities in the flow field. The correlation equations are converted into spectral form by their Fourier-transform. The set of equations are made to determinate by neglecting the quintuple correlations in comparison to the fourth- order correlation terms. Finally by integration of the energy spectrum over all wave numbers and have obtained the energy equation of decaying of temperature fluctuations in dusty fluid homogeneous turbulence for four point correlations. The obtained results have been shown by graphically at different Prandtl no. and at the different state of temperature. It is also determined the values of the constant appear at the energy equation by using the values of the parameters which exist in it for different fluids. It has also been shown the effects of the parameters by graphically.},
     year = {2017}
    }
    

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  • TY  - JOUR
    T1  - Temperature Fluctuations in Dusty Fluid Homogeneous Turbulence at Four Point Correlations
    AU  - Abdul Malek
    AU  - Md. Abul Kalam Azad
    AU  - Md. Abu Bkar Pk
    Y1  - 2017/09/30
    PY  - 2017
    N1  - https://doi.org/10.11648/j.ajam.20170505.12
    DO  - 10.11648/j.ajam.20170505.12
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
    SP  - 132
    EP  - 144
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20170505.12
    AB  - In this study the temperature fluctuations in dusty fluid homogeneous turbulence prior to the final period is considered by using the four point correlation equations for fluctuating quantities in the flow field. The correlation equations are converted into spectral form by their Fourier-transform. The set of equations are made to determinate by neglecting the quintuple correlations in comparison to the fourth- order correlation terms. Finally by integration of the energy spectrum over all wave numbers and have obtained the energy equation of decaying of temperature fluctuations in dusty fluid homogeneous turbulence for four point correlations. The obtained results have been shown by graphically at different Prandtl no. and at the different state of temperature. It is also determined the values of the constant appear at the energy equation by using the values of the parameters which exist in it for different fluids. It has also been shown the effects of the parameters by graphically.
    VL  - 5
    IS  - 5
    ER  - 

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