Temperature Fluctuations in Dusty Fluid Homogeneous Turbulence at Four Point Correlations
American Journal of Applied Mathematics
Volume 5, Issue 5, October 2017, Pages: 132-144
Received: May 8, 2017; Accepted: May 25, 2017; Published: Sep. 30, 2017
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Authors
Abdul Malek, Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh
Md. Abul Kalam Azad, Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh
Md. Abu Bkar Pk, Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh
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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.
Keywords
Four-Point Correlation, Decay, Temperature Fluctuations, Final Period, Dust Particles, Prandtl No
To cite this article
Abdul Malek, Md. Abul Kalam Azad, Md. Abu Bkar Pk, Temperature Fluctuations in Dusty Fluid Homogeneous Turbulence at Four Point Correlations, American Journal of Applied Mathematics. Vol. 5, No. 5, 2017, pp. 132-144. doi: 10.11648/j.ajam.20170505.12
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
[1]
S. Corrsin, On the spectrum of isotropic temperature fluctuations in isotropic turbulence, J. Apll. Phys, Vol.22, pp 469-473, 1951b.
[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.
[5]
P. G. Saffman, On the stability of laminar flow of a dusty gas. J. Fluid Mech., Vol.13pp 120-128,1962.
[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.
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