First-Order Reactant of Homogeneous Dusty Fluid Turbulence Prior to the Final Period of Decay in a Rotating System for the Case of Multi-Point and Multi-Time at Four-Point Correlation

M. Abu Bkar Pk; M. Monuar Hossain; M. Abul Kalam Azad

doi:doi:10.11648/j.pamj.20140304.11

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First-Order Reactant of Homogeneous Dusty Fluid Turbulence Prior to the Final Period of Decay in a Rotating System for the Case of Multi-Point and Multi-Time at Four-Point Correlation

M. Abu Bkar Pk, M. Monuar Hossain, M. Abul Kalam Azad

Published in Pure and Applied Mathematics Journal (Volume 3, Issue 4)

Received: 20 July 2014 Accepted: 3 August 2014 Published: 10 August 2014

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Abstract

In this paper following Deissler’s approach and taking Fourier transform, the decay for the concentration of a dilute contaminant undergoing a first-order chemical reaction in dusty fluid homogeneous turbulence at times prior to the ultimate phase in a rotating system for the case of multi-point and multi-time at four point correlation is studied. Here two and three point correlations between fluctuating quantities have been considered and the quadruple correlations are ignored in comparison to the second and third order correlations. Taking Fourier transform the correlation equations are converted to spectral form. Finally, integrating the energy spectrum over all wave numbers we obtained the decay law for the concentration fluctuations of first order reactant in homogeneous dusty fluid turbulence prior to the final period of decay in a rotating system for the case of multi-point and multi-time at four-point correlation.

Published in	Pure and Applied Mathematics Journal (Volume 3, Issue 4)
DOI	10.11648/j.pamj.20140304.11
Page(s)	78-86
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

Correlation Function, Deissler’s Method, Dusty Fluid Turbulence, First Order Chemical Reactant, Fourier-Transformation, Multi-point and multi-time, Navier-Stokes Equation, Rotating System

References

[1]	Azad, M.A.K., M.A.Aziz and M. S. Alam Sarker, “The 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. 2011.
[2]	Bkar Pk, M.A., M.S.Alam Sarker and M.A.K. Azad, “Decay of MHD turbulence prior to the ultimate phase in presence of dust particle for four-point correlation.” Int .J. of Appl.Math and Mech.9 (10):34-57.2013.
[3]	Bkar Pk, M.A., M.A.K. Azad and M.S.Alam Sarker, “Decay of energy of MHD turbulence for four-point correlation.” International Journal of Engineering Research & Technology.1 (9):pp1-13. 2012.
[4]	Bkar Pk. M.A., M.A.K.Azad and M.S.Alam.Sarker, “First-order reactant in homogeneous turbulence prior to the ultimate phase of decay for four-point correlation in presence of dust particle,”Res.J.Appl.Sci.Eng. Technol.,5(2):585-595. 2013(a).
[5]	Bkar Pk. M.A., M.A.K.Azad and M.S.Alam.Sarker, “Decay of dusty fluid MHD turbulence for four-point correlation in a rotating system.”J.Sci. Res.5 (1):77-90.2013(b).
[6]	Chandrasekhar, S., “The invariant theory of isotropic turbulence in magneto-hydrodynamics,” Proc. Roy.Soc., London, and A204:435-449. 1951.
[7]	Corrsin, S., “On the spectrum of isotropic temperature fluctuations in an isotropic turbulence.” J.Apll.Phys 22:469-473.1951.
[8]	Deissler, R.G., “On the decay of homogeneous turbulence before the final period.” Phys.Fluid, 1:111-121. 1958.
[9]	Deissler, R.G., “A theory of decaying homogeneous turbu lence.” Phys. Fluid, 3:176-187. 1960.
[10]	Kishore, N, and Y.T. Golsefid. “The effect of Coriolis force on acceleration covariance in MHD turbulent flow of a dusty incompressible fluid.” Astr. Space Sci.: 150, 89. 1988.
[11]	Kumar, P. and S.R.Patel, “First-order reactant in homogeneous turbulence before the final period of decay.” Phys .Fluids, 17: 1362-1368. 1974.
[12]	Kumar, P. and S.R.Patel, “On first-order reactant in homogeneous turbulence.”Int. J. Eng. Sci., 13:305-315. 1975.
[13]	Loeffler, A.L and R.G. Deissler, “Decay of temperature fluctuations in homogeneous turbulence before the final period.” Int. J. Heat Mass Trans., 1(4): 312-324. 1961.
[14]	Hossain.M.M, M.A.Bkar Pk and M.S. A. Sarker “Homogeneous fluid turbulence before the final period of decay for four-point correlation in a rotating system for first-order reactant.” American Journal of Theoretical and Applied Statistics, 3(4):81-89. 2014.
[15]	Shimomura. Y. and A.Yoshizawa, “Statistical analysis of an isotropic turbulent viscosity in a rotating system.” J. Physical Soc., Japan, 55(6): 1904-1917. 1986.
[16]	Shimomura, Y. “A statistical derived two-equation model of turbulent scalar flux in a rotating system.” J .Physical Soc., Japan, 58: 352. 1989.
[17]	Sarker, M. S. A. and N. Kishore, “Decay of MHD turbulence before the final period.” Int. J. Engng Sci., 29(11):1479-1485. 1991.
[18]	Sarker. M. S.A, and S.F. Ahmed, 2011. Fiber motion in dusty fluid turbulent flow with two point correlation. J. Sci. Res. 3(2): 283-290.

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M. Abu Bkar Pk, M. Monuar Hossain, M. Abul Kalam Azad. (2014). First-Order Reactant of Homogeneous Dusty Fluid Turbulence Prior to the Final Period of Decay in a Rotating System for the Case of Multi-Point and Multi-Time at Four-Point Correlation. Pure and Applied Mathematics Journal, 3(4), 78-86. https://doi.org/10.11648/j.pamj.20140304.11

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ACS Style

M. Abu Bkar Pk; M. Monuar Hossain; M. Abul Kalam Azad. First-Order Reactant of Homogeneous Dusty Fluid Turbulence Prior to the Final Period of Decay in a Rotating System for the Case of Multi-Point and Multi-Time at Four-Point Correlation. Pure Appl. Math. J. 2014, 3(4), 78-86. doi: 10.11648/j.pamj.20140304.11

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AMA Style

M. Abu Bkar Pk, M. Monuar Hossain, M. Abul Kalam Azad. First-Order Reactant of Homogeneous Dusty Fluid Turbulence Prior to the Final Period of Decay in a Rotating System for the Case of Multi-Point and Multi-Time at Four-Point Correlation. Pure Appl Math J. 2014;3(4):78-86. doi: 10.11648/j.pamj.20140304.11

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@article{10.11648/j.pamj.20140304.11,
  author = {M. Abu Bkar Pk and M. Monuar Hossain and M. Abul Kalam Azad},
  title = {First-Order Reactant of Homogeneous Dusty Fluid Turbulence Prior to the Final Period of Decay in a Rotating System for the Case of Multi-Point and Multi-Time at Four-Point Correlation},
  journal = {Pure and Applied Mathematics Journal},
  volume = {3},
  number = {4},
  pages = {78-86},
  doi = {10.11648/j.pamj.20140304.11},
  url = {https://doi.org/10.11648/j.pamj.20140304.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20140304.11},
  abstract = {In this paper following Deissler’s approach and taking Fourier transform, the decay for the concentration of a dilute contaminant undergoing a first-order chemical reaction in dusty fluid homogeneous turbulence at times prior to the ultimate phase in a rotating system for the case of multi-point and multi-time at four point correlation  is studied. Here two and three point correlations between fluctuating quantities have been considered and the quadruple correlations are ignored in comparison to the second and third order correlations. Taking Fourier transform the correlation equations are converted to spectral form. Finally, integrating the energy spectrum over all wave numbers we obtained the decay law for the concentration fluctuations of first order reactant in homogeneous dusty fluid turbulence prior to the final period of decay in a rotating system for the case of multi-point and multi-time at four-point correlation.},
 year = {2014}
}

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TY  - JOUR
T1  - First-Order Reactant of Homogeneous Dusty Fluid Turbulence Prior to the Final Period of Decay in a Rotating System for the Case of Multi-Point and Multi-Time at Four-Point Correlation
AU  - M. Abu Bkar Pk
AU  - M. Monuar Hossain
AU  - M. Abul Kalam Azad
Y1  - 2014/08/10
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.20140304.11
DO  - 10.11648/j.pamj.20140304.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 78
EP  - 86
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20140304.11
AB  - In this paper following Deissler’s approach and taking Fourier transform, the decay for the concentration of a dilute contaminant undergoing a first-order chemical reaction in dusty fluid homogeneous turbulence at times prior to the ultimate phase in a rotating system for the case of multi-point and multi-time at four point correlation  is studied. Here two and three point correlations between fluctuating quantities have been considered and the quadruple correlations are ignored in comparison to the second and third order correlations. Taking Fourier transform the correlation equations are converted to spectral form. Finally, integrating the energy spectrum over all wave numbers we obtained the decay law for the concentration fluctuations of first order reactant in homogeneous dusty fluid turbulence prior to the final period of decay in a rotating system for the case of multi-point and multi-time at four-point correlation.
VL  - 3
IS  - 4
ER  -

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Author Information

M. Abu Bkar Pk

Department of Applied Mathematics, University of Rajshahi, Rajshahi-6205, Bangladesh
M. Monuar Hossain

Department of Civil & Environmental Engineering, Uttara University, Dhaka-1230, Bangladesh
M. Abul Kalam Azad

Department of Applied Mathematics, University of Rajshahi, Rajshahi-6205, Bangladesh

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Plain Text BibTeX RIS

APA Style

M. Abu Bkar Pk, M. Monuar Hossain, M. Abul Kalam Azad. (2014). First-Order Reactant of Homogeneous Dusty Fluid Turbulence Prior to the Final Period of Decay in a Rotating System for the Case of Multi-Point and Multi-Time at Four-Point Correlation. Pure and Applied Mathematics Journal, 3(4), 78-86. https://doi.org/10.11648/j.pamj.20140304.11

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ACS Style

M. Abu Bkar Pk; M. Monuar Hossain; M. Abul Kalam Azad. First-Order Reactant of Homogeneous Dusty Fluid Turbulence Prior to the Final Period of Decay in a Rotating System for the Case of Multi-Point and Multi-Time at Four-Point Correlation. Pure Appl. Math. J. 2014, 3(4), 78-86. doi: 10.11648/j.pamj.20140304.11

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AMA Style

M. Abu Bkar Pk, M. Monuar Hossain, M. Abul Kalam Azad. First-Order Reactant of Homogeneous Dusty Fluid Turbulence Prior to the Final Period of Decay in a Rotating System for the Case of Multi-Point and Multi-Time at Four-Point Correlation. Pure Appl Math J. 2014;3(4):78-86. doi: 10.11648/j.pamj.20140304.11

Copy | Download

@article{10.11648/j.pamj.20140304.11,
  author = {M. Abu Bkar Pk and M. Monuar Hossain and M. Abul Kalam Azad},
  title = {First-Order Reactant of Homogeneous Dusty Fluid Turbulence Prior to the Final Period of Decay in a Rotating System for the Case of Multi-Point and Multi-Time at Four-Point Correlation},
  journal = {Pure and Applied Mathematics Journal},
  volume = {3},
  number = {4},
  pages = {78-86},
  doi = {10.11648/j.pamj.20140304.11},
  url = {https://doi.org/10.11648/j.pamj.20140304.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20140304.11},
  abstract = {In this paper following Deissler’s approach and taking Fourier transform, the decay for the concentration of a dilute contaminant undergoing a first-order chemical reaction in dusty fluid homogeneous turbulence at times prior to the ultimate phase in a rotating system for the case of multi-point and multi-time at four point correlation  is studied. Here two and three point correlations between fluctuating quantities have been considered and the quadruple correlations are ignored in comparison to the second and third order correlations. Taking Fourier transform the correlation equations are converted to spectral form. Finally, integrating the energy spectrum over all wave numbers we obtained the decay law for the concentration fluctuations of first order reactant in homogeneous dusty fluid turbulence prior to the final period of decay in a rotating system for the case of multi-point and multi-time at four-point correlation.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - First-Order Reactant of Homogeneous Dusty Fluid Turbulence Prior to the Final Period of Decay in a Rotating System for the Case of Multi-Point and Multi-Time at Four-Point Correlation
AU  - M. Abu Bkar Pk
AU  - M. Monuar Hossain
AU  - M. Abul Kalam Azad
Y1  - 2014/08/10
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.20140304.11
DO  - 10.11648/j.pamj.20140304.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 78
EP  - 86
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20140304.11
AB  - In this paper following Deissler’s approach and taking Fourier transform, the decay for the concentration of a dilute contaminant undergoing a first-order chemical reaction in dusty fluid homogeneous turbulence at times prior to the ultimate phase in a rotating system for the case of multi-point and multi-time at four point correlation  is studied. Here two and three point correlations between fluctuating quantities have been considered and the quadruple correlations are ignored in comparison to the second and third order correlations. Taking Fourier transform the correlation equations are converted to spectral form. Finally, integrating the energy spectrum over all wave numbers we obtained the decay law for the concentration fluctuations of first order reactant in homogeneous dusty fluid turbulence prior to the final period of decay in a rotating system for the case of multi-point and multi-time at four-point correlation.
VL  - 3
IS  - 4
ER  -

Copy | Download