Effects of First-Order Reactant on MHD Turbulence at Four-Point Correlation

M. Abu Bkar Pk; Abdul Malek; M. Abul Kalam Azad

doi:doi:10.11648/j.acm.20150401.13

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Effects of First-Order Reactant on MHD Turbulence at Four-Point Correlation

M. Abu Bkar Pk, Abdul Malek, M. Abul Kalam Azad

Published in Applied and Computational Mathematics (Volume 4, Issue 1)

Received: 1 January 2015 Accepted: 18 January 2015 Published: 30 January 2015

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Abstract

The purpose of this study is to determine the effect of first order reactant of MHD fluid turbulence for four-point correlations earlier than the ending phase. Three and four point correlation equations are obtained. The correlation equations are changed to spectral type by their Fourier-transform. By neglecting the quintuple correlations in comparison to the fourth order correlation terms. As a final point integrating the energy spectrum over all wave numbers and we obtained the energy decompose rule of MHD turbulence for magnetic field fluctuations due to the effect of first order reactant and the result has been shown graphically.

Published in	Applied and Computational Mathematics (Volume 4, Issue 1)
DOI	10.11648/j.acm.20150401.13
Page(s)	11-19
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), 2015. Published by Science Publishing Group

Keywords

Correlation Function, Deissler’s Method, First Order Chemical Reactant, Fourier-Transformation, Navier-Stokes Equation, MHD Turbulence

References

[1]	Azad M.A.K, Aziz M.A and Sarker M.S.A, “Statistical theory of certain distribution functions in MHD turbulent flow for velocity and concentration undergoing a first order reaction in a rotating system.” Bangladesh Journal of Scientific and Industrial Research, 46(1):59-68. 2011.
[2]	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 & Technology.1 (9):pp1-13. 2012.
[3]	Bkar Pk. M.A., M. A. K. Azad and M. S. Alam Sarker, “First-order reactant in homogeneou 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. 2013a.
[4]	Bkar Pk, M.A., M.S.Alam Sarker and M.A.K. Azad, “Decay of MHD turbulence before the final period for four-point correlation in a rotating system.” Res. J. Appl. Sci. Eng. Technol., 6(15), 2789-2798. 2013b.
[5]	Chandrasekhar, S., “The invariant theory of isotropic turbulence in magneto-hydrodynamics,” Proc. Roy. Soc., London, and A204:435-449. 1951.
[6]	Corrsin, S., “On the spectrum of isotropic temperature fluctuations in isotropic turbulence.”J. Apll. Phys 22:469-473.1951.
[7]	Deissler, R.G., “On the decay of homogeneous turbulence before the final period.” Phys.Fluid, 1:111-121. 1958.
[8]	Deissler, R.G., “A theory of decaying homogeneous turbulence.” Phys. Fluid, 3:176-187. 1960.
[9]	Islam, M.A. and M.S.A Sarker, “First order reactant in MHD turbulence before the final period of decay for the case of multi-point and multi-time.” Indian J. pure appl. Math., 32(8):1173-1184. 2001.
[10]	Sarker, M. S. A. and N. Kishore, “Decay of MHD turbulence before the final period.” Int. J. Engng Sci., 29(11):1479-1485. 1991.
[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, “First order reactant in homogeneous turbulence before the final period for the case of multi-point and multi-time.” Int. Eng. Sci, 13:305-315.1975.
[13]	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. 2014b.
[14]	Bkar Pk, M.A., M. M. Hossain and M. A. K. 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 and Applied Mathematics Journal, 3(4):78-86.2014a.
[15]	Funada T, Tuitiya Y and Ohji M, ‘The effect of coriolis force on turbulent motion in presence of strong magnetic field.” Journal of the Physical Society Japan, 44:1020-1028. 1978.

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APA Style

M. Abu Bkar Pk, Abdul Malek, M. Abul Kalam Azad. (2015). Effects of First-Order Reactant on MHD Turbulence at Four-Point Correlation. Applied and Computational Mathematics, 4(1), 11-19. https://doi.org/10.11648/j.acm.20150401.13

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ACS Style

M. Abu Bkar Pk; Abdul Malek; M. Abul Kalam Azad. Effects of First-Order Reactant on MHD Turbulence at Four-Point Correlation. Appl. Comput. Math. 2015, 4(1), 11-19. doi: 10.11648/j.acm.20150401.13

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AMA Style

M. Abu Bkar Pk, Abdul Malek, M. Abul Kalam Azad. Effects of First-Order Reactant on MHD Turbulence at Four-Point Correlation. Appl Comput Math. 2015;4(1):11-19. doi: 10.11648/j.acm.20150401.13

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@article{10.11648/j.acm.20150401.13,
  author = {M. Abu Bkar Pk and Abdul Malek and M. Abul Kalam Azad},
  title = {Effects of First-Order Reactant on MHD Turbulence at Four-Point Correlation},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {1},
  pages = {11-19},
  doi = {10.11648/j.acm.20150401.13},
  url = {https://doi.org/10.11648/j.acm.20150401.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150401.13},
  abstract = {The purpose of this study is to determine the effect of first order reactant of MHD fluid turbulence for four-point correlations earlier than the ending phase. Three and four point correlation equations are obtained. The correlation equations are changed to spectral type by their Fourier-transform. By neglecting the quintuple correlations in comparison to the fourth order correlation terms. As a final point integrating the energy spectrum over all wave numbers and we obtained the energy decompose rule of MHD turbulence for magnetic field fluctuations due to the effect of first order reactant and the result has been shown graphically.},
 year = {2015}
}

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TY  - JOUR
T1  - Effects of First-Order Reactant on MHD Turbulence at Four-Point Correlation
AU  - M. Abu Bkar Pk
AU  - Abdul Malek
AU  - M. Abul Kalam Azad
Y1  - 2015/01/30
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20150401.13
DO  - 10.11648/j.acm.20150401.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 11
EP  - 19
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20150401.13
AB  - The purpose of this study is to determine the effect of first order reactant of MHD fluid turbulence for four-point correlations earlier than the ending phase. Three and four point correlation equations are obtained. The correlation equations are changed to spectral type by their Fourier-transform. By neglecting the quintuple correlations in comparison to the fourth order correlation terms. As a final point integrating the energy spectrum over all wave numbers and we obtained the energy decompose rule of MHD turbulence for magnetic field fluctuations due to the effect of first order reactant and the result has been shown graphically.
VL  - 4
IS  - 1
ER  -

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Author Information

M. Abu Bkar Pk

Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh
Abdul Malek

Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh
M. Abul Kalam Azad

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

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APA Style

M. Abu Bkar Pk, Abdul Malek, M. Abul Kalam Azad. (2015). Effects of First-Order Reactant on MHD Turbulence at Four-Point Correlation. Applied and Computational Mathematics, 4(1), 11-19. https://doi.org/10.11648/j.acm.20150401.13

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ACS Style

M. Abu Bkar Pk; Abdul Malek; M. Abul Kalam Azad. Effects of First-Order Reactant on MHD Turbulence at Four-Point Correlation. Appl. Comput. Math. 2015, 4(1), 11-19. doi: 10.11648/j.acm.20150401.13

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AMA Style

M. Abu Bkar Pk, Abdul Malek, M. Abul Kalam Azad. Effects of First-Order Reactant on MHD Turbulence at Four-Point Correlation. Appl Comput Math. 2015;4(1):11-19. doi: 10.11648/j.acm.20150401.13

Copy | Download

@article{10.11648/j.acm.20150401.13,
  author = {M. Abu Bkar Pk and Abdul Malek and M. Abul Kalam Azad},
  title = {Effects of First-Order Reactant on MHD Turbulence at Four-Point Correlation},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {1},
  pages = {11-19},
  doi = {10.11648/j.acm.20150401.13},
  url = {https://doi.org/10.11648/j.acm.20150401.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150401.13},
  abstract = {The purpose of this study is to determine the effect of first order reactant of MHD fluid turbulence for four-point correlations earlier than the ending phase. Three and four point correlation equations are obtained. The correlation equations are changed to spectral type by their Fourier-transform. By neglecting the quintuple correlations in comparison to the fourth order correlation terms. As a final point integrating the energy spectrum over all wave numbers and we obtained the energy decompose rule of MHD turbulence for magnetic field fluctuations due to the effect of first order reactant and the result has been shown graphically.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Effects of First-Order Reactant on MHD Turbulence at Four-Point Correlation
AU  - M. Abu Bkar Pk
AU  - Abdul Malek
AU  - M. Abul Kalam Azad
Y1  - 2015/01/30
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20150401.13
DO  - 10.11648/j.acm.20150401.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 11
EP  - 19
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20150401.13
AB  - The purpose of this study is to determine the effect of first order reactant of MHD fluid turbulence for four-point correlations earlier than the ending phase. Three and four point correlation equations are obtained. The correlation equations are changed to spectral type by their Fourier-transform. By neglecting the quintuple correlations in comparison to the fourth order correlation terms. As a final point integrating the energy spectrum over all wave numbers and we obtained the energy decompose rule of MHD turbulence for magnetic field fluctuations due to the effect of first order reactant and the result has been shown graphically.
VL  - 4
IS  - 1
ER  -

Copy | Download