MHD Convection Flow of Two Immiscible Fluids in an Inclined Channel with Heat Generation / Absorption

Hasan Nihal Zaidi; Naseem Ahmad

doi:doi:10.11648/j.ajam.20160402.13

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MHD Convection Flow of Two Immiscible Fluids in an Inclined Channel with Heat Generation / Absorption

Hasan Nihal Zaidi, Naseem Ahmad

Published in American Journal of Applied Mathematics (Volume 4, Issue 2)

Received: 21 February 2016 Accepted: 5 March 2016 Published: 28 March 2016

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Abstract

Megnetohydrodynamic (MHD) convection flow of two immiscible fluids in an inclined channel in the presence of an applied magnetic field is investigated. Both fluids are assumed to be Newtonian and heat generating or absorbing and having constant transport properties. The channel walls are maintained at different temperature. The resulting coupled and non-linear equations of momentum and energy are solved analytically by using the regular perturbation method valid for small value of ε=PrEc. The influence of various parameters on velocity field and temperature field for heat absorption and heat generation are discussed with the aid of the graphs.

Published in	American Journal of Applied Mathematics (Volume 4, Issue 2)
DOI	10.11648/j.ajam.20160402.13
Page(s)	80-91
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), 2016. Published by Science Publishing Group

Keywords

MHD Convection, Two-Phase Flow/Immiscible Fluids, Heat Generation/Absorption, Regular Perturbation Method

References

[1]	Hartmann, J., 1937, “Hg-dynamics I Theory of the Laminar Flow of an Electrically Conductive Liquid in a Homogeneous Magnetic Field,” kgl Danskevidenskab Selkab Mat Fys Medd., 15.
[2]	Seigel, R., 1958, “Effect of Magnetic Field on Forced convective Heat transfer in a Parallel Plate Channel,” J Appl. Mech. 25, 415.
[3]	Osterle, J. F., Young, F. J., 1961, “Natural Convection between Heated Vertical Plates in a Horizontal Magnetic Field,” J. Fluid Mech. 11, pp. 512-518.
[4]	Perlmutter, M., and Seigal, R., 1961, “Heat Transfer to an Electrically Conducting Fluid Flowing in a Channel with Transverse Magnetic Field,” NACA TN D-875.
[5]	Romig, M. F., 1961, “The Influence of Electric and Magnetic Fields on Heat Transfer to Electrically Conducting Fluids,” Adv. Heat Transfer vol 1, New York, Academic Press.
[6]	Umavathi, J. C., 1996, “A Note on Magnetoconvection in a Vertical Enclosure,” Int. J. Nonlinear Mechanics 31, pp. 371-376.
[7]	Thome, R. J., 1964, Effect of Transverse Magnetic Field on Vertical Two Phase Flow through a Rectangular Channel, Argonne National Laboratory Report No. ANL 6854.
[8]	Lohrasbi, J., and Sahai, V., 1988, “Magnetohydrodynamic Heat Transfer in Two Phases Flow between Parallel Plates,’’ Appl. Sci. Res. 45, pp. 53-66.
[9]	Malashetty, M. S., and Leela, V., 1991, “Magnetohydrodynamic Heat Transfer in Two Fluid Flow,” Proceeding of the National Heat Transfer, Conf. AIChE &ASME, HTD, p. 159.
[10]	Malashetty, M. S., and Leela, V., 1992, “Magnetohydrodynamic Heat Transfer in Two Phase Flow,” Int. J Eng. Sci., 30, pp. 371-377.
[11]	Chamkah, A. J., 2000, “Flow of Two Immiscible Fluid in Porous and Nonporous Channels,” J. Fluid Eng. 122, pp. 117-124.
[12]	Prakash, S., 1970, “Liquid Flowing Down an Open Inclined Channel,” Indian J. Pure Appl. Math., 2, pp. 1093-109.
[13]	Verma, P. D., and Vyas, H. K., 1980, “Viscous Flow Down an Open Inclined Channel with Naturally Permeability Bed,” Indian J. Pure Appl. Math. 11, pp.165-172.
[14]	Malashetty, M. S., and. Umavathi, J. C., 1997, “Two-Phase Magnetohydrodynamic Flow and Heat Transfer in an Inclined Channel,” Int. J. of Multiphase Flow, 23, pp. 545–560.
[15]	Malashetty, M. S., Umavathi, J. C., and Prathap, Kumar, J., 2001, “Convective Magnetohydrodynamic Two Fluid Flow and Heat Transfer in an Inclined Channel,” Heat and Mass Transfer, 37, pp. 259–264.
[16]	Wang, X., and Robillard, L., 1995, “Mixed Convection in an Inclined Channel with Localized Heat Sources,” Numerical Heat Transfer-Part-A: Application, 28, pp.355-373.
[17]	Umavathi, J. C., Chamkah, A. J., and Shekar, M., 2014, “Flow and Heat Transfer of Two Micropolar Fluids Separated by a Viscous Fluid Layer,” International Journal of Microscale and Nanoscale Thermal and Fluid Transport Phenomena, 5, pp. 23-49.
[18]	Chamkah, A. J., Mansour, M. A., and Ahmad, S. E., 2010, “Double-Diffusive Natural Convection in Inclined Finned Triangular Porous Enclosures in the Presence of Heat Generation/Absorption Effects.” Heat and Mass Transfer, 46, pp. 757-768.

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APA Style

Hasan Nihal Zaidi, Naseem Ahmad. (2016). MHD Convection Flow of Two Immiscible Fluids in an Inclined Channel with Heat Generation / Absorption. American Journal of Applied Mathematics, 4(2), 80-91. https://doi.org/10.11648/j.ajam.20160402.13

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ACS Style

Hasan Nihal Zaidi; Naseem Ahmad. MHD Convection Flow of Two Immiscible Fluids in an Inclined Channel with Heat Generation / Absorption. Am. J. Appl. Math. 2016, 4(2), 80-91. doi: 10.11648/j.ajam.20160402.13

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AMA Style

Hasan Nihal Zaidi, Naseem Ahmad. MHD Convection Flow of Two Immiscible Fluids in an Inclined Channel with Heat Generation / Absorption. Am J Appl Math. 2016;4(2):80-91. doi: 10.11648/j.ajam.20160402.13

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@article{10.11648/j.ajam.20160402.13,
  author = {Hasan Nihal Zaidi and Naseem Ahmad},
  title = {MHD Convection Flow of Two Immiscible Fluids in an Inclined Channel with Heat Generation / Absorption},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {2},
  pages = {80-91},
  doi = {10.11648/j.ajam.20160402.13},
  url = {https://doi.org/10.11648/j.ajam.20160402.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160402.13},
  abstract = {Megnetohydrodynamic (MHD) convection flow of two immiscible fluids in an inclined channel in the presence of an applied magnetic field is investigated. Both fluids are assumed to be Newtonian and heat generating or absorbing and having constant transport properties. The channel walls are maintained at different temperature. The resulting coupled and non-linear equations of momentum and energy are solved analytically by using the regular perturbation method valid for small value of ε=PrEc. The influence of various parameters on velocity field and temperature field for heat absorption and heat generation are discussed with the aid of the graphs.},
 year = {2016}
}

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TY  - JOUR
T1  - MHD Convection Flow of Two Immiscible Fluids in an Inclined Channel with Heat Generation / Absorption
AU  - Hasan Nihal Zaidi
AU  - Naseem Ahmad
Y1  - 2016/03/28
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160402.13
DO  - 10.11648/j.ajam.20160402.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 80
EP  - 91
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160402.13
AB  - Megnetohydrodynamic (MHD) convection flow of two immiscible fluids in an inclined channel in the presence of an applied magnetic field is investigated. Both fluids are assumed to be Newtonian and heat generating or absorbing and having constant transport properties. The channel walls are maintained at different temperature. The resulting coupled and non-linear equations of momentum and energy are solved analytically by using the regular perturbation method valid for small value of ε=PrEc. The influence of various parameters on velocity field and temperature field for heat absorption and heat generation are discussed with the aid of the graphs.
VL  - 4
IS  - 2
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Author Information

Hasan Nihal Zaidi

Department of Basic Sciences, College of Preparatory Year, University of Hail, Hail, Kingdom of Saudi Arabia
Naseem Ahmad

Department of Mathematics, Jamia Millia Islamia, New Delhi, India

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APA Style

Hasan Nihal Zaidi, Naseem Ahmad. (2016). MHD Convection Flow of Two Immiscible Fluids in an Inclined Channel with Heat Generation / Absorption. American Journal of Applied Mathematics, 4(2), 80-91. https://doi.org/10.11648/j.ajam.20160402.13

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ACS Style

Hasan Nihal Zaidi; Naseem Ahmad. MHD Convection Flow of Two Immiscible Fluids in an Inclined Channel with Heat Generation / Absorption. Am. J. Appl. Math. 2016, 4(2), 80-91. doi: 10.11648/j.ajam.20160402.13

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AMA Style

Hasan Nihal Zaidi, Naseem Ahmad. MHD Convection Flow of Two Immiscible Fluids in an Inclined Channel with Heat Generation / Absorption. Am J Appl Math. 2016;4(2):80-91. doi: 10.11648/j.ajam.20160402.13

Copy | Download

@article{10.11648/j.ajam.20160402.13,
  author = {Hasan Nihal Zaidi and Naseem Ahmad},
  title = {MHD Convection Flow of Two Immiscible Fluids in an Inclined Channel with Heat Generation / Absorption},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {2},
  pages = {80-91},
  doi = {10.11648/j.ajam.20160402.13},
  url = {https://doi.org/10.11648/j.ajam.20160402.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160402.13},
  abstract = {Megnetohydrodynamic (MHD) convection flow of two immiscible fluids in an inclined channel in the presence of an applied magnetic field is investigated. Both fluids are assumed to be Newtonian and heat generating or absorbing and having constant transport properties. The channel walls are maintained at different temperature. The resulting coupled and non-linear equations of momentum and energy are solved analytically by using the regular perturbation method valid for small value of ε=PrEc. The influence of various parameters on velocity field and temperature field for heat absorption and heat generation are discussed with the aid of the graphs.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - MHD Convection Flow of Two Immiscible Fluids in an Inclined Channel with Heat Generation / Absorption
AU  - Hasan Nihal Zaidi
AU  - Naseem Ahmad
Y1  - 2016/03/28
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160402.13
DO  - 10.11648/j.ajam.20160402.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 80
EP  - 91
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160402.13
AB  - Megnetohydrodynamic (MHD) convection flow of two immiscible fluids in an inclined channel in the presence of an applied magnetic field is investigated. Both fluids are assumed to be Newtonian and heat generating or absorbing and having constant transport properties. The channel walls are maintained at different temperature. The resulting coupled and non-linear equations of momentum and energy are solved analytically by using the regular perturbation method valid for small value of ε=PrEc. The influence of various parameters on velocity field and temperature field for heat absorption and heat generation are discussed with the aid of the graphs.
VL  - 4
IS  - 2
ER  -

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