Influence of Anisotropy on Thermosolutal Convection in Porous Media with Magnetic Field Effect

Christian Akowanou; Faras Issiako; Macaire Agbomahena; Regis Hontinfinde

doi:doi:10.11648/j.ijfmts.20220802.11

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Influence of Anisotropy on Thermosolutal Convection in Porous Media with Magnetic Field Effect

Christian Akowanou, Faras Issiako, Macaire Agbomahena, Regis Hontinfinde

Published in International Journal of Fluid Mechanics & Thermal Sciences (Volume 8, Issue 2)

Received: 9 May 2022 Accepted: 6 June 2022 Published: 21 June 2022

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Abstract

In the present study, both anisotropy and magnetic field effects on bi-diffusive natural convection in a rectangular cavity filled with a porous medium saturated by a binary fluid are investigated analytically for fully developed flow regime. The cavity is heated isothermally by the sides and its horizontal walls are thermally insulated or conducted. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction that is arbitrary to the gravity field. On the basis of the generalized Brinkman-extended Darcy model of newtonian fluids on steady flow through porous media, analytical expressions were obtained for the flow and thermal fields, the concentration of speaces, the average Nusselt and Sherwood numbers in terms of the Darcy number, the anisotropic permeability ratio, the orientation angle of the principal axes and the Hartmann number. The limiting case corresponding to pure porous media (Da→0) and pure fluid media (Da→∞) for the thermal conditions mentioned on the cavity completed these results in order to compare them to those obtained in the literature. It is found that, Nusselt and Sherwood numbers increase by increasing anisotropic parameters of the porous medium while increasing magnetic field magnitude greatly reduces the intensity of the flow and thus affects significantly heat and mass transfer.

Published in	International Journal of Fluid Mechanics & Thermal Sciences (Volume 8, Issue 2)
DOI	10.11648/j.ijfmts.20220802.11
Page(s)	23-33
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), 2022. Published by Science Publishing Group

Keywords

Porous Medium, Thermosolutal Convection, Magnetic Field, Anisotropy

References

[1]	BEJAN A., 1985. "The Method of Scale Analysis: Natural Convection in a Porous Medium". In Natural Convection: Fundamentals and Applications, S. Kakac et al. (eds), Hemisphere, Bristol P. A.
[2]	DEGAN G., 1997. Numerical and Analytical Study of Natural Convection in Porous Anisotropic Medium. Philosophae Doctor (Ph.D.) thesis (Ecole Polytechnique de Montréal).
[3]	Nield. D. A., (1968). Onset of Thermohaline Convection in Porous Medium, Water Resources Research, 4, 553-560.
[4]	D. A. Nield, A. Bejan, Convection in Porous Media, third ed., Springer-Verlag (2006).
[5]	W. Zheng and Robillard, ‘convection in a Square Cavity Filled with in anisotropic porous saturated with water Near 4°C’ International Journal of Heat and mass Transfer, vol, 44, N°18, pp, 3463. 3463, 2001.
[6]	Smail BENISSAAD, Nabil OUAZAA1, Étude analytique et numérique de la convection naturelle bidiffusive dans un milieu poreux confiné 24-27 Mai 2011, SFT’11, Perpignan, France."
[7]	Akowanou Chr (2007) Convective transfer in subjected porous cavities a transverse magnetic field J. Rech. Sci. Univ. Lomé (Togo), 2007, série E, 9 (1): 1-11.
[8]	CORMACK D. E., LEAL L. G. and IMBERGER, 1974. "Natural Convection in a Shallow Cavity with Differentially Heated End Walls. Part 1, Asymptotic Theory". J. Fluid Mech., 65: 209-230.
[9]	P. VASSEUR M., HASNAOUI E., BILGEN L. and ROBILLARD, 1993. "Natural Convection in an Inclined Fluid Layer with a Transverse Magnetic Field: Analogy with a Porous Medium". Journal of Heat Transfer, Vol. 117: 121-129.
[10]	BIRIKH R. V., 1996. "Thermocapillary Convection in a Horizontal Layer of Liquid". J. Appl. Mech. Tech. Phys., 3: 69-72.
[11]	GARANDET J. P. et ALBOUSSIERE T., 1992. "Buoyancy Driven Convection in a Rectangular Enclosure with a Transverse Magnetic Field". In J. Heat Mass Transfer, 35 (4): 741-748.
[12]	Akowanou and all, Convective transfer in porous cavities subjected to a transverse magnetic field.
[13]	Attia Abbas (2007), suppression des instabilités thermosolutale par l'action d'un champ magnétique. thèse de magistère université de mentouri constantine algérie.

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APA Style

Christian Akowanou, Faras Issiako, Macaire Agbomahena, Regis Hontinfinde. (2022). Influence of Anisotropy on Thermosolutal Convection in Porous Media with Magnetic Field Effect. International Journal of Fluid Mechanics & Thermal Sciences, 8(2), 23-33. https://doi.org/10.11648/j.ijfmts.20220802.11

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ACS Style

Christian Akowanou; Faras Issiako; Macaire Agbomahena; Regis Hontinfinde. Influence of Anisotropy on Thermosolutal Convection in Porous Media with Magnetic Field Effect. Int. J. Fluid Mech. Therm. Sci. 2022, 8(2), 23-33. doi: 10.11648/j.ijfmts.20220802.11

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AMA Style

Christian Akowanou, Faras Issiako, Macaire Agbomahena, Regis Hontinfinde. Influence of Anisotropy on Thermosolutal Convection in Porous Media with Magnetic Field Effect. Int J Fluid Mech Therm Sci. 2022;8(2):23-33. doi: 10.11648/j.ijfmts.20220802.11

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@article{10.11648/j.ijfmts.20220802.11,
  author = {Christian Akowanou and Faras Issiako and Macaire Agbomahena and Regis Hontinfinde},
  title = {Influence of Anisotropy on Thermosolutal Convection in Porous Media with Magnetic Field Effect},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {8},
  number = {2},
  pages = {23-33},
  doi = {10.11648/j.ijfmts.20220802.11},
  url = {https://doi.org/10.11648/j.ijfmts.20220802.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20220802.11},
  abstract = {In the present study, both anisotropy and magnetic field effects on bi-diffusive natural convection in a rectangular cavity filled with a porous medium saturated by a binary fluid are investigated analytically for fully developed flow regime. The cavity is heated isothermally by the sides and its horizontal walls are thermally insulated or conducted. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction that is arbitrary to the gravity field. On the basis of the generalized Brinkman-extended Darcy model of newtonian fluids on steady flow through porous media, analytical expressions were obtained for the flow and thermal fields, the concentration of speaces, the average Nusselt and Sherwood numbers in terms of the Darcy number, the anisotropic permeability ratio, the orientation angle of the principal axes and the Hartmann number.  The limiting case corresponding to pure porous media (Da→0) and pure fluid media (Da→∞) for the thermal conditions mentioned on the cavity completed these results in order to compare them to those obtained in the literature. It is found that, Nusselt and Sherwood numbers increase by increasing anisotropic parameters of the porous medium while increasing magnetic field magnitude greatly reduces the intensity of the flow and thus affects significantly heat and mass transfer.},
 year = {2022}
}

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TY  - JOUR
T1  - Influence of Anisotropy on Thermosolutal Convection in Porous Media with Magnetic Field Effect
AU  - Christian Akowanou
AU  - Faras Issiako
AU  - Macaire Agbomahena
AU  - Regis Hontinfinde
Y1  - 2022/06/21
PY  - 2022
N1  - https://doi.org/10.11648/j.ijfmts.20220802.11
DO  - 10.11648/j.ijfmts.20220802.11
T2  - International Journal of Fluid Mechanics & Thermal Sciences
JF  - International Journal of Fluid Mechanics & Thermal Sciences
JO  - International Journal of Fluid Mechanics & Thermal Sciences
SP  - 23
EP  - 33
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20220802.11
AB  - In the present study, both anisotropy and magnetic field effects on bi-diffusive natural convection in a rectangular cavity filled with a porous medium saturated by a binary fluid are investigated analytically for fully developed flow regime. The cavity is heated isothermally by the sides and its horizontal walls are thermally insulated or conducted. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction that is arbitrary to the gravity field. On the basis of the generalized Brinkman-extended Darcy model of newtonian fluids on steady flow through porous media, analytical expressions were obtained for the flow and thermal fields, the concentration of speaces, the average Nusselt and Sherwood numbers in terms of the Darcy number, the anisotropic permeability ratio, the orientation angle of the principal axes and the Hartmann number.  The limiting case corresponding to pure porous media (Da→0) and pure fluid media (Da→∞) for the thermal conditions mentioned on the cavity completed these results in order to compare them to those obtained in the literature. It is found that, Nusselt and Sherwood numbers increase by increasing anisotropic parameters of the porous medium while increasing magnetic field magnitude greatly reduces the intensity of the flow and thus affects significantly heat and mass transfer.
VL  - 8
IS  - 2
ER  -

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Author Information

Christian Akowanou

Laboratory of Science Ingineering and Mathematic (LSIMA), National University of Science, Technology, Engineering and Mathematics (UNSTIM), Abomey, Republic of Benin
Faras Issiako

Laboratory of Energetic and Applied Mechanics (LEMA), University of Abomey Calavi, Polytechnic School of Abomey Calavi (EPAC-UAC), Abomey Calavi, Republic of Benin
Macaire Agbomahena

Laboratory of Telecommunication and Applied Computer Engineering (LETIA), University of Abomey Calavi, Polytechnic School of Abomey Calavi (EPAC-UAC), Abomey Calavi, Republic of Benin
Regis Hontinfinde

Laboratory of Science Ingineering and Mathematic (LSIMA), National University of Science, Technology, Engineering and Mathematics (UNSTIM), Abomey, Republic of Benin

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APA Style

Christian Akowanou, Faras Issiako, Macaire Agbomahena, Regis Hontinfinde. (2022). Influence of Anisotropy on Thermosolutal Convection in Porous Media with Magnetic Field Effect. International Journal of Fluid Mechanics & Thermal Sciences, 8(2), 23-33. https://doi.org/10.11648/j.ijfmts.20220802.11

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ACS Style

Christian Akowanou; Faras Issiako; Macaire Agbomahena; Regis Hontinfinde. Influence of Anisotropy on Thermosolutal Convection in Porous Media with Magnetic Field Effect. Int. J. Fluid Mech. Therm. Sci. 2022, 8(2), 23-33. doi: 10.11648/j.ijfmts.20220802.11

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AMA Style

Christian Akowanou, Faras Issiako, Macaire Agbomahena, Regis Hontinfinde. Influence of Anisotropy on Thermosolutal Convection in Porous Media with Magnetic Field Effect. Int J Fluid Mech Therm Sci. 2022;8(2):23-33. doi: 10.11648/j.ijfmts.20220802.11

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@article{10.11648/j.ijfmts.20220802.11,
  author = {Christian Akowanou and Faras Issiako and Macaire Agbomahena and Regis Hontinfinde},
  title = {Influence of Anisotropy on Thermosolutal Convection in Porous Media with Magnetic Field Effect},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {8},
  number = {2},
  pages = {23-33},
  doi = {10.11648/j.ijfmts.20220802.11},
  url = {https://doi.org/10.11648/j.ijfmts.20220802.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20220802.11},
  abstract = {In the present study, both anisotropy and magnetic field effects on bi-diffusive natural convection in a rectangular cavity filled with a porous medium saturated by a binary fluid are investigated analytically for fully developed flow regime. The cavity is heated isothermally by the sides and its horizontal walls are thermally insulated or conducted. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction that is arbitrary to the gravity field. On the basis of the generalized Brinkman-extended Darcy model of newtonian fluids on steady flow through porous media, analytical expressions were obtained for the flow and thermal fields, the concentration of speaces, the average Nusselt and Sherwood numbers in terms of the Darcy number, the anisotropic permeability ratio, the orientation angle of the principal axes and the Hartmann number.  The limiting case corresponding to pure porous media (Da→0) and pure fluid media (Da→∞) for the thermal conditions mentioned on the cavity completed these results in order to compare them to those obtained in the literature. It is found that, Nusselt and Sherwood numbers increase by increasing anisotropic parameters of the porous medium while increasing magnetic field magnitude greatly reduces the intensity of the flow and thus affects significantly heat and mass transfer.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Influence of Anisotropy on Thermosolutal Convection in Porous Media with Magnetic Field Effect
AU  - Christian Akowanou
AU  - Faras Issiako
AU  - Macaire Agbomahena
AU  - Regis Hontinfinde
Y1  - 2022/06/21
PY  - 2022
N1  - https://doi.org/10.11648/j.ijfmts.20220802.11
DO  - 10.11648/j.ijfmts.20220802.11
T2  - International Journal of Fluid Mechanics & Thermal Sciences
JF  - International Journal of Fluid Mechanics & Thermal Sciences
JO  - International Journal of Fluid Mechanics & Thermal Sciences
SP  - 23
EP  - 33
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20220802.11
AB  - In the present study, both anisotropy and magnetic field effects on bi-diffusive natural convection in a rectangular cavity filled with a porous medium saturated by a binary fluid are investigated analytically for fully developed flow regime. The cavity is heated isothermally by the sides and its horizontal walls are thermally insulated or conducted. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction that is arbitrary to the gravity field. On the basis of the generalized Brinkman-extended Darcy model of newtonian fluids on steady flow through porous media, analytical expressions were obtained for the flow and thermal fields, the concentration of speaces, the average Nusselt and Sherwood numbers in terms of the Darcy number, the anisotropic permeability ratio, the orientation angle of the principal axes and the Hartmann number.  The limiting case corresponding to pure porous media (Da→0) and pure fluid media (Da→∞) for the thermal conditions mentioned on the cavity completed these results in order to compare them to those obtained in the literature. It is found that, Nusselt and Sherwood numbers increase by increasing anisotropic parameters of the porous medium while increasing magnetic field magnitude greatly reduces the intensity of the flow and thus affects significantly heat and mass transfer.
VL  - 8
IS  - 2
ER  -

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