Effect of Anisotropic Permeability on Thermosolutal Convection in a Porous Cavity Saturated by a Non-newtonian Fluid

Yovogan Julien; Fagbemi Latif; Koube Bocco Sèlidji Marius; Kouke Dieudonné; Degan Gérard

doi:doi:10.11648/j.ijfmts.20200604.13

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Effect of Anisotropic Permeability on Thermosolutal Convection in a Porous Cavity Saturated by a Non-newtonian Fluid

Yovogan Julien, Fagbemi Latif, Koube Bocco Sèlidji Marius, Kouke Dieudonné, Degan Gérard

Published in International Journal of Fluid Mechanics & Thermal Sciences (Volume 6, Issue 4)

Received: 13 November 2020 Accepted: 30 November 2020 Published: 16 December 2020

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Abstract

In this paper, an analytical study is reported on double-diffusive natural convection in a shallow porous cavity saturated with a non-Newtonian fluid by using the Darcy model with the Boussinesq approximations. A Cartesian coordinate system is chosen with the x- and y- axes at the geometrical center of the cavity and the y’-axis vertically upward. The top and bottom horizontal boundaries are subject to constant heat (q) and mass (j) fluxes. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction that is oblique to the gravity vector. The permeabilities along the two principal axes of the porous matrix are denoted by K1 and K2. The anisotropy of the porous layer is characterized by the permeability ratio K*=K₁/K₂ and the orientation angle φ, deﬁned as the angle between the horizontal direction and the principal axis with the permeability K2. The viscous dissipations are negligible. Based on parallel flow approximation theory, the problem is solved analytically, in the limit of a thin layer and documented the effects of the physical parameters describing this investigation. Solutions for the flow ﬁelds, Nusselt and Sherwood numbers are obtained explicitly in terms of the governing parameters of the problem.

Published in	International Journal of Fluid Mechanics & Thermal Sciences (Volume 6, Issue 4)
DOI	10.11648/j.ijfmts.20200604.13
Page(s)	124-131
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

Heat Transfer, Mass Transfer, Isotropy, Anisotropy

References

[1]	Jaluria, Y. (2003). Thermal processing of materials: From basic research to engineering. Journal of Heat Transfer 125, 957-979.
[2]	Getachew, D., D. Poulikakos and W. J. Minkowycz. 1998. “Double-diffusive in a porous cavity saturated with non-Newtonian Fluid”. Journal of Thermophysics and Heat Transfer 12, 437-446.
[3]	Benhadji, K. and P. Vasseur. 2001. “Double diffusive convection in a shallow porous cavity ﬁlled with a non-Newtonian fluid”. International Communications in Heat and Mass Transfer 28, 763-772.
[4]	Makayssi, T., M. Lamsaadi, M. Nami, M. Hasnaoui, A. Raji and A. Bahlaoui. 2008. “Natural double-diffusive convection in a shallow horizontal rectangular cavity uniformly heated and salted from the side and ﬁlled with non-Newtonian power-law fluids: the cooperating case”, Energy conversion and Management 49, 2016-2025.
[5]	Srinivasacharya, D., Swamy Reddy, G. 2012. Double Diffusive Natural Convection in Power-Law Fluid Saturated Porous Medium with Soret and Dufour Effects J. of the Braz. Soc. of Mech. Sci. Eng. Vol. XXXIV, No. 4, pp. 525-530.
[6]	Salma Parvin, Rehena Nasrin, Alim, M. A., Hossain, N. F. 2013 Double diffusive natural convective flow characteristics in a cavity Procedia Engineering Vol. 56, pp. 480 488.
[7]	Raju Chowdhury, Salma Parvin, and Md. Abdul Hakim Khan. 2016. Finite element analysis of double-diffusive natural convection in a porous triangular enclosure ﬁlled with Al₂O₃-water nanofluid in presence of heat generation Heliyon. 2016 Aug; 2 (8): e00140.
[8]	Ariyan Zare Ghadi, Ali Haghighi Asl, Mohammad Sadegh Valipour. 2014. Numerical modelling of double-diffusive natural convection within an arc shaped enclosure ﬁlled with a porous medium Journal of Heat and Mass Transfer Research Vol. 1 pp. 83-91.
[9]	Sabyasachi Mondal and Precious Sibanda. 2016. An Unsteady Double-Diffusive Natural Convection in an Inclined Rectangular Enclosure with Different Angles of Magnetic Field International Journal of Computational Methods, Vol. 13, No. 041641015.
[10]	BIHICHE, K., LAMSAADI, M., NAMI, M., ELHARFI, H., KADDIRI, M., LOUARAYCHI, A. 2017. Double-diffusive and Soret-induced convection in a shallow horizontal layer lled with non-Newtonian power-law uids 13me Congrs de Mcanique 11 - 14 Avril 2017 (Mekns, MAROC).
[11]	Girinath Reddy, M., Dinesh, P. A. 2018. Double Diffusive Convection and Internal Heat Generation with Soret and Dufour Effects over an Accelerating Sur- face with Variable Viscosity and Permeability Advances in Physics Theories and Applications, Vol. 69, pp. 7-25.
[12]	Mahapatra, T. R., Saha, B. C. Pal, D. 2018 Magnetohydrodynamic double- diffusive natural convection for nanofluid within a trapezoidal enclosure. Comp. Appl. Math. 37, 61326151 (2018) doi: 10.1007/s40314-018-0676-5.
[13]	Abdelraheem M. Aly and Mitsuteru Asai (October 22nd 2015). Double- Diffusive Natural Convection with Cross-Diffusion Effects in an Anisotropic Porous Enclosure Using ISPH Method, Mass Transfer - Advancement in Process Modelling, Marek Solecki, Intech Open, DOI: 10.5772/60879.
[14]	Ostwald, W. 1925. “Ueber die Geschwindigkeitsfunktion der Viskositat Disperser Système”, L, Kolloïd-Z, Vol. 36, pp. 99-117.
[15]	PASCAL, H. 1983. “Rheological Behaviour Effect of Non Newtonian Fluids on Steady and Unsteady Flow Through a Porous Media”, International Journal for Numerical and Analytical Methods in Geomechanics, vol. 7, pp. 289-303.
[16]	PASCAL, H. 1986. “Rheological effects of Non Newtonian Behaviour of Displacing Fluids on Stability of a Moving Interface in Radial Oil Displacement Mechanism in Porous Media”, International Journal Engineering Science, vol. 24, No. 9, pp. 1465-1476.
[17]	AMARI, B., VASSEUR, P., and BILGEN, E. 1994. “Natural Convection of Non Newtonian Fluids in a Horizontal Porous Layer”, Wrme-und Stoffbertragung, vol. 29, pp. 185-193.
[18]	MAMOU, M., VASSEUR, P., BILGEN, E., and GOBIN, D. 1995. “Double- Diffusive Convection in an Inclined Slot Filled with Porous Medium”, Eur. J. Me- chanics, B/Fluids, vol. 14, pp. 629-652.
[19]	KALLA, L., MAMOU M., VASSEUR, P. and ROBILLARD, L. 1999. “Mul- tiple Steady States for Natural Convection in a Shallow Porous Cavity Subject to Uniform Heat Fluxes”, International Communications in Heat Mass Transfer, vol. 26, No. 6, pp. 761-770.

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APA Style

Yovogan Julien, Fagbemi Latif, Koube Bocco Sèlidji Marius, Kouke Dieudonné, Degan Gérard. (2020). Effect of Anisotropic Permeability on Thermosolutal Convection in a Porous Cavity Saturated by a Non-newtonian Fluid. International Journal of Fluid Mechanics & Thermal Sciences, 6(4), 124-131. https://doi.org/10.11648/j.ijfmts.20200604.13

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ACS Style

Yovogan Julien; Fagbemi Latif; Koube Bocco Sèlidji Marius; Kouke Dieudonné; Degan Gérard. Effect of Anisotropic Permeability on Thermosolutal Convection in a Porous Cavity Saturated by a Non-newtonian Fluid. Int. J. Fluid Mech. Therm. Sci. 2020, 6(4), 124-131. doi: 10.11648/j.ijfmts.20200604.13

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AMA Style

Yovogan Julien, Fagbemi Latif, Koube Bocco Sèlidji Marius, Kouke Dieudonné, Degan Gérard. Effect of Anisotropic Permeability on Thermosolutal Convection in a Porous Cavity Saturated by a Non-newtonian Fluid. Int J Fluid Mech Therm Sci. 2020;6(4):124-131. doi: 10.11648/j.ijfmts.20200604.13

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@article{10.11648/j.ijfmts.20200604.13,
  author = {Yovogan Julien and Fagbemi Latif and Koube Bocco Sèlidji Marius and Kouke Dieudonné and Degan Gérard},
  title = {Effect of Anisotropic Permeability on Thermosolutal Convection in a Porous Cavity Saturated by a Non-newtonian Fluid},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {6},
  number = {4},
  pages = {124-131},
  doi = {10.11648/j.ijfmts.20200604.13},
  url = {https://doi.org/10.11648/j.ijfmts.20200604.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20200604.13},
  abstract = {In this paper, an analytical study is reported on double-diffusive natural convection in a shallow porous cavity saturated with a non-Newtonian fluid by using the Darcy model with the Boussinesq approximations. A Cartesian coordinate system is chosen with the x- and y- axes at the geometrical center of the cavity and the y’-axis vertically upward. The top and bottom horizontal boundaries are subject to constant heat (q) and mass (j) fluxes. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction that is oblique to the gravity vector. The permeabilities along the two principal axes of the porous matrix are denoted by K1 and K2. The anisotropy of the porous layer is characterized by the permeability ratio K*=K1/K2 and the orientation angle φ, deﬁned as the angle between the horizontal direction and the principal axis with the permeability K2. The viscous dissipations are negligible. Based on parallel flow approximation theory, the problem is solved analytically, in the limit of a thin layer and documented the effects of the physical parameters describing this investigation. Solutions for the flow ﬁelds, Nusselt and Sherwood numbers are obtained explicitly in terms of the governing parameters of the problem.},
 year = {2020}
}

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TY  - JOUR
T1  - Effect of Anisotropic Permeability on Thermosolutal Convection in a Porous Cavity Saturated by a Non-newtonian Fluid
AU  - Yovogan Julien
AU  - Fagbemi Latif
AU  - Koube Bocco Sèlidji Marius
AU  - Kouke Dieudonné
AU  - Degan Gérard
Y1  - 2020/12/16
PY  - 2020
N1  - https://doi.org/10.11648/j.ijfmts.20200604.13
DO  - 10.11648/j.ijfmts.20200604.13
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  - 124
EP  - 131
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20200604.13
AB  - In this paper, an analytical study is reported on double-diffusive natural convection in a shallow porous cavity saturated with a non-Newtonian fluid by using the Darcy model with the Boussinesq approximations. A Cartesian coordinate system is chosen with the x- and y- axes at the geometrical center of the cavity and the y’-axis vertically upward. The top and bottom horizontal boundaries are subject to constant heat (q) and mass (j) fluxes. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction that is oblique to the gravity vector. The permeabilities along the two principal axes of the porous matrix are denoted by K1 and K2. The anisotropy of the porous layer is characterized by the permeability ratio K*=K1/K2 and the orientation angle φ, deﬁned as the angle between the horizontal direction and the principal axis with the permeability K2. The viscous dissipations are negligible. Based on parallel flow approximation theory, the problem is solved analytically, in the limit of a thin layer and documented the effects of the physical parameters describing this investigation. Solutions for the flow ﬁelds, Nusselt and Sherwood numbers are obtained explicitly in terms of the governing parameters of the problem.
VL  - 6
IS  - 4
ER  -

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Author Information

Yovogan Julien

Department of the Energizing Genius and Environment, National University of Sciences, Technologies, Engineering and Mathematics (UNSTIM), Abomey, Republic of Benin
Fagbemi Latif

Department of Renewable Energy and Energizing System, University of Abomey Calavi, Abomey Calavi, Republic of Benin
Koube Bocco Sèlidji Marius

Department of Physics, National University of Sciences, Technologies, Engineering and Mathematics (UNSTIM), Abomey, Republic of Benin
Kouke Dieudonné

Department of Renewable Energy and Energizing System, University of Abomey Calavi, Abomey Calavi, Republic of Benin
Degan Gérard

Department of the Energizing Genius and Environment, National University of Sciences, Technologies, Engineering and Mathematics (UNSTIM), Abomey, Republic of Benin

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APA Style

Yovogan Julien, Fagbemi Latif, Koube Bocco Sèlidji Marius, Kouke Dieudonné, Degan Gérard. (2020). Effect of Anisotropic Permeability on Thermosolutal Convection in a Porous Cavity Saturated by a Non-newtonian Fluid. International Journal of Fluid Mechanics & Thermal Sciences, 6(4), 124-131. https://doi.org/10.11648/j.ijfmts.20200604.13

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ACS Style

Yovogan Julien; Fagbemi Latif; Koube Bocco Sèlidji Marius; Kouke Dieudonné; Degan Gérard. Effect of Anisotropic Permeability on Thermosolutal Convection in a Porous Cavity Saturated by a Non-newtonian Fluid. Int. J. Fluid Mech. Therm. Sci. 2020, 6(4), 124-131. doi: 10.11648/j.ijfmts.20200604.13

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AMA Style

Yovogan Julien, Fagbemi Latif, Koube Bocco Sèlidji Marius, Kouke Dieudonné, Degan Gérard. Effect of Anisotropic Permeability on Thermosolutal Convection in a Porous Cavity Saturated by a Non-newtonian Fluid. Int J Fluid Mech Therm Sci. 2020;6(4):124-131. doi: 10.11648/j.ijfmts.20200604.13

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@article{10.11648/j.ijfmts.20200604.13,
  author = {Yovogan Julien and Fagbemi Latif and Koube Bocco Sèlidji Marius and Kouke Dieudonné and Degan Gérard},
  title = {Effect of Anisotropic Permeability on Thermosolutal Convection in a Porous Cavity Saturated by a Non-newtonian Fluid},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {6},
  number = {4},
  pages = {124-131},
  doi = {10.11648/j.ijfmts.20200604.13},
  url = {https://doi.org/10.11648/j.ijfmts.20200604.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20200604.13},
  abstract = {In this paper, an analytical study is reported on double-diffusive natural convection in a shallow porous cavity saturated with a non-Newtonian fluid by using the Darcy model with the Boussinesq approximations. A Cartesian coordinate system is chosen with the x- and y- axes at the geometrical center of the cavity and the y’-axis vertically upward. The top and bottom horizontal boundaries are subject to constant heat (q) and mass (j) fluxes. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction that is oblique to the gravity vector. The permeabilities along the two principal axes of the porous matrix are denoted by K1 and K2. The anisotropy of the porous layer is characterized by the permeability ratio K*=K1/K2 and the orientation angle φ, deﬁned as the angle between the horizontal direction and the principal axis with the permeability K2. The viscous dissipations are negligible. Based on parallel flow approximation theory, the problem is solved analytically, in the limit of a thin layer and documented the effects of the physical parameters describing this investigation. Solutions for the flow ﬁelds, Nusselt and Sherwood numbers are obtained explicitly in terms of the governing parameters of the problem.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Effect of Anisotropic Permeability on Thermosolutal Convection in a Porous Cavity Saturated by a Non-newtonian Fluid
AU  - Yovogan Julien
AU  - Fagbemi Latif
AU  - Koube Bocco Sèlidji Marius
AU  - Kouke Dieudonné
AU  - Degan Gérard
Y1  - 2020/12/16
PY  - 2020
N1  - https://doi.org/10.11648/j.ijfmts.20200604.13
DO  - 10.11648/j.ijfmts.20200604.13
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  - 124
EP  - 131
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20200604.13
AB  - In this paper, an analytical study is reported on double-diffusive natural convection in a shallow porous cavity saturated with a non-Newtonian fluid by using the Darcy model with the Boussinesq approximations. A Cartesian coordinate system is chosen with the x- and y- axes at the geometrical center of the cavity and the y’-axis vertically upward. The top and bottom horizontal boundaries are subject to constant heat (q) and mass (j) fluxes. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction that is oblique to the gravity vector. The permeabilities along the two principal axes of the porous matrix are denoted by K1 and K2. The anisotropy of the porous layer is characterized by the permeability ratio K*=K1/K2 and the orientation angle φ, deﬁned as the angle between the horizontal direction and the principal axis with the permeability K2. The viscous dissipations are negligible. Based on parallel flow approximation theory, the problem is solved analytically, in the limit of a thin layer and documented the effects of the physical parameters describing this investigation. Solutions for the flow ﬁelds, Nusselt and Sherwood numbers are obtained explicitly in terms of the governing parameters of the problem.
VL  - 6
IS  - 4
ER  -

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