Bi-stability Study of Double Diffusive Convection Using the Carreau- Yasuda Model in a Shallow Horizontal Porous Layer Filled with a Non- Newtonian Fluid

Authors

  • Sara Bensilakhal Laboratoire Matériaux et Environnement, LME, Université de Médéa, 26000 Médéa, Algeria
  • Redha Rebhi Department of Mechanical Engineering, Faculty of Technology, University of Medea, Medea 26000, Algeria
  • Noureddine Hadidi Department of Process Engineering and Environment, Faculty of Technology, University of Medea, Medea 26000, Algeria
  • Giulio Lorenzini Department of Engineering and Architecture, University of Parma, Parco Area delle Scienze, 181/A, 43124 Parma, Italy
  • Yacine Kerchiche National Polytechnic School of Algiers, Algeria
  • Younes Menni Department of Technology, University Center Salhi Ahmed Naama (Ctr. Univ. Naama), P.O. Box 66, Naama 45000, Algeria
  • Houari Ameur Department of Technology, University Center Salhi Ahmed Naama (Ctr. Univ. Naama), P.O. Box 66, Naama 45000, Algeria
  • Hijaz Ahmad Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy

DOI:

https://doi.org/10.37934/arfmts.101.1.137159

Keywords:

Non-linear convection, porous layer, non-Newtonian liquid, shear-thinning fluid, Bi-stability, Hopf bifurcation

Abstract

The onset of non-linear convection in a horizontal porous layer saturated by a shear- thinning liquid is studied. The Carreau-Yasuda model is utilized for modeling the behavior of the working medium. Constant fluxes of heat and mass are imposed on the horizontal walls of the cavity, while the vertical sides are assumed adiabatic and impermeable. The parallel flow approximation and the finite difference approach are used to conduct the investigation analytically and numerically, respectively. By considering an infinitesimal perturbation, the linear stability analysis of the diffusive and convective states is conducted based on the finite element method. The theory of linear stability is employed to determine the critical Rayleigh number for the onset of motion from the rest state as well as the onset of Hopf bifurcation, transition from the stationary to oscillatory convection. Overall, the Carreau-Yasuda rheological parameters have a significant impact on the thresholds of convection. The most interesting findings of this study is highlighting the existence of a bi-stability phenomenon, i.e., the existence of two steady-state solutions, which was not observed before in non-Newtonian fluids convection.

Author Biographies

Sara Bensilakhal, Laboratoire Matériaux et Environnement, LME, Université de Médéa, 26000 Médéa, Algeria

sarbensilakhal@gmail.com

Redha Rebhi, Department of Mechanical Engineering, Faculty of Technology, University of Medea, Medea 26000, Algeria

redhareb@gmail.com

Noureddine Hadidi, Department of Process Engineering and Environment, Faculty of Technology, University of Medea, Medea 26000, Algeria

nohadidi@gmail.com

Giulio Lorenzini, Department of Engineering and Architecture, University of Parma, Parco Area delle Scienze, 181/A, 43124 Parma, Italy

lorenzini.unipr@gmail.com

Yacine Kerchiche, National Polytechnic School of Algiers, Algeria

yakerchiche@gmail.com

Younes Menni, Department of Technology, University Center Salhi Ahmed Naama (Ctr. Univ. Naama), P.O. Box 66, Naama 45000, Algeria

menniyounes.cfd@gmail.com

Houari Ameur, Department of Technology, University Center Salhi Ahmed Naama (Ctr. Univ. Naama), P.O. Box 66, Naama 45000, Algeria

houari_ameur@yahoo.fr

Hijaz Ahmad, Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy

hijaz555@gmail.com

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Published

2023-01-15

How to Cite

Sara Bensilakhal, Redha Rebhi, Noureddine Hadidi, Lorenzini, G., Yacine Kerchiche, Younes Menni, Houari Ameur, & Hijaz Ahmad. (2023). Bi-stability Study of Double Diffusive Convection Using the Carreau- Yasuda Model in a Shallow Horizontal Porous Layer Filled with a Non- Newtonian Fluid. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 101(1), 137–159. https://doi.org/10.37934/arfmts.101.1.137159

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