Hysteresis and Bistability Bifurcation Induced by Combined Fluid Shear Thickening and Double-Diffusive Convection in Shallow Porous Enclosures Filled with Non-Newtonian Power-Law Fluids

  • Saleh Khir Department of Mechanical Engineering, University of Medea, Medea, Algeria; LERM-Renewable Energy and Materials Laboratory, University of Medea, Medea, Algeria; Laboratoire de Mécanique Physique et Modélisation Mathématique (LMP2M), Université Yahia Fares de Médéa, Médéa, Algérie https://orcid.org/0009-0004-6018-1453
  • Redha Rebhi Department of Mechanical Engineering, University of Medea, Medea, Algeria; LERM-Renewable Energy and Materials Laboratory, University of Medea, Medea, Algeria https://orcid.org/0000-0003-3019-9156
  • Mohamed Kezrane Department of Mechanical Engineering, University of Medea, Medea, Algeria; Laboratoire de Mécanique Physique et Modélisation Mathématique (LMP2M), Université Yahia Fares de Médéa, Médéa, Algérie https://orcid.org/0009-0001-3558-4128
  • Mohamed Naceur Borjini Université de Monastir, Ecole Nationale d'Ingénieurs de Monastir, Laboratoire de Métrologie et des Systems Énergétiques, Monastir, Tunisia
DOI: https://doi.org/10.26565/2312-4334-2024-1-17
Keywords: Bi-stability, Thermosolutal convection, Power-law fluid, Porous layer, non-Newtonian binary fluid

Abstract

This paper presents a numerical study of the linear and non-linear stability of thermosolutal convection within a porous medium saturated by a non-Newtonian binary fluid. The power-law model is utilized for modeling the behavior of the working medium. The given statement implies that the horizontal boundaries experience thermal and solutal flow rates, whereas the vertical walls are impermeable and thermally isolated. The relevant factors that govern the problem being investigated are the Rayleigh number, , the power-law index, , the cavity aspect ratio, , the Lewis number, , and the buoyancy ratio, . An analytical solution is obtained for shallow enclosures ( ) using the parallel flow approximation and a modified form of the Darcy equation. By solving the entire set of governing equations, a numerical investigation of the same phenomenon was conducted. One of the most intriguing discoveries from this research is that it identifies a bi-stability phenomenon, this particular phenomenon signifies the existence of two stable solutions. The results obtained from both methods demonstrate a good level of agreement across a diverse range of these governing parameters.

Downloads

Download data is not yet available.

References

A.A. Mohamad, Num. Heat Transf. Part A, 27, 6 (1995). https://doi.org/10.1080/10407789508913727

G. H. R. Kefayati, Energy. 107 (2016). https://doi.org/10.1016/j.energy.2016.05.044

R. Bennacer, and D. Gobin. Int. J. Heat Mass Transf. 39,13 (1996). https://doi.org/10.1016/0017-9310(95)00350-9

G.H. R. Kefayati, Int. J. Heat Mass Transf. 89 (2015). https://doi.org/10.1016/j.ijheatmasstransfer.2015.05.058

Q.Y. Zhu, et al., Int. J. Heat Mass Transf. 104, (2017). https://doi.org/10.1016/j.ijheatmasstransfer.2016.09.018

P. Kennedy, and R. Zheng. Flow analysis of injection molds, (Carl Hanser Verlag GmbH Co KG, 2013), pp. I–XXIX.

G. De-Vahl Davis, Int. J. Numer. Methods Fluids. 3, 3 (1983). https://doi.org/10.1002/fld.1650030305

O. Aydin et al., Int. J. Heat Mass Transf. 42,13 (1999). https://doi.org/10.1016/S0017-9310(98)00319-6

Y. Liu, and Y. Hu, Nanoscale Res. Lett. 12, 446 (2017). https://doi.org/10.1186/s11671-017-2185-7

M. Omid, et al., Physics reports. 790, (2019). https://doi.org/10.1016/j.physrep.2018.11.004.

S. Fatih, and H.F. Öztop, Int. J. Heat Mass Transf. 129, (2019). https://doi.org/10.1016/j.ijheatmasstransfer.2018.09.101

P.A. Hajatzadeh, et al., Ener. Conv. Manage. 198, (2019). https://doi.org/10.1016/j.enconman.2019.111886

N.O. Moraga, et al., Int. J. Thermal Sci. 107, (2016). https://doi.org/10.1016/j.ijthermalsci.2016.04.007

A.A. Jahanbakhshi, et al., J. Therm Anal Calorim. 133, (2018). https://doi.org/10.1007/s10973-018-7219-6

M. Lamsaadi, et al., Num. Heat Transf, Part A: Applications, 49,10 (2006). https://doi.org/10.1080/10407780500324988

T. Makayssi, et al., Ener. Conv. Manage, 49, 8 (2008). https://doi.org/10.1016/j.enconman.2008.02.008

G.H.R. Kefayati, Computers & Fluids. 114, (2015), https://doi.org/10.1016/j.compfluid.2015.02.009

G. Żyła, et al., Diamond and Related Materials, 74, (2017). https://doi.org/10.1016/j.diamond.2017.02.008

G.B. Kim, et al., Int. J. Heat Mass Transf. 46,19 (2003). https://doi.org/10.1016/S0017-9310(03)00149-2

D. Getachew, et al., Journal of Thermophysics and Heat Transfer. 12, 3 (1998). https://doi.org/10.2514/2.6357

A. Moradi, et al., J. Therm Anal Calorim. 137, 5 (2019). https://doi.org/10.1007/s10973-019-08076-0

S.K, Jena, et al., Journal of the Taiwan Institute of Chemical Engineers. 51, (2015). https://doi.org/10.1016/j.jtice.2015.01.007

S. Lounis, et al., CFD Letters. 14, 3 (2022). https://doi.org/10.37934/cfdl.14.3.96118

R. Rebhi, et al., Int. J. Heat Mass Transf. 100, (2016). https://doi.org/10.1016/j.ijheatmasstransfer.2016.04.060

R. Rebhi, et al., J. Fluid Mech. 812, (2017). https://doi.org/10.1017/jfm.2016.787

R. Rebhi, et al., Physics of Fluids. 33, 7 (2021), https://doi.org/10.1063/5.0051058

K. Bihiche, et al., J. Non-Newt. Fluid Mech. 283, (2020). https://doi.org/10.1016/j.jnnfm.2020.104349.

K. Benhadji, and P. Vasseur. Int. Comm. Heat Mass Transfer. 28,6 (2001). https://doi.org/10.1016/S0735-1933(01)00280-9

B. Amari, et al., Wärme- und Stoffübertragung. 29, 3 (1994). https://doi.org/10.1007/BF01548603

G.H.R. Kefayati, Int. J. Heat Mass Transf. 94, (2016). https://doi.org/10.1016/j.ijheatmasstransfer.2015.11.043

D.A. Nield, et al., Transp Porous Med. 83, (2010). https://doi.org/10.1007/s11242-009-9455-5

M. Devakar, et al., J. Assoc. Arab Univ. Basic Appl. Sci. 23, (2017). https://doi.org/10.1016/j.jaubas.2016.04.001

S.J. Uphill, et al., Colloid Surf. A. 460, (2014). https://doi.org/10.1016/j.colsurfa.2014.05.008

A.L.N. Narayana, et al., Journal of Porous Media. 12,10 (2009). https://doi.org/10.1615/JPorMedia.v12.i10.40

R. Tsai, and J.S. Huang, Comp. Mater. Sci. 47, 1 (2009). https://doi.org/10.1016/j.commatsci.2009.06.009

Q.Y. Zhu, et al., Int. J. Heat Mass Transf. 104, (2017). https://doi.org/10.1016/j.ijheatmasstransfer.2016.09.018

M. Madhu, et al., Int. Comm. Heat Mass Transfer. 117, (2020). https://doi.org/10.1016/j.icheatmasstransfer.2020.104761

N. Ben Khelifa, et al., J. Non-Newt. Fluid Mech, 169-170, (2012). https://doi.org/10.1016/j.jnnfm.2011.11.002

S. Bensilakhal, et al., J. Advanced Research in Fluid Mechanics and Thermal Sciences. 101, 1 (2023). https://doi.org/10.37934/arfmts.101.1.137159.

M. Naimi, et al., Engineering Computations. 17, 6 (2000), https://doi.org/10.1108/02644400010340570

C.H. Chen, et al., Physics Letters A. 370, 1 (2007), https://doi.org/10.1016/j.physleta.2007.05.024

M. Lamsaadi, et al., Num. Heat Transf. Part A: Applications. 53, 2 (2007), https://doi.org/10.1080/10407780701454055

M. Lamsaadi, et al., Ener. Conv. Manage. 47, 15-16 (2006), https://doi.org/10.1016/j.enconman.2005.10.028

M. H. Matin, et al., J. Non-Newt. Fluid Mech. 197, (2013), https://doi.org/10.1016/j.jnnfm.2013.02.002

Z.Z. Alloui, et al., J. Non-Newt. Fluid Mech. 196, (2013), https://doi.org/10.1016/j.jnnfm.2013.01.008

S. Khali, et al., Journal of Thermophysics and Heat Transfer. 36, 2 (2022), https://doi.org/10.2514/1.T6405

M. Ohta, et al., Numerical Heat Transfer: Part A: Applications. 41, 4 (2002), https://doi.org/10.1080/104077802317261218

M. Hojjat, et al., Int. Comm. Heat Mass Transfer. 38, 2 (2011), https://doi.org/10.1016/j.icheatmasstransfer.2010.11.019

S.V. Solomatov, and A.C. Barr, Phys. Earth Planet. Int. 155, 1-2 (2006), https://doi.org/10.1016/j.pepi.2005.11.001

V.S. Solomatov, and A. C. Barr, Phys. Earth Planet. Int. 165, 1-2 (2007), https://doi.org/10.1016/j.pepi.2007.06.007

H. Pascal, Int. J. Numer. Analy. Methods Geomech. 7, 3 (1983), https://doi.org/10.1002/nag.1610070303

H. Pascal, Int. J. Engng Sci. 24, 9 (1986), https://doi.org/10.1016/0020-7225(86)90157-6

S.R. De Groot, and P. Mazur, Non-equilibrium thermodynamics, (Courier Corporation, 2013)

W. Bian, et al., Chem. Eng. Commun. 129, 1 (1994), https://doi.org/10.1080/00986449408936252

W. Bian, et al., Int. J. heat and fluid flow. 15, 5 (1994), https://doi.org/10.1016/0142-727X(94)90052-3

P. Vasseur, et al., Num Heat Transf. 15, 2 (1989), https://doi.org/10.1080/10407788908944686

R.V. Dharmadhikari, and D.D. Kale. Chem. Eng. Sci. 40, 3 (1985), https://doi.org/10.1016/0009-2509(85)85113-7

H.T. Chen, and C.K. Chen. J. Heat Transfer. 110, 1 (1988), https://doi.org/10.1115/1.3250462

H.T. Chen, and C.K. Chen. Int. Comm. Heat Mass Transfer. 15, 5 (1988), https://doi.org/10.1016/0735-1933(88)90051-6

Published
2024-03-05
Cited
How to Cite
Khir, S., Rebhi, R., Kezrane, M., & Borjini, M. N. (2024). Hysteresis and Bistability Bifurcation Induced by Combined Fluid Shear Thickening and Double-Diffusive Convection in Shallow Porous Enclosures Filled with Non-Newtonian Power-Law Fluids. East European Journal of Physics, (1), 203-220. https://doi.org/10.26565/2312-4334-2024-1-17
Issue
No. 1 (2024): East European Journal of Physics
Section
Original Papers

Copyright (c) 2024 Saleh Khir, Redha Rebhi, Mohamed Kezrane, Mohamed Naceur Borjini

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors who publish with this journal agree to the following terms:

    • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
    • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
    • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).