Mathematical modelling of free convection in a square cavity filled with a bidisperse porous medium for large values of Rayleigh number

Authors

  • Cornelia REVNIC University of Medicine and Pharmacy, Faculty of Pharmacy, 8, V. Babe¸s Street, 400012 Cluj-Napoca, Romania, e-mail: cornelia.revnic@umfcluj.ro https://orcid.org/0000-0002-5610-1957
  • Flavius PĂTRULESCU Department of Mathematics, Technical University of Cluj-Napoca, 28, Memorandumului Street, 400114 Cluj-Napoca, Romania, e-mail: Flavius.Patrulescu@math.utcluj.ro https://orcid.org/0000-0002-1604-0037

DOI:

https://doi.org/10.24193/subbmath.2022.4.16

Keywords:

Numerical results, free convection, square cavity, bidisperse porous medium, nonuniform grid.

Abstract

A free convection problem for bidisperse porous media is considered. The numerical solutions are obtained using an algorithm based on an nonuniform grid. Results for some values of the governing parameters when Rayleigh number is equal to 10⁴ are provided.

Mathematics Subject Classification (2010): 76R10, 76S05, 76M20, 65N06.

Received 08 September 2020; Accepted 14 December 2020.

References

Baytas, A.C., Pop, I., Free convection in oblique enclosures filled with a porous medium, Int. J. Heat Mass Transf., 42 (1999), 1047-1057.

Beckermann, C., Viskanta, R., Ramadhyani, S., A numerical study on non-Darcian natural convection in a vertical enclosure filled with a porous medium, Numer. Heat Transfer, 10 (1986), 446-469.

Bejan, A., On the boundary layer regime in a vertical enclosure filled with a porous medium, Lett. Heat Mass Transf., 6 (1979), 93-102.

Bufnea, D., Niculescu, V., Silaghi, G, Sterca, A., Babe¸s-Bolyai University’s high performance computing center, Stud. Univ. Babe¸s-Bolyai Inform., 61(2016), 54-69.

C˘atina¸s, T., Extension of some particular interpolation operators to a triangle with one curved side, Appl. Math. Comp., 315(2017), 286-297.

C˘atina¸s, T., Extension of some generalized Hermite-type interpolation operators to the triangle with one curved side, Numer. Funct. Anal. Optim., 40(2019), 1939-1963.

Chiorean, I., C˘atina¸s, T., Trˆımbi¸ta¸s, R., Numerical Analysis, Cluj University Press, Cluj-Napoca, 2010.

Gentile, M., Straughan, B., Bidispersive thermal convection with relatively large macropores, J. Fluid Mech., 898(2020), A14-1.

Gross, R., Bear, M.R., Hickox, C.E., The application of flux-corrected transport (FCT) to high Rayleigh number natural convection in a porous medium, In: Proceedings of the 7th International Heat Transfer Conference, San Francisco, CA, 1986.

Ingham, D.B., Pop, I. (Eds.), Transport Phenomena in Porous Media, vol. III, Elsevier, Oxford, 2005.

Manole, D.M., Lage, J.L., Numerical benchmark results for natural convection in a porous medium cavity, Heat Mass Transf. Porous Media ASME Conf., 105(1992), 44-59.

Micula, S., Pop, I., Numerical results for the classical free convection flow problem in a square porous cavity using spline functions, Int. J. Numer. Methods Heat Fluid Flow, 31(2021), no. 3, 753-765.

Moya, S.L., Ramos, E., Sen, M., Numerical study of natural convection in a tilted rectangular porous material, Int. J. Heat Mass Transfer, 30(1987), 630-645.

Nield, D.A., Bejan, A., Convection on Porous Media (Fifth Edition), Springer, New- York, 2017.

Nield, D.A., Kuznetsov, A.V., Heat transfer in bidisperse porous media, in: D.B. Ingham, I. Pop (Eds.), Transport in Porous Media, vol. III, Elsevier, Oxford, 2005, 34-59.

Nield, D.A., Kuznetsov, A.V., Natural convection about a vertical plate embedded in a bidisperse porous medium, Int. J. Heat Mass Transfer, 51(2008), 1658-1664.

Rees, D.A.S., Nield, D.A., Kuznetsov, A.V., Vertical free convective boudary-layer flow in a bidisperse porous medium, ASME J. Heat Transfer, 130(2008), 1-9.

Revnic, C., Gro¸san, T., Pop, I., Ingham, D.B., Free convection in a square cavity filled with a bidisperse porous medium, Int. J. Therm. Sci., 48(2009), 1826-1833.

Revnic, C., Gro¸san, T., Pop, I., Ingham, D.B., Magnetic field effect on the unsteady free convection flow in a square cavity filled with a porous medium with a constant heat generation, Int. J. Heat Mass Transf., 54(2011), no. 9-10, 1734-1742.

Straughan, B., Convection with Local Thermal Non-Equilibrium and Microfluidic Effects, Springer, Heidelberg, 2015.

Strikwerda, J.C., Finite Difference Schemes and Partial Differential Equations (Second Edition), SIAM, Philadelphia, 2004.

V˘ac˘ara¸s, V., Major, Z.Z., Mure¸sanu, D.F., Krausz, T.L., M˘arginean, I., Buzoianu, D.A., Effect of glatiramer acetate on peripheral blood brain-derived neurotrophic factor and phosphorylated trkB levels in relapsing- remitting multiple sclerosis, CNS & Neurological Disorders-Drug Targets, 13(2014), 647-651.

Walker, K.L., Homsy, G.M., Convection in a porous cavity, J. Fluid Mech., 76(1978), 338-363.

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Published

2022-12-02

How to Cite

REVNIC, C., & PĂTRULESCU, F. (2022). Mathematical modelling of free convection in a square cavity filled with a bidisperse porous medium for large values of Rayleigh number. Studia Universitatis Babeș-Bolyai Mathematica, 67(4), 891–903. https://doi.org/10.24193/subbmath.2022.4.16

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