The numerical study of magnetoconvection in a cylinder filled with a porous medium saturated by a metallic nanofluid consisting of aluminum nanoparticles and binary base fluid is performed. The sidewalls of the enclosure are rigid, impermeable, and adiabatic, while the horizontal walls are maintained at uniform temperatures and concentrations. The flow of the nanofluid at the porous layers is described by the Brinkman-Forscheimer extended Darcy law using the Boussinesq approximation. The finite volume method is used to solve the conservation equations for energy, concentration, and momentum. The effect of varying Hartmann, Rayleigh, Darcy, Soret and Dufour, and Prandtl numbers, buoyancy ratio, geometric aspect ratio on the axial and radial velocities, and the heat and mass transfer is studied.

nanofluid, magnetoconvection, porous medium, extension of the law of Darcy, Soret and Dufour effects.

Received: August 26, 2021; Revised: October 4, 2021; Accepted: November 10, 2021; Published: March 15, 2022

How to cite this article: M. El Hamma, M. Taibi, A. Rtibi, K. Gueraoui and M. Bernatchou, Effect of magnetic field on thermosolutal convection in a cylindrical cavity filled with nanofluid, taking into account Soret and Dufour effects, JP Journal of Heat and Mass Transfer 26 (2022), 1-26. http://dx.doi.org/10.17654/0973576322009

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

Reference:

[1] A. Rtibi, M. Hasnaoui and A. Amahmid, Analytico-numerical study of optimal separation of species in an inclined Darcy-Brinkman porous cavity saturated with a binary mixture, Acta Astronautica 98 (2014), 71-85.
[2] M. A. Sheremet, I. Pop and A. Ishak, Double-diffusive mixed convection in a porous open cavity filled with a nanofluid using Buongiorno’s model, Transport in Porous Media 109(1) (2015), 131-145.
[3] S. Chen, B. Yang, K. H. Luo, X. Xiong and C. Zheng, Double diffusion natural convection in a square cavity filled with nanofluid, International Journal of Heat and Mass Transfer 95 (2016), 1070-1083.
[4] M. Afranda, D. Toghraie, A. Karimipour and S. Wongwises, A numerical study of natural convection in a vertical annulus filled with gallium in the presence of magnetic field, Journal of Magnetism and Magnetic Materials 430 (2017), 22-28.
[5] M. J. Uddin, S. K. Rasel, M. M. Rahman and K. Vajravelu, Natural convective heat transfer in a nanofluid-filled square vessel having a wavy upper surface in the presence of a magnetic field, Thermal Science and Engineering Progress 19 (2020), 100660. DOI:https://doi.org/10.1016/j.tsep.2020.100660.
[6] A. Rtibi, M. Hasnaoui and A. Amahmid, On the optimization of the species separation in an inclined Darcy-Brinkman porous cavity under the effect of an external magnetic field, J. Appl. Fluid Mech. 11 (2018), 1059-1071.
[7] M. A. Teamah, A. F. Elsafty, M. Z. Elfeky and E. Z. El-Gazzar, Numerical simulation of double-diffusive natural convective flow in an inclined rectangular enclosure in the presence of magnetic field and heat source, part A: Effect of Rayleigh number and inclination angle, Alexandria Engineering Journal 50 (2011), 269-282.
[8] S. Hussain, M. Jamal and B. P. Geridonmez, Impact of power law fluid and magnetic field on double diffusive mixed convection in staggered porous cavity considering Dufour and Soret effects, International Communications in Heat and Mass Transfer 121 (2021), 105549. https://doi.org/10.1016/j.icheatmasstransfer.2021.105549.
[9] M. Sammouda, K. Gueraoui, M. Driouich, M. Cherraj and Y. Haddad, The magnetic field effect on thermo-solutal natural convection in non-Darcy porous media with non-uniform porosity saturated by an electrically conducting fluid, AES-ATEMA International Conference Series - Advances and Trends in Engineering Materials and their Applications, Vol. 2014, 2014, pp. 187-198.
[10] A. R. Aghaei, Gh. A. Sheikhzadeh and H. Khorasanizadeh, Effect of magnetic field on heat transfer of nanofluid with variable properties on the inclined enclosure, Iranian Journal of Mechanical Engineering 15(1) (2014), 28-38.
[11] M. Mharzi, M. Daguenet and S. Daoudi, Thermosolutal natural convection in a vertically layered fluid-porous medium heated from the side, Energy Conversion and Management 41 (2000), 1065-1090.
[12] A. F. Al-Mudha, A. M. Rashad, S. E. Ahmed, A. J. Chamkha and S. M. M. El-Kabeir, Soret and Dufour effects on unsteady double diffusive natural convection in porous trapezoidal enclosures, International Journal of Mechanical Sciences 140 (2018), 172-178.
[13] D. Kushawaha, S. Yadav and D. K. Singh, Thermo-solute natural convection with heat and mass lines in a uniformly heated and soluted rectangular enclosure for low Prandtl number fluids, International Journal of Thermal Sciences 148 (2020), 10.1016/j.ijthermalsci.2019.106160.
[14] F. Keramat, P. Dehghan, M. Mofarahi and C. HaLee, Numerical analysis of natural convection of alumina water nanofluid in H-shaped enclosure with a V shaped baffle, Journal of the Taiwan Institute of Chemical Engineers 111 (2020), 63-72.
[15] I. Filahi, M. Bourich, M. Hasnaoui and A. Amahmid, Analytical and numerical study of Soret and Dufour effects on thermosolutal convection in a horizontal Brinkman porous layer with a stress-free upper boundary, Math. Probl. Eng. 2020 (2020), Article ID 4046570, 17 pp. https://doi.org/10.1155/2020/4046570.
[16] F. H. Ali, H. K. Hamzah, K. Egab, M. Aricı and A. Shahsavar, Non-Newtonian nanofluid natural convection in a U-shaped cavity under magnetic field, International Journal of Mechanical Sciences 186 (2020), 105887. DOI: 10.1016/j.ijmecsci.2020.105887.
[17] R. Slimani, A. Aissa, F. Mebarek-Oudina, U. Khan, M. Sahnoun, A. J. Chamkha and M. A. Medebber, Natural convection analysis flow of Al2O3-Cu/water hybrid nanofluid in a porous conical enclosure subjected to the magnetic field, The European Physical Journal Applied Physics 92 (2020), 10 pp. 10.1051/epjap/2020200260.
[18] A. Mansour, M. Ait Ahmed, A. Amahmid, M. Hasnaoui, I. Filahi and Y. Dahani, Magnetic field effect on multiplicity of solutions induced by thermosolutal convection in a Bénard square porous cavity submitted to horizontal concentration gradient, J. Appl. Fluid Mech. 14(5) (2021), 1307-1316.
[19] A. I. Alsabery, E. Gedik, A. J. Chamkha and I. Hashim, Impacts of heated rotating inner cylinder and two-phase nanofluid model on entropy generation and mixed convection in a square cavity, Heat and Mass Transfer 56 (2020), 321-338.
[20] A. I. Alsabery, T. Tayebi, H. T. Kadhim, M. Ghalambaz, I. Hashim and A. J. Chamkha, Impact of two-phase hybrid nanofluid approach on mixed convection inside wavy lid-driven cavity having localized solid block, Journal of Advanced Research 30 (2021), 63-74.
[21] F. Selimefendigil, M. A. Ismael and A. J. Chamkha, Mixed convection in superposed nanofluid and porous layers in square enclosure with inner rotating cylinder, International Journal of Mechanical Sciences 124-125 (2017), 95-108.
[22] A. J. Chamkha, A. S. Dogonchi and D. D. Ganji, Magneto-hydrodynamic flow and heat transfer of a hybrid nanofluid in a rotating system among two surfaces in the presence of thermal radiation and Joule heating, AIP Advances 9(2) (2019), 15 pp. https://doi.org/10.1063/1.5086247.
[23] H. E. Patel, T. Sundararajan and S. K. Das, An experimental investigation into the thermal conductivity enhancement in oxide and metallic nanofluids, Journal of Nanoparticle Research 12 (2010), 1015-1031.
[24] R. Nawaz, L. Zada, F. Ullah, H. Ahmad, M. Ayaz, I. Ahmad and T. A. Nofal, An extension of optimal auxiliary function method to fractional order high dimensional equations, Alexandria Engineering Journal 60(5) (2021), 4809-4818.
[25] A. Mrabti, Numerical simulation of natural convection flows in a cylindrical geometry with a vertical axis subjected to the effect of a magnetic field or a solutal gradient, Ph.D. Dissertation, Department of Physics, University Mohamed V of Rabat, 1999.
[26] M. Sammouda, Theoretical and numerical modeling of the natural and thermosolutal convection in a porous media with variable porosity, Ph.D. Dissertation, Department of Physics, University Mohamed V of Rabat, 2012.
[27] S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, New York, 1980.
[28] A. Bounouar, K. Gueraoui, M. Taibi, A. Lahlou, M. Driouich, M. Sammouda and S. Men-La-Yakhaf, Numerical and mathematical modeling of unsteady heat transfer within a spherical cavity, Applications Laser in Medicine, Contemporary Engineering Sciences 9(24) (2016), 1183-1199.
[29] S. P. Frankel, Convergence rates of iterative treatments of partial differential equations, Math. Tables Aids Comput. 4 (1950), 65-75.