Numerical study on the effect of magnetic field and discrete heating on free convection in a porous container

Document Type : Article

Authors

1 Mathematical Modelling and Applied Computation Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

2 Department of Mathematics, Kongunadu Polytechnic College, D. Gudalur, Dindigul, Tamilnadu, India

Abstract

A study has been executed numerically on buoyancy induced convection current in a porous container of square shape with the existence of a uniform magnetic flux. The vertical wall situated at the left side is heated with two discrete heaters and the constant temperature is maintained in the right side. There is no thermal transfer in the horizontal walls. This study involves Brinkman Forchheimer-Darcy extended model. The non-dimensional leading equations are evaluated by the finite volume method. The consequences are examined for different values of the porosity, direction of the magnetic flux, Hartmann number, Rayleigh number and Darcy number. The results interpret that the Hartmann number and the average thermal energy transport are disproportionate to each other. Also the averaged heat transfer and the Darcy number are proportionate to each other.

Keywords


References:
1. Walker, K.L. and Homsy, G.M. "Convection in a porous cavity", J. of Fluid Mech., 87(3), pp. 449-474 (1978).
2. Nithiarasu, P., Seetharamu, K.N., and Sundararajan, T. "Natural convective heat transfer in a  fluid saturated variable porosity medium", Int. J. of Heat and Mass Transfer, 40, pp. 3955-3967 (1997).
3. Sankar, M., Bhuvaneswari, M., Sivasankaran, S., et al. "Buoyancy induced convection in a porous cavity with partially thermally active side walls", Int. J. of Heat and Mass Transfer, 54, pp. 5173-5182 (2011).
4. Sivasankaran, S., Do, Y., and Sankar, M. "Effect of discrete heating on natural convection in a rectangular porous enclosure", Transport in Porous Media, 86, pp. 291-311 (2011).
5. Beckermann, C., Ramadhyani, S., and Viskanta, R. "Natural convection  flow and heat transfer between a fluid layer and a porous layer inside a rectangular enclosure", ASME J. of Heat Transfer, 109, pp. 363- 370 (1987).
6. Sivasankaran, S., Malleswaran, A., Bhuvaneswari, M., et al. "Hydro-magnetic mixed convection in a liddriven cavity with partially thermally active walls", Sci. Iran. Trans. Mech. Eng. B, 24(1), pp. 153-163 (2017).
7. Oztop, H.F., Al-Salem, K., Varol, Y., et al. "Natural convection heat transfer in a partially opened cavity filled with porous media", Int. J. of Heat and Mass Transfer, 54, pp. 2253-2261 (2011).
8. Alturaihi, M.H., Jassim, L., Alguboori, A.R., et al. "Porosity influence on natural convection heat transfer from a circular cylinder in a square porous enclosure", J. Mech. Engg. Research and Developments, 43, pp. 236-254 (2020).
9. Zhao, F.Y., Liu, D., and Tang G.F. "Natural convection in a porous enclosure with a partial heating and salting element", Int. J. of Therm. Sci., 47, pp. 569- 583 (2008).
10. Janagi, K., Sivasankaran, S., Bhuvaneswari, M., et al. "Numerical study on free convection of cold water in a square porous cavity heated with sinusoidal wall temperature", Int. J. of Numerical Methods for Heat & Fluid Flow, 27(4), pp. 1000-1014 (2017).
11. Shahzad, F., Sagheer, M., and Hussain, S. "Transport of MHD nanofluid in a stratified medium containing gyrotactic microorganisms due to a stretching sheet", Scientia Iranica: Trans. on Mech. Eng. B, 28(6), pp. 3786-3805 (2022).
12. Sivasankaran, S. and Ho, C.J. "Effect of temperature dependent properties on MHD convection of water near its density maximum in a cavity", Int. J. of Therm. Sci., 47, pp. 1184-1194 (2008).
13. Afsar Khan, A., Batool, R., Kousar, N. "Examining the behavior of MHD micropolar fluid over curved stretching surface based on the modified Fourier law", Scientia Iranica: Trans. on Mech. Eng. B, 28(1), pp. 223-230 (2021).
14. Sivasankaran, S. and Bhuvaneswari, M. "Effect of thermally active zones and direction of magnetic field on hydromagnetic convection in an enclosure", Therm. Sci., 15(2), pp. S367-S382 (2011).
15. Bhuvaneswari, M., Sivasankaran, S. and Kim, Y.J. "Magneto convection in a square enclosure with sinusoidal temperature distributions on both side walls", Numer. Heat Transfer, A, 59, pp. 167-184 (2011).
16. Sivasankaran, S., Malleswaran, A., Lee, J., et al. "Hydro-magnetic combined convection in a lid-driven cavity with sinusoidal boundary conditions on both sidewalls", Int. J. of Heat and Mass Transfer, 54, pp. 512-525 (2011).
17. Colak, E., Oztop, H.F., and Ekici, O. "MHD mixed convection in a chamfered lid-driven cavity with partial heating", Int. J. of Heat and Mass Transfer, 156, 119901 (2020).
18. Mondal, P. and Mahapatra, T.R. "MHD doubledi ffusive mixed convection and entropy generation of nanofluid in a trapezoidal cavity", Int. J. of Mech. Sci., 208, 106665 (2021).
19. Roy, N.C. "MHD natural convection of a hybrid nanofluid in an enclosure with multiple heat sources", Alexandria Engrg. J., 61(2), pp. 1679-1694 (2022).
20. Sivasankaran, S., Anandhan, S.S., and Hakeem, A.A.K. "Mixed convection in a lid-driven cavity with sinusoidal boundary temperature at the bottom wall in the presence of magnetic field", Sci. Iran. Trans. on Mech. Eng. B, 23(3), pp. 1027-1036 (2016).
21. Khan, S.U., Ali, N., Shehzad, S.A., et al. "Analysis of the second-grade fluid flow in a porous channel by Cattaneo-Christov and generalized Fick's theories", Sci. Iran, Trans. on Mech. Eng. B, 27(4), pp. 1945- 1954 (2020).
22. Chamkha, A.J., Mansour, M.A., Rashad, A.M., et al. "Magnetohydrodynamic mixed convection and entropy analysis of nanofluid in gamma-shaped porous cavity", J. of Thermophysics and Heat Transfer, 34(10), pp. 1- 12 (2020).
23. Niranjan, H., Sivashankaran, S., and Bhuvaneswari, M. "Chemical reaction, Soret and Dufour effects on MHD convection stagnation point flow with radiation and slip condition", Sci. Iran, Trans. on Mech. Eng. B., 24(2), pp. 698-706 (2017).
24. Jasim, L.M. "Numerical investigation of the magnetic field effects on natural convection within a porous horizontal cylindrical annulus", J. Porous Media, 24(2), pp. 13-27 (2021).
25. Giwa S.O., Sharifpur, M., Ahmadi, M.H., et al. "A review of magnetic field influence on natural convection heat transfer performance of nanofluids in square cavities", J. of Thermal Anal. and Calorimetry, 145, pp. 2581-2623 (2021).
26. Ghaffarpasand, O. and Fazeli, D. "Numerical analysis of MHD mixed convection flow in a parallelogramic porous enclosure filled with nanofluid and in presence of magnetic field induction", Scientia Iranica: Trans. on Mech. Eng. B, 25(3), pp. 1789-0-180 (2018).
27. Ahmed, S.E. and Rashed, Z.Z. "MHD natural convection in a heat generating porous medium-filled wavy enclosures using Buongiorno's nanofluid model", Case Studies in Thermal Eng., 14, 100430 (2019).
28. Sheikholeslami, M., Ganji, D.D., Li, Z., et al. "Numerical simulation of thermal radiative heat transfer effects on Fe3O4 ethylene glycol nanofluid EHD flow in a porous enclosure", Scientia Iranica: Trans. on Mech. Eng. B, 26(3), pp. 1405-1414 (2019).
29. Beg, O.A., Venkatadri, K., Ramachandra Prasad, V., et al. "Numerical simulation of hydromagnetic Marangoni convection flow in a Darcian porous semiconductor melt enclosure with buoyancy and heat generation effects", Materials Sci. and Engrg: B, 261, 114722 (2020).
30. Ali, F.H., Hamzah, H.K., Hussein, A.K., et al. "MHD mixed convection due to a rotating circular cylinder in a trapezoidal enclosure filled with a nanofluid saturated with a porous media", Int. J. of Mech. Sci., 181(1), 105688 (2020).
31. Shehzad, S.A., Sheikholeslami, M., Ambreen, T., et al. "Convective MHD  flow of hybrid-nanofluid within an elliptic porous enclosure", Physics Letters A, 384(28), 126727 (2020).
32. Al-Farhany, K., Al-Chlaihawi, K.K., Al-dawody, M.F., et al. "Effects of fins on magnetohydrodynamic conjugate natural convection in a nanofluid-saturated porous inclined enclosure", Int. Commun. in Heat and Mass Transfer, 126, 105413 (2021).
33. Dogonchi, A.S., Tayebi, T., Karimi, N., et al. "Thermal-natural convection and entropy production behavior of hybrid nanoliquid flow under the effects of magnetic field through a porous wavy cavity embodies three circular cylinders", J. of the Taiwan Institute of Chemical Engineers, 124, pp. 162-173 (2021).
34. Abderrahmane, A., Hatami, M., Medebber, M.A., et al. "Non-Newtonian nanofluid natural convective heat transfer in an inclined half-annulus porous enclosure using FEM", Alexandria Eng. J., 61(7), pp. 5441-5453 (2022).