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Magnetic field and internal heat generation effects on the free convection in a rectangular cavity filled with a porous medium. (English) Zbl 1157.80332
Summary: A numerical investigation of the steady magnetohydrodynamics free convection in a rectangular cavity filled with a fluid-saturated porous medium and with internal heat generation has been performed. A uniform magnetic field, inclined at an angle $\gamma $ with respect to the horizontal plane, is externally imposed. The values of the governing parameters are the inclined angle $\gamma = 0, \pi /6, \pi /4$ and $\pi /2$, Hartmann number $Ha = 0, 1, 5$, 10 and 50, Rayleigh number $Ra = 10, 100, 10^{3}$ and $10^{5}$, and the aspect ratio $a = 0.01$, 0.2, 0.5 and 1 (square cavity). It is shown that the intensity of the core convection is considerably affected by the considered parameters. It is also found that the local Nusselt number $Nu_Y$ decreases on the bottom wall as $\gamma $ increases (magnetic field changes its direction from the horizontal to the vertical direction) and vice versa for the top wall of the cavity. The reported results are in good agreement with the available published work in the literature.

80A20Heat and mass transfer, heat flow
76W05Magnetohydrodynamics and electrohydrodynamics
76S05Flows in porous media; filtration; seepage
76R10Free convection (fluid mechanics)
76M20Finite difference methods (fluid mechanics)
80M20Finite difference methods (thermodynamics)
Full Text: DOI
[1] Nield, D. A.; Bejan, A.: Convection in porous media, (2006) · Zbl 1256.76004
[2] , Transport phenomena in porous media (2005)
[3] , Handbook of porous media (2005)
[4] Bejan, A.; Dincer, I.; Lorente, S.; Miguel, A. F.; Reis, A. H.: Porous and complex flows structures in modern technologies, (2004)
[5] Pop, I.; Ingham, D. B.: Convective heat transfer: mathematical and computational modelling of viscous fluids and porous media, (2001)
[6] De Lemos, M. J. S.: Turbulence in porous media: modeling and applications, (2006)
[7] , Emerging topics in heat and mass transfer in porous media (2008)
[8] Martynenko, O.; Khramtsov, P.: Free-convective heat transfer, (2005)
[9] Acharya, S.; Golstein, R. J.: Natural convection in an externally heated vertical or inclined square box containing internal energy sources, J. heat transfer 107, 855-866 (1985)
[10] Ozoe, H.; Okada, K.: The effect of the direction of the external magnetic field on the three-dimensional natural convection in cubical enclosure, Int. J. Heat mass transfer 32, 1939-1954 (1989) · Zbl 0682.76073 · doi:10.1016/0017-9310(89)90163-4
[11] Lee, J. -H.; Goldstein, R. J.: An experimental study on natural convection heat transfer in an inclined square enclosure containing internal energy sources, J. heat transfer 110, 345-349 (1988)
[12] Fusegi, T.; Hyun, J. M.; Kuwahara, K.: Natural convection in a differentially heated square cavity with internal heat generation, Numer. heat transfer A 21, 215-229 (1992)
[13] Venkatachalappa, M.; Subbaraya, C. K.: Natural convection in a rectangular enclosure in the presence of a magnetic field with uniform heat flux from the side walls, Acta mech. 96, 13-26 (1993) · Zbl 0775.76180 · doi:10.1007/BF01340696
[14] Shim, Y. M.; Hyun, J. M.: Transient confined natural convection with internal heat generation, Int. J. Heat fluid flow 18, 328-333 (1997)
[15] Hossain, M. A.; Wilson, M.: Natural convection flow in a fluid-saturated porous medium enclosed by non-isothermal walls with heat generation, Int. J. Therm. sci. 41, 447-454 (2002)
[16] Garandet, J. P.; Albussoiere, T.; Moreau, R.: Buoyancy driven convection in a rectangular enclosure with a transverse magnetic field, Int. J. Heat mass transfer 35, 741-748 (1992) · Zbl 0753.76194 · doi:10.1016/0017-9310(92)90242-K
[17] Alchaar, S.; Vasseur, P.; Bilgen, E.: Natural convection heat transfer in a rectangular enclosure with a transverse magnetic field, J. heat transfer 117, 668-673 (1995)
[18] Kanafer, K.; Chamkha, A. J.: Hydromagnetic natural convection from an inclined porous square enclosure with heat generation, Numer. heat transfer A 33, 891-910 (1998)
[19] Chamkha, A. J.; Al-Naser, H.: Double-diffusive convection in an inclined porous enclosure with opposing temperature and concentration gradients, Int. J. Therm. sci. 40, 227-244 (2001)
[20] Mahmud, S.; Tasnim, S. H.; Mamun, M. A. H.: Thermodynamic analysis of mixed convection in a channel with transverse hydromagnetic effect, Int. J. Therm. sci. 42, 731-740 (2003)
[21] Hossain, Md.A.; Rees, D. A. S.: Natural convection flow of water near its density maximum in a rectangular enclosure having isothermal walls with heat generation, Heat mass transfer 41, 367-374 (2005)
[22] Hossain, M. A.; Hafiz, M. Z.; Rees, D. A. S.: Buoyancy and thermo capillary driven convection flow of an electrically conducting fluid in an enclosure with heat generation, Int. J. Therm. sci. 44, 676-684 (2005)
[23] Ece, M. C.; Büyük, E.: Natural-convection flow under a magnetic field in an inclined rectangular enclosure heated and cooled on adjacent walls, Fluid dyn. Res. 38, 564-590 (2006) · Zbl 1178.76322 · doi:10.1016/j.fluiddyn.2006.04.002
[24] Nield, D. A.: Impracticality of MHD convection in a porous medium, Transport porous med. 73, 379-380 (2008)
[25] Barletta, A.; Lazzari, S.; Magayri, E.; Pop, I.: Mixed convection with heating effect in a vertical porous annulus with a radially varying magnetic field, Int. J. Heat mass transfer 51, No. 25 -- 26, 5777-5784 (2008) · Zbl 1153.80310 · doi:10.1016/j.ijheatmasstransfer.2008.05.018
[26] Smith, G. D.: Numerical solution of partial differential equations: finite difference method, Numerical solution of partial differential equations: finite difference method (2004)
[27] Haajizadeh, M.; Ozguc, A. F.; Tien, C. L.: Natural convection in a vertical porous enclosure with internal heat generation, Int. J. Heat mass transfer 27, 1893-1902 (1984) · Zbl 0553.76078 · doi:10.1016/0017-9310(84)90171-6
[28] Al-Najem, N. M.; Khanafer, K. M.; El-Refaee, M. M.: Numerical study of laminar natural convection in tilted enclosure with transverse magnetic field, Int. J. Numer. methods heat fluid flow 8, 651-672 (1998) · Zbl 0962.76580 · doi:10.1108/09615539810226094
[29] Mandar, V. J.; Gaitonde, U. N.; Sushanta, K. M.: Analytical study of natural convection in a cavity with volumetric heat generation, J. heat transfer 128, 176-182 (2006)