zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Magnetic field effect on the unsteady free convection flow in a square cavity filled with a porous medium with a constant heat generation. (English) Zbl 1217.80084
Summary: The effects of an inclined magnetic field and heat generation on unsteady free convection within a square cavity filled with a fluid-saturated porous medium have been investigated numerically. The top and bottom horizontal walls of the enclosure are adiabatic whereas the vertical walls are kept at constant but different temperatures. The physical problems are represented mathematically by a set of partial differential equations along with the corresponding boundary conditions. By using an implicit finite-difference scheme, namely the ADI method (alternative direction implicit), the non-dimensional governing equations are numerically solved. The influential parameters are the Rayleigh number $Ra$, the inclination angle $\gamma $ of the magnetic field relative to the gravity vector g, the Hartmann number $Ha$ and the heat generation parameter $Q$. In the present study, the obtained results are presented in terms of streamlines, isotherms and average Nusselt number along the hot wall. The result shows that with increasing $Ha$, the diffusive heat transfer become prominent even though the Rayleigh number increases.
80A20Heat and mass transfer, heat flow
76R10Free convection (fluid mechanics)
76S05Flows in porous media; filtration; seepage
76W05Magnetohydrodynamics and electrohydrodynamics
80M20Finite difference methods (thermodynamics)
76M20Finite difference methods (fluid mechanics)
Full Text: DOI
[1] Nield, D. A.; Bejan, A.: Convection in porous media, (2006) · Zbl 1256.76004
[2] D.B. Ingham, I. Pop (Eds.), Transport Phenomena in Porous Media, vol. III, Pergamon, Oxford, 2005.
[3] , Handbook of porous media (2005)
[4] Bejan, A.; Dincer, I.; Lorente, S.; Miguel, A. F.; Reis, A. H.: Porous and complex flow structures in modern technologies, (2004)
[5] I. Pop, D.B. Ingham, Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media, Pergamon, Oxford, 2001.
[6] Acharya, S.; Goldstein, R. J.: Natural convection in an externally heated vertical or inclined square box containing internal energy sources, ASME J. Heat transfer 107, 855-866 (1985)
[7] Ozoe, H.; Maruo, E.: Magnetic and gravitational natural convection of melted silicon -- two-dimensional numerical computations for the rate of heat transfer, Japan soc. Mech. eng. 30, 774-784 (1987)
[8] Lee, J. -H.; Goldstein, R. J.: An experimental study on natural convection heat transfer in an inclined square enclosure containing internal energy sources, ASME J. Heat transfer 110, 345-349 (1988)
[9] Fusegi, T.; Hyun, J. M.; Kuwahara, K.: Natural convection in a differentially heated square cavity with internal heat generation, Numer. heat transper part A 21, 215-229 (1992)
[10] 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 mechanica 96, 13-26 (1993) · Zbl 0775.76180 · doi:10.1007/BF01340696
[11] Shim, Y. M.; Hyun, J. M.: Transient confined natural convection with internal heat generation, Int. J. Heat fluid flow 18, 328-333 (1997)
[12] Hossain, M. A.; Wilson, M.: Natural convection flow in a fluid-saturated porous medium enclosed by non-isothermal walls with heat generation, Int. J. Thermal sci. 41, 447-454 (2002)
[13] Hossain, M. 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)
[14] Martynenko, O. G.; Khramtsov, P. P.: Free-convective heat transfer, (2005)
[15] Poulikakos, D.; Bejan, A.: Unsteady natural convection in a porous layer, Phys. fluids 26, 1183-1191 (1983) · Zbl 0513.76082 · doi:10.1063/1.864266
[16] N. Banu, D.A.S. Rees, I. Pop, Steady and unsteady free convection in porous cavities with internal heat generation, in: Heat Transfer 1998, Proceedings of 11th IHTC, vol. 4, pp. 375-380, Kyongju (1998).
[17] Saeid, N. H.; Pop, I.: Transient free convection in a porous cavity filled with a porous medium, Int. J. Heat mass transfer 47, 1917-1924 (2004) · Zbl 1106.76457 · doi:10.1016/j.ijheatmasstransfer.2003.10.014
[18] Pakdee, W.; Rattanadecho, P.: Unsteady effect on natural convective heat transfer through porous media in cavity due to top surface partial convection, Appl. thermal eng. 26, 2316-2326 (2006)
[19] Aldabbagh, L. B. Y.; Manesh, H. F.; Mohamad, A. A.: Unsteady natural convection inside aporous enclosure heated from the side, J. porous media 11, 73-83 (2007)
[20] Kumari, M.; Nath, G.: Unsteady natural convection flow in a square cavity filled with a porous medium due to impulsive change in wall temperature, Transport porous media 77, 463-474 (2009)
[21] Garandet, J. P.; Alboussiere, 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
[22] Alchaar, S.; Vasseur, P.; Bilgen, E.: The effect of a magnetic field on natural convection in a shallow cavity heated from below, Chem. eng. Commun. 134, 195-209 (1995)
[23] Chamkha, A. J.; Al-Naser, H.: Hydromagnetic double-diffusive convection in a rectangular enclosure with uniform side heat and mass fluxes and opposing temperature and concentration gradients, Int. J. Thermal sci. 41, 936-948 (2002) · Zbl 1101.76055
[24] Mahmud, S.; Tasnim, S. H.; Mamun, M. A. H.: Thermodynamic analysis of mixed convection in a channel with transverse hydromagnetic effect, Int. J. Thermal sci. 42, 731-740 (2003)
[25] Hossain, M. A.; Hafiz, M. Z.; Rees, D. A. S.: Buoyancy and thermocapillary driven convection flow of an electrically conducting fluid in an enclosure with heat generation, Int. J. Thermal sci. 44, 676-684 (2005)
[26] 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
[27] Zeng, M.; Wang, Q. W.; Ozoe, H.: Natural convection of diamagnetic fluid in an enclosure filled with porous medium under magnetic field, Prog. comput. Fluid dyn. 9, 77-85 (2009)
[28] Mahdy, A.; Mohamed, R. A.; Hady, F. M.: Influence of magnetic field on natural convection flow near a wavy cone in porous media, Latin am. Appl. res. 38, 155-160 (2008)
[29] Ramambason, D. S. R.; Vasseur, P.: Influence of a magnetic field on natural convection in a shallow porous enclosure saturated with a binary fluid, Acta mechanica 191, 21-35 (2007) · Zbl 1140.76466 · doi:10.1007/s00707-007-0444-x
[30] Postelnicu, A.: Influence of a magnetic field on heat and mass transfer by natural convection from vertical surfaces in porous media considering Sorét and dufour effects, Int. J. Heat mass transfer 47, 1467-1472 (2004) · Zbl 1045.76568 · doi:10.1016/j.ijheatmasstransfer.2003.09.017
[31] Nield, D. A.: Impracticality of MHD convection in a porous medium, Transport porous media 73, 379-380 (2008)
[32] Walker, K. L.; Homsy, G. M.: Convection in a porous cavity, J. fluid mech. 76, 338-363 (1978) · Zbl 0383.76063
[33] Bejan, A.: On the boundary layer regime in a vertical enclosure filled with a porous medium, Lett. heat mass transfer 6, 93-102 (1979)
[34] Beckermann, C.; Viskanta, R.; Ramadhyani, S.: A numerical study of non-darcian natural convection in a vertical enclosure filled with a porous medium, Num. heat transfer 10, 557-570 (1986)
[35] R.J. Gross, M.R. Bear, C.E. Hickox, The application of flux-corrected transport (FCT) to high Rayleigh number natural convection in a porous medium, in: Proc. 7th Int. Heat Transfer Conf., San Francisco, CA, 1986.
[36] D.M. Manole, J.L. Lage, Numerical benchmark results for natural convection in a porous medium cavity, HTD-vol. 216, Heat and Mass Transfer in Porous Media, ASME Conference 1992, pp. 55-60.
[37] Moya, S. L.; Ramos, E.; Sen, M.: Numerical study of natural convection in a tilted rectangular porous material, Int. J. Heat mass transfer 30, 741-756 (1987)
[38] Baytas, A. C.; Pop, I.: Free convection in oblique enclosures filled with a porous medium, Int. J. Heat mass transfer 42, 1047-1057 (1999) · Zbl 0983.76089 · doi:10.1016/S0017-9310(98)00208-7
[39] A-L-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