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Evanescent Magnetic Field Effect on Transient State of Natural Convection


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Abstract


This paper numerically investigates the effect of an externally evanescent magnetic field on flow patterns and heat transfer of fluid in a square cavity. The horizontal walls of the enclosure are assumed to be insulated while the vertical walls are kept isothermal. A control volume finite element method is used to solve the conservation equations. The effect of constant Hartmann number on Nusselt number was studied. Validation tests with existing data demonstrate the aptitude of the present method to produce accurate results. The effects of inclination magnetic field angle from 0° to 90° on streamlines distributions are shown for different value of Hartmann number. For Grashof number equal to 10^5, the values of relaxation time of the magnetic field are chosen, so that the Lorentz force acts only during the startup transient of the natural convection flow. The Nusselt number was calculated for different values of the inverse relaxation time varying from 0 to +∞. The magnitude and the number of oscillations of the Nusselt number were observed. It has been found that no oscillation was seen at relaxation time equal to 20. Stream lines maps are plotted for different values of dimensionless time. The effect of relaxation time on the transition from single-cell to double-cell configuration was observed.
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Keywords


Cavity; Convection; Heat Transfer; Magnetic Field; Finite Element Method

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References


G. M. Oreper, J. Szekely, The effect of an externally imposed magnetic field on bouyancy driven flow in a rectangular cavity, Journal of Crystal Growth, (64) (1983) 505-515.
http://dx.doi.org/10.1016/0022-0248(83)90335-4

I. L. Ozoe, M. Maruo, Magnetic and gravitational natural convection of melted silicon two dimensional numerical computations for the rate of heat transfer, JSME, (30) (1987) 774-7784.
http://dx.doi.org/10.1299/jsme1987.30.774

H. Ozoe, K. Okada, The effect of the direction of the external magnetic field on the three-dimensional natural convection in a cubical enclosure, Int. J Heat Mass Transfer, (32) No. 10 (1989) 1939-1954.
http://dx.doi.org/10.1016/0017-9310(89)90163-4

N. I. Wakayama, Behavior of flow under gradient magnetic fields, Journal Appli. Phys., (69) No.4 (1992) 2734-3736.
http://dx.doi.org/10.1063/1.348629

N. I. Wakayama, Effect of a decreasing magnetic field on the flow nitrogen gas, Chem. Phys. Lett., 185 (5-6) (1991).449-491.
http://dx.doi.org/10.1016/0009-2614(91)80240-x

N. I. Wakayama, B. Bai, A. Tabe, J. Qi, Quantitative analysis of air convection caused by magnetic field coupling, AIAA J., 37 (12) (1999) 1538-1543.
http://dx.doi.org/10.2514/2.652

J.P. Garandet, T. Alboussiere, R. Moreau, Bouyancy drive convection in a rectangular enclosure with a transverse magnetic field, Int. J. Heat Mass Transfer, (35) No. 4 (1992) 741-748.
http://dx.doi.org/10.1016/0017-9310(92)90242-k

N. Rudraiah, R.M. Barron, M. Venkatachalappa, C.K. Subbaraya, Effect of a magnetic field on free convection in a rectangular enclosure, Int. J. Engng Sci., (33) No. 8 (1995) 1075-1084.
http://dx.doi.org/10.1016/0020-7225(94)00120-9

S. Alchaar, P. Vasseur, E. Bilgen, Natural convection heat transfer in a rectangular enclosure with a transverse magnetic field, ASME Journal Heat Transfer, (117) (1995) 668-73.
http://dx.doi.org/10.1115/1.2822628

S. Al Chaar, P. Vasseur, E. Bilgen, The effect of a magnetic field on natural convection in a shallow cavity heated from below, Chem. Eng Comm., (134) (1995) 195-209.
http://dx.doi.org/10.1080/00986449508936332

P. Vasseur, M. Hasnaoui, E. Bilgen, L. Robillard, Natural convection in an inclined fluid layer with a transverse magnetic field: analogy with a porous medium, ASME Journal of Heat Transfer, (117) (1995) 121-129.
http://dx.doi.org/10.1115/1.2822290

N.M. Al-Najem, K.M. Khanafer, M.M. EL-Refaee, Numerical study of laminar convection in tilted enclosure with transverse magnetic field, International Journal of Numerical Methods for Heat and Fluid Flow, (8) N°5/6 (1998) 651-673.
http://dx.doi.org/10.1108/09615539810226094

Y. Lijum, R. Jianxun, S.Yaozu, G.Zengyuan, Free convection of a gas induced by a magnetic quadrupole field, Journal of Magnetism and Magnetic Materials, 261 (2003) 377-384.
http://dx.doi.org/10.1016/s0304-8853(02)01487-7

M. A. Hassain, M. Z. Hafiz, D. A. S. Rees, Buoycancy and thermocapillary driven convection flow of an electrically conducting fluid in a enclosure with heat generation, International Journal of Thermal Sciences, 44 (2005) 676-684.
http://dx.doi.org/10.1016/j.ijthermalsci.2004.11.005

M. Cem Ece, E. Büyük, Natural convection flow under a magnetic field in a inclined rectangular enclosure heated and cooled on adjacent walls, Fluid Dynamics Research, 38 (2006) 564-590.
http://dx.doi.org/10.1016/j.fluiddyn.2006.04.002

R. C. Chaudhary, A. Jain, Magnetohydrodynamic transient convection flow past a vertical surface embedded in a porous medium with oscillating temperature, Turkish J. Eng. Env. Sci. 32 (2008) 13-22.

M. A. Teamah, Numerical simulation of double diffusive natural convection in rectangular enclosure in the presences of magnetic field and heat source, Int. J. of Thermal Sciences 47 (2008) 237-248.
http://dx.doi.org/10.1016/j.ijthermalsci.2007.02.003

A. Ishak, R. Nazar, I. Pop, Magnetohydrodynamic (MHD) flow and heat transfer due to a stretching cylinder, Energy Conversion and Management 49 (2008) 3265-3269.
http://dx.doi.org/10.1016/j.enconman.2007.11.013

L. C. Woods, The thermodynamics of fluid systems, Oxford University press, Oxford, 1975.
http://dx.doi.org/10.1017/s0022112077211153

H. J. Saabas, B. R. Baliga, Co-located equal-order control-volume finite-element method for multidimensional, incompressible fluid flow, Part I: Formulation, Numerical Heat Transfer Part B 26 (1994) 381-407.
http://dx.doi.org/10.1080/10407799408914936

H. J. Saabas, B. R. Baliga, Co-located equal-order control-volume finite-element method for multidimensional, incompressible fluid flow, Part II: Verification, Numerical Heat Transfer Part B 26 (1994) 409-424.
http://dx.doi.org/10.1080/10407799408914937

C. Prakash, An improved control volume finite-element method for heat and mass transfer, and for fluid flow using equal order velocity-pressure interpolation, Numerical Heat Transfer 9 (1986) 253-276.
http://dx.doi.org/10.1080/10407788608913477

N. A. Hookey, A CVFEM for two-dimensional viscous compressible fluid flow, Ph.D. thesis, McGill University, Montreal, Quebec, 1989.

D. Elkaim, M. Reggio, R. Camarero, Numerical solution of reactive laminar flow by a control-volume based finite-element method and the vorticity-stream function formulation, Numerical Heat Transfer 20 (part B) (1991) 223-240.
http://dx.doi.org/10.1080/10407799108945003

H. Abbassi, S. Turki, S. Ben Nasrallah, Mixed convection in a plane channel with a built-in triangular prism, Numerical Heat Transfer 39 (Part A) (3) (2001) 307-320.
http://dx.doi.org/10.1080/104077801300006607

M. Magherbi, A. El Jery, A. Ben Brahim, Magnetic field effects on the flow patters and the entropy generation of natural convection in square cavity, JP Journal of Heat and Mass Transfer, 3 (2) (2009) 147-166.
http://dx.doi.org/10.1615/ichmt.2009.conv.620

G. N. Ivey, Experiments on transient natural convection in a cavity, Journal of Fluid Mechanics 144 (1984) 389-401.
http://dx.doi.org/10.1017/s0022112084001658

S. G. Schladow, Oscillatory motion in aside-heated cavity, Journal of Fluid Mechanics 213 (1990) 589-610.
http://dx.doi.org/10.1017/s0022112090002464


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