Effect of a Magnetic Field on Buoyancy-Driven Convection in Differentially Heated Square Cavity

Abstract

Steady, laminar, natural-convection flow in the presence of a magnetic field in a cavity heated from left and cooled from right is considered. In our formulation of the governing equations, mass, momentum, energy and induction equations are applied to the cavity. To solve the governing differential equations a finite volume code based on PATANKAR's SIMPLER method is utilized. Numerical predictions are obtained for a wide range of Rayleigh number (Ra) and Hartmann number (Ha) at the Prandtl number Pr = 0 733. When the magnetic field is relatively strengthened, the thermal field resembles that of a conductive distribution, and the fluid in much of the interior is nearly stagnant. Further, when the magnetic field is weak and the Rayleigh number is high, the convection is dominant and vertical temperature stratification is predominant in the core region. However, for sufficiently large Ha, the convection is suppressed and the temperature stratification in the core region diminishes. The numerical results show that the effect of the magnetic field is to decrease the rate of convective heat transfer and the average Nusselt number decreases as Hartmann number increases. The results are presented for Rayleigh number from 10 4 up to 10 6 and are in form of streamlines, isotherms, and Nusselt number for various Rayleigh and Hartman numbers.

Mixed Convection in Lid-Driven Cavity with Inclined Magnetic Field

“…Then, two-dimensional unsteady simulation of MHD natural convection in a laterally and volumetrically heated square enclosure filled with liquid-metal was examined by Sarris et al (2005). Different thermal boundary conditions with the existence of magnetic field on natural convection are discussed by Oztop et al (2009) and Pirmohammadi et al (2009). Ishak (2011) studied the effect of radiation on magnetohydrodynamic (MHD) boundary layer flow of a viscous fluid over an exponentially stretching sheet.…”

Effect of Magnetic Field on Mixed Convection Heat Transfer in a Lid-Driven Square Cavity

“…Then, [14] investigated the significance of transverse magnetic field in tilted enclosure numerically. Different thermal boundary conditions with the existence of magnetic field on natural convection are discussed by [15,16]. Recently, [17][18][19] investigated natural convection heat transfer and fluid flow in a cavity filled with nanofluid using the Lattice Boltzmann method.…”

Numerical simulation of thermomagnetic convection of air in a porous square enclosure under a magnetic quadrupole field using LTNE models

“…Magnetic field effect on the heat transfer and fluid flow has received much attention in recent years due to its importance in electronic packaging, purification of molten metals, crystal growth in liquids and many others [8][9][10][11]. Saleh et al [12] analyzed the effect of a magnetic field on steady convection in a trapezoidal enclosure filled with a fluid-saturated porous medium by the finite difference method.…”