Three-dimensional buoyant convection in a rectangular cavity with differentially heated walls in a strong magnetic field

Abstract

Three-dimensional buoyant convection in a rectangular cavity with a horizontal temperature gradient in a strong, uniform magnetic ÿeld is considered. The walls of the cavity are electrically insulating. An asymptotic solution to the problem in the inertialess approximation is obtained for high values of the Hartmann number, Ha. In the presence of either the vertical or the horizontal longitudinal ÿelds, the three-dimensional ow is characterised by high-velocity jets at the walls of the cavity parallel to the magnetic ÿeld. The velocity of the jets is O(Ha) times higher than in the bulk of the uid. On the other hand, in the presence of the horizontal transverse magnetic ÿeld, the velocity in the core is O(Ha) times higher than in the other two cases. However, no jets are present in the parallel layers. The analysis of the convective heat transfer for low values of the Peclet number shows that either the vertical, or the longitudinal ÿeld is the most e cient in damping of the convective heat transfer, depending on the dimensions of the cavity.

Quasi-two-dimensional convection in a three-dimensional laterally heated box in a strong magnetic field normal to main circulation

“…result in significant three-dimensional effects, especially if the so-called parallel layers are involved. Examples of such flows include buoyant convection in a cavity in a vertical and transverse magnetic fields, 4,8,[13][14][15][16][17] flows with Hunt's jets, [18][19][20][21] flows in bends, 22,23 circular ducts in a nonuniform magnetic field, 24,25 etc. In some situations, usually involving a pair of parallel electrically insulating walls transverse to the sufficiently strong magnetic field, the flow becomes quasi-twodimensional ͑Q2D͒.…”

“…26 Models of Q2D flows have been developed for the flow between parallel planes in a uniform magnetic field, 27,28 a nonuniform magnetic field, 29,30 or buoyant convection in a uniform field. 7,8,11,12 More elaborate Q2D models have been developed by Pothérat et al, 31,32 which take into account small but finite Ekman pumping in the Hartmann layers.…”

Effect of a Partition on Hydro-Magnetic Convection in an Enclosure

“…They found that a vertical magnetic field strongly reduces both the integral and local heat transfer coefficients. Aleksandrova and Molokov [1] studied buoyancy-induced convection in a rectangular cavity with a horizontal temperature gradient in a strong uniform magnetic field. They found that the flow pattern differs significantly for different magnetic field orientations.…”

Effect of temperature dependent properties on MHD convection of water near its density maximum in a square cavity

“…Some reports on this can be found in literature [1][2][3][4][5]. The process of manufacturing materials in industrial problems involve an electrically conducting fluid subjected to a magnetic field [6][7][8][9]. The fluid properties like viscosity and thermal conductivity are varying with temperature in nature.…”