Showing papers on "Hartmann number published in 1995"

Natural Convection Heat Transfer in a Rectangular Enclosure With a Transverse Magnetic Field

Abstract: The effect of a transverse magnetic field on buoyancy-driven convection in a shallow rectangular cavity is numerically investigated (horizontal Bridgman configuration). The enclosure is insulated on the top and bottom walls while it is heated from one side and cooled from the other. Both cases of a cavity with all rigid boundaries and a cavity with a free upper surface are considered. The study covers the range of the Rayleigh number, Ra, from 10 2 to 10 5 , the Hartmann number, Ha, from 0 to 10 2 , the Prandtl number, Pr, from 0.005 to 1 and aspect ratio of the cavity, A, from 1 to 6. Comparison is made with an existing analytical solution (Garandet et al.), based on a parallel flow approximation, and its range of validity is delineated. Results are presented for the velocity and temperature profiles and heat transfer in terms of Ha number. At high Hartmann numbers, both analytical and numerical analyses reveal that the velocity gradient in the core is constant outside the two Hartmann layers at the vicinity of the walls normal to the magnetic field.

Combined surface tension and buoyancy-driven convection in a rectangular open cavity in the presence of a magnetic field

Abstract: A numerical study is conducted to understand the effect of magnetic field on the flow driven by the combined mechanism of buoyancy and thermocapillarity in a rectangular open cavity filled with a low Prandtl number fluid (Pr = 0.054). The two side walls are maintained at uniform but different temperatures θh and θc (θh > θc), while the horizontal top and bottom walls are adiabatic. A finite difference scheme consisting of the ADI (Alternating Direction Implicit) method, which incorporates upwind differencing for non-linear convective terms and the SLOR (Successive Line Over Relaxation) method are used to solve the coupled non-linear governing equations. Computations are carried out for a wide range of Grashof number Gr ranging from 2 × 104 to 2 × 106, Marangoni number Ma from 0 to 105 and Hartmann number Ha from 0 to 100. The detailed flow structure and the associated heat transfer characteristics inside the cavity are presented. At large Ma, two counter-rotating cells are formed at the upper half and lower half of the enclosure. As Ha increases, the temperature field resembles that of a conduction type and the streamlines are elongated in nature in the horizontal direction. The upper cell is crowded and stretched along the free surface. The average Nusselt number increases with Ma but decreases with Ha.

Natural Convection in an Inclined Fluid Layer With a Transverse Magnetic Field: Analogy With a Porous Medium

Abstract: In this paper the effect of a transverse magnetic field on buoyancy-driven convection in an inclined two-dimensional cavity is studied analytically and numerically. A constant heat flux is applied for heating and cooling the two opposing walls while the other two walls are insulated. The governing equations are solved analytically, in the limit of a thin layer, using a parallel flow approximation and an integral form of the energy equation. Solutions for the flow fields, temperature distributions, and Nusselt numbers are obtained explicitly in terms of the Rayleigh and Hartmann numbers and the angle of inclination of the cavity. In the high Hartmann number limit it is demonstrated that the resulting solution is equivalent to that obtained for a porous layer on the basis of Darcy's model. In the low Hartmann number limit the solution for a fluid layer in the absence of a magnetic force is recovered. In the case of a horizontal layer heated from below the critical Rayleigh number for the onset of convection is derived in term of the Hartmann number. A good agreement is found between the analytical predictions and the numerical simulation of the full governing equations. 23 refs., 8 figs.

Hydromagnetic natural convection in a tilted rectangular porous enclosure

Abstract: A study is made of natural convection within an inclined porous layer saturated by an electrically conducting fluid in the presence of a magnetic field. The long side walls of the cavity are maintained at a uniform heat flux condition, while the short side walls are thermally insulated. On the basis of a parallel flow model, the problem is solved analytically to obtain a set of closed-form solutions. Scale analysis is applied to the case of a boundary layer flow regime in a vertical enclosure. Comparison between the fully numerical and analytical solutions is presented for 0 ≤, Ra ≤, 103 ≤, Ha ≤, 10, and -180 ° ≤, Φ ≤, 180°, where Ra, Ha, and Φ denote the Rayleigh number, Hartmann number, and inclination of the enclosure, respectively. It is found that the analytical solutions can faithfully predict the influence of a magnetic field on the flow structure and heat transfer for a wide range of the governing parameters. For a boundary layer flow regime in a vertical cavity the results of the scale analysis a...

Liquid‐metal buoyant convection in a vertical cylinder with a strong vertical magnetic field and with a nonaxisymmetric temperature

Abstract: In this paper the buoyant convection of a liquid metal in a circular cylinder with a vertical axis and with electrically insulating walls is treated. There is an externally applied, uniform, vertical magnetic field. A nonaxisymmetric heat flux at the vertical wall of the cylinder produces a nonaxisymmetric temperature, which drives a nonaxisymmetric liquid motion. The magnetic field is sufficiently strong that inertial effects and convective heat transfer can be neglected. For large values of the Hartmann number Ha, the liquid region is divided into an inviscid core, Hartmann layers with an O(Ha−1) dimensionless thickness adjacent to the horizontal top and bottom walls, and a side layer with an O(Ha−1/2) dimensionless thickness adjacent to the vertical wall. The characteristic velocity is chosen as the magnitude of the core velocity for an axisymmetric temperature. For an axisymmetric temperature, the core velocity is O(1), and the flow circuit is completed by an O(Ha1/2) vertical velocity inside the side layer. A nonaxisymmetric temperature drives much larger, O(Ha) azimuthal and vertical velocities inside the side layer. This high‐velocity side layer produces an O(Ha1/2) velocity across the core. Perfect axisymmetry is a special case for which a vertical magnetic field strongly suppresses buoyant convection. With a deviation from axisymmetry, electromagnetic suppression of buoyant convection is weaker: there are strong jets adjacent to the vertical wall and a strong flow across the core.

Heat transfer characteristics of rectangular coolant channels with various aspect ratios in the plasma-facing components under fully developed MHD laminar flow

Abstract: Convective heat transfer in MHD laminar flow through rectangular channels in the plasma-facing components of a fusion reactor has been analyzed numerically to investigate the effects of channel aspect ratio, defined as the ratio of the lengths of the plasma-facing side to the other side. The adverse effect of the nonuniformity of surface heat flux on Nusselt number (Nu) at the plasma-facing side can be alleviated by increasing the aspect ratio of a rectangular duct. At the center and corner of the plasma-facing side of a square duct, the Nu of non-MHD flow are 6.8 and 2.2, respectively, for uniform surface heat flux. In the presence of a strong magnetic field, Nu at the center and corner increases to 22 and 3.6, respectively. However, when the heat flux is highly nonuniform, as in the plasma-facing components, Nu decreases from 22 to 3.1 at the center and from 3.6 to 3.1 at the corner. When the aspect ratio is increased to 4, Nu at the center and corner increase to 5 and 4.7. Along the circumference of a rectangular channel, there are locations where the wall temperature is equal to or less than the bulk coolant temperature, thus making the Nu with conventional definition infinity or negative. The ratio between Nu of MHD flow and Nu of non-MHD flow for various aspect ratios is constant in the region of Hartmann number of more than 200 at least. On the other hand, its ratio increases monotonously with increasing the aspect ratio.

Magnetohydrodynamic turbulence with net currents

Abstract: Recent work concerning magnetohydrodynamic (MHD) turbulence with net electric currents is reviewed. Most of the problems considered derive from those encountered in toroidal confinement devices. In the presence of net currents and externally imposed dc magnetic fields, the standard symmetries of “homogeneous turbulence” theory do not apply, and spatially periodic boundary conditions may not be invoked. The turbulence which results tends to be less than fully developed, and its properties are not controlled by Reynolds-like numbers alone. Its description requires occasional departures from the strict MHD framework. Recognizable structures are plentiful in unstable regimes, and include paired helical vortices and helical distortions of the current channel; these may be “large scale” or “small scale”, depending upon the value of the on-axis Hartmann number at which the pinch ratio is raised above its critical value. Plasma rotation, due to departures from strict charge neutrality, may be used to suppress this MHD activity. Unsolved problems in microscopic plasma kinetic theory add uncertainty to the macroscopic MHD predictions, particularly in connection with the viscous stress tensor.

Magnetohydrodynamic flow through a right-angel bend

Abstract: Magnetohydrodynamic (MHD) flow through a 90{degrees} bend, in which the flow is turned from the direction perpendicular to magnetic field lines into a direction aligned with the field, is characterized by strong three-dimensional effects leading to additional pressure drop and large deformations in the velocity distribution. Since such bends are basic elements of a fusion reactor blanket, the question whether the additional pressure drop exceeds unacceptable limits or whether the change in flow distribution may lead to unfavorable heat transfer conditions as to be answered. To investigate MHD flows in a right angle bend, several experiments have been performed in a wide range of the relevant parameters. In the lower range of the interaction parameter N (N {much_lt} 10{sup 4}) the total pressure drop over the whole bend shows a pronounced N-dependence but only a weak dependence on the Hartmann number M. Both effects can be combined to a pressure drop correlation. At higher values of N and M the experimental results for pressure drop and potential distribution agree rather well with theoretical ones obtained on the basis of an asymptotic approach for high N and M. It can be shown theoretically and confirmed by the experiment that, even atmore » high N and M the additional pressure drop in a right angle bend is not excessively high. For the investigated bend with conducting channel walls the predicted flow distribution does not show any stagnant zone at the high heat flux walls in the perfectly aligned part of the duct. This result, however, could not be checked experimentally because there is still no reliable velocity measurement technique available for field-aligned flows.« less