Effect of an External Magnetic Field on the 3-D Unsteady Natural Convection in a Cubical Enclosure (original) (raw)
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Investigation of Magneto Hydrodynamic Natural Convection Flows in a 3-D Rectangular Enclosure
Journal of Applied Fluid Mechanics, 2016
The article deals with magnetic field of free convective flows in cavities similar to those used in artificial growth of single crystals from melts (horizontal Bridgman configurations) and having aspect ratios an equal to "4". The combined effect of wall electrical conductivity and vertical direction of the magnetic field on the buoyancy induced flow of mercury was investigated numerically. The validation of the numerical method was achieved by comparison with both experimental and analytical data found in the literature. The plotted results for variation of velocity, temperature and Nusselt number in terms of the Hartmann number Ha and Rayleigh number "Ra" showed a considerable decrease in convection intensity as the magnetic field is increased, especially for values of "Gr" situated around 10 7. The calculations also showed that the vertically directed magnetic field (perpendicular to the x-z plane) is the most effective in controlling the flow and hence the speed of growth of the crystal. Also, wall electrical conductivity enhances damping by changing the distribution of the induced electric current to one which augments the magnitude of the Lorentz force.
2016
Buoyancy-driven magneto hydrodynamic flow in a liquidmetal filled cubic enclosure is investigated by three dimensional numerical simulations. The enclosure is heated and cooled along two opposite vertical walls, all other walls being adiabatic. A uniform magnetic field is applied orthogonally to the gravity vector and to the temperature gradient (i.e., parallel to the isothermal walls). The Prandtl number is = 0.019 (characteristic of Galium); the Rayleigh number is made to vary from 10 to 10, the Hartmann number between 30 to 120 and the electrical conductance of the walls between 0 and 1. The Navier–Stokes equations, for the electrical potential, are solved by a finite volume method using the CFD package CFX-4 with some necessary adaptations. Steady-state conditions are assumed. In all cases, a three-dimensional flow with complex secondary motions and a complex current pattern is established. The results show that the dynamic and temperature fields are strongly affected by variati...
Natural Convection of Liquid Metals in an Inclined Enclosure in the Presence of a Magnetic Field
The problem of steady, laminar, natural convective flow of electrically-conducting liquid metals such as gallium and germanium in an inclined rectangular enclosure in the presence of a uniform magnetic field is considered. Transverse gradient of heat is applied on two opposing walls of the inclined enclosure while the other two walls are adiabatic. A magnetic field is applied normal to the non-insulated walls. The problem is formulated in terms of the vorticity – stream function procedure. A numerical solution based on the finite-difference method is obtained. Representative results illustrating the effects of the enclosure inclination angle and the Hartmann number for two different Rayleigh numbers on the contour maps of the streamlines and temperature as well as the profiles of velocity components and temperature at mid-section of the enclosure are reported. In addition, results for the average Nusselt number are presented and discussed for various parametric conditions.
Natural Convection in an Enclosure: Effect of Magnetic Field Dependent Thermal Conductivity
In this paper, the natural convection heat transfer process is investigated inside an annular enclosure filled with a magnetic nanofluid (Fe 3 O 4 magnetic nanoparticles dispersed in Kerosene). A uniform magnetic field (H) is applied along the axial direction of the enclosure. Thermal conductivity (k) is considered as a function of magnetic field. A nonlinear relationship between magnetic field and thermal conductivity in the magnetic nanofluid (MNF) is assumed and interpolated. Finite element method is utilized to solve the governing equations and calculate the Nusselt number and it is presented as a function of volume fraction and magnetic field strength. The results show the significant effect of applied magnetic field on heat transfer rate, more specifically on Nu, in the enclosure when higher volume fractions of nanoparticles are used. Thermal conductivity enhancement as a result of using magnetic field can be used for various applications such as thermal energy storage in which the heat transfer needs to be accurately controlled.
Experimental Thermal and Fluid Science, 2006
The effect of an electric current supplied from outside on the natural convection of liquid metal under a uniform magnetic field is studied both experimentally and numerically. A cubic enclosure filled with the liquid metal is heated and cooled from the facing electro-conductive vertical sidewalls while other four walls are thermally and electrically insulated. A horizontal magnetic field is applied parallel to the hot and cold walls. Two electrodes to apply an electric current to the liquid metal are inserted at the center of the hot and cold electro-conductive sidewalls, respectively. With applying the magnetic field only, the natural convection is damped out by the Lorentz force which is the interaction between the induced electric current and the external magnetic field. When both the magnetic field and the additional electric current are applied, the convection pattern and heat transfer rate from the hot wall to the cold wall become different compared to the case of the magnetic field only.
Magneto-natural convection in square cavities with a source-sink pair on different walls
Magnetohydrodynamic natural convection fluid flow and heat transfer in a square enclosure with a pair of source and sink on its walls, filled with liquid Gallium fluid with Prandtl number of 0.02 has been investigated numerically. The heat source and heat sink are maintained at a constant temperature T h and Tc, respectively with T h > Tc. By variation of relative location of the heat source and sink on the walls of the enclosure, five different cases are generated. The governing equations written in terms of the primitive variables are solved numerically using the finite volume method and the SIMPLER algorithm. Using the developed code, a parametric study is performed, and the effects of the Rayleigh number, the Hartman number, and the locations of the source and sink on the fluid flow and heat transfer inside the enclosure are investigated. The results show that the flow and temperature distributions inside the enclosure are affected by the strength of the magnetic field, the Rayleigh number, and the relative location of the heat source and sink. The magnetic field decreases the rate of heat transfer, suppresses the convection heat transfer, and tends to slows down the flow velocity in the cavity. Moreover in some cases the magnetic field changes the flow pattern inside the enclosure.
Magnetic field effects on natural convection flow of a non-Newtonian fluid in an L-shaped enclosure
Journal of Thermal Analysis and Calorimetry, 2018
The effect of magnetic field on natural convection heat transfer in an L-shaped enclosure filled with a non-Newtonian fluid is investigated numerically. The governing equations are solved by finite-volume method using the SIMPLE algorithm. The power-law rheological model is used to characterize the non-Newtonian fluid behavior. It is revealed that heat transfer rate decreases for shear-thinning fluids (of power-law index, n \ 1) and increases for shear-thickening fluids (n [ 1) in comparison with the Newtonian ones. Thermal behavior of shear-thinning and shear-thickening fluids is similar to that of Newtonian fluids for the angle of enclosure a \ 60°and a [ 60°, respectively. Keywords Magnetohydrodynamics (MHD) Á Natural convection Á Newtonian fluid Á Non-Newtonian fluid Á Enclosure List of symbols AR Aspect ratio B o Magnetic induction (T) g Gravitational acceleration (m s-2) Ha Hartmann number K Thermal conductivity (W m-1 K-1) L Specific length (m) n Power-law index Nu Local Nusselt number P Pressure (Pa) Pr Prandtl number Ra Rayleigh number Re Reynolds number T Wall temperature (K) u Velocity in x-direction (m s-1) v Velocity in y-direction (m s-1) U Dimensionless velocity in x-direction V Dimensionless velocity in y-direction x Distance along x-coordinate y Distance along y-coordinate Greek letters b Thermal expansion coefficient (k-1) l Dynamic viscosity (kg m-1 s-1) q Density (kg m-3) h Dimensionless temperature
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IEEE Transactions on Plasma Science, 2000
The buoyancy-driven magnetohydrodynamic flow in a liquid-metal-filled square enclosure is investigated by 2-D numerical simulation. The enclosure is differentially heated at two opposite vertical walls, the horizontal walls being adiabatic, and a uniform magnetic field is applied orthogonal to the gravity vector. To solve the governing nonlinear differential equations (mass, momentum, and energy), a finite-volume code based on Patankar's SIMPLER method is utilized. The results are obtained for a Rayleigh number (Ra) of 5 × 10 6 , with a Prandtl number of 0.0091 (characteristic of Na at 150 • C) and a Hartmann number (Ha) between 100 and 700. The fluid properties are considered as a function of temperature so that the values of these properties at the hot wall are lower than that of the cold wall. It is found that the resistance to fluid motion is stronger near the hot wall and the flow intensity increases in this region. Thus, due to continuity, the form of the streamlines changes, and the symmetry of the isotherms is broken.