Effect of Magnetic Field on Free Convection in Inclined Cylindrical Annulus Containing Molten Potassium (original) (raw)
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Energies, 2020
Natural convection of liquid metal in an annular enclosure under the influence of azimuthal static magnetic field was numerically studied. The liquid metal in the enclosure whose cross-sectional area is square was heated from an inner vertical wall and cooled from an outer vertical wall both isothermally whereas the other two horizontal walls were assumed to be adiabatic. The static azimuthal magnetic field was imposed by a long straight electric coil that was located at the central axis of the annular enclosure. The computations were carried out for the Prandtl number 0.025, the Rayleigh number 104, 5 × 105 and 107, and the Hartmann number 0–100,000 by using an in-house code. It was found that the contour map of the electric potential was similar to that of the Stokes stream function of the velocity regardless of the Hartmann number. Likewise, the contour map of the pressure was similar to the Stokes stream function of the electric current density in the case of the high Hartmann n...
Magneto-thermal-convection stability in an inclined cylindrical annulus filled with a molten metal
International Journal of Numerical Methods for Heat & Fluid Flow, 2020
Purpose-Metal-cooled reactors generally use molten metals such as sodium, potassium or a combination of sodium and potassium because of their excellent heat transfer properties so that the reactor can operate at much lower pressures and higher temperatures. The purpose of this paper is to investigate the stability of natural convection in an inclined ring filled with molten potassium under the influence of a radial magnetism. Design/methodology/approach-A numerical simulation of electrically conductive fluid natural convection stability is performed on an inclined cylindrical annulus under the influence of a radial magnetism. The upper and lower walls are adiabatic, while the internal and external cylinders are kept at even temperatures. The equations governing this fluid system are solved numerically using finite volume method. The SIMPLER algorithm is used for pressure-speed coupling in the momentum equation. Findings-Numerical results for various effective parameters that solve the problem in the initial oscillatory state are discussed in terms of isobars, isotherms and flow lines in the annulus for a wide range of Hartmann numbers (0 # Ha # 80), inclination angles (0 # g # 90°) and radii ratios l # 6. The dependency stability diagrams between complicated situations with the critical value of the Rayleigh number RaCr and the corresponding frequency FrCr are established on the basis of the numeric data of this investigation. The angle of inclination and the radii ratio of the annulus have a significant effect on the stabilization of the magneto-convective flux and show that the best stabilization of the natural oscillatory convection is obtained by the intensity of the strongest magnetic field, the high radii ratio and inclination of the annulus at g = 30°.
International Journal of Heat and Fluid Flow, 2011
The main objective of this article is to study the effect of magnetic field on the combined buoyancy and surface tension driven convection in a cylindrical annular enclosure. In this study, the top surface of the annulus is assumed to be free, and the bottom wall is insulated, whereas the inner and the outer cylindrical walls are kept at hot and cold temperatures respectively. The governing equations of the flow system are numerically solved using an implicit finite difference technique. The numerical results for various governing parameters of the problem are discussed in terms of the streamlines, isotherms, Nusselt number and velocity profiles in the annuli. Our results reveal that, in tall cavities, the axial magnetic field suppresses the surface tension flow more effectively than the radial magnetic field, whereas, the radial magnetic field is found to be better for suppressing the buoyancy driven flow compared to axial magnetic field. However, the axial magnetic field is found to be effective in suppressing both the flows in shallow cavities. From the results, we also found that the surface tension effect is predominant in shallow cavities compared to the square and tall annulus. Further, the heat transfer rate increases with radii ratio, but decreases with the Hartmann number.
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.
ScienceDirect, 2017
Presets work aims to investigate the natural convection inside a cylindrical annulus mold containing molten gallium under a horizontal magnetic field in three-dimensional coordinates. The modeling system is a vertical cylindrical annulus which is made by two co-axial cylinders of internal and external radii. The internal and external walls are maintained isothermal but in different temperatures. The upper and lower sides of annulus are also considered adiabatic while it is filled by an electrical conducting fluid. Three dimensional cylindrical coordinates as r θ z (, ,) are used to respond the velocity components as u v w (, ,). The governing equations are steady, laminar and Newtonian using the Boussinesq approximation. Equations are nonlinear and they must be corresponded by applying the finite volume approach; so that the hybrid-scheme is applied to discretize equations. The results imply that magnetic field existence leads to generate the Lorentz force in opposite direction of the buoyancy forces. Moreover the Lorentz force and its corresponded electric field are more significant in both Hartmann layer and Roberts layer, respectively. The strong magnetic field is required to achieve better quality products in the casting process of a liquid metal with a higher Prandtl number.
2017
In this study the effect of magnetic Reynolds number variation on magnetic distribution of natural convection heat transfer in an enclosure is numerically investigated. The geometry is a two dimensional enclosure which the left wall is hot, the right wall is cold and the top and bottom walls are adiabatic. Fluid is molten sodium with Pr=0.01 and natural convection heat transfer for Rayleigh number, Ra=105 , and magnetic Reynolds numbers 10-1, 10-3 and 10-5 are considered and the governing equations including continuum, momentum, energy and magnetic induction are solved together concurrent. The numerical method finite volume and simpler algorithm for coupling the velocity and pressure is used. The results show for high magnetic Reynolds number the non-dimensional magnetic field in X and Y directions approximately are constant because diffusion of magnetic Reynolds number is more than advection but as magnetic Reynolds number increases the magnetic field in enclosure is not equal to a...
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.
Effect of magnetic field on the heat and mass transfer in a rotating horizontal annulus
This paper presents the effect of an axial magnetic field imposed on incompressible flow of electrically conductive fluid between two horizontal coaxial cylinders. The imposed magnetic field is assumed uniform and constant, we also take into account the effect of heat generation due to viscous dissipation for some cases. The inner and outer cylinders are maintained at different and uniform temperatures and concentrations. The movement of the fluid is due to the rotation of the cylinders with a constant speed. An exact solution of the governing equations for momentum and energy are obtained in the form of Bessel functions. A finite difference implicit scheme was used in the numerical solution to solve the governing equations of convection flow and mass transfer. The concentration and temperature distributions were obtained with and without the magnetic field. The results show that for different values of the Hartmann number, the concentration between the two cylinders decreases as the Hartmann number increases. Also, it is found that by increasing the Hartmann number, the local Nusselt and Sherwood numbers decreases.
Effect of an axial magnetic field on the heat and mass transfer in rotating annulus
International Journal of Physical Sciences, 2014
This study is interested in the effect of an axial magnetic field imposed on incompressible flow of electrically conductive fluid between two horizontal coaxial cylinders. The imposed magnetic field is assumed uniform and constant. The effect of heat generation due to viscous dissipation is also taken into account. The inner and outer cylinders are maintained at different uniform temperatures and concentrations. The movement of the fluid is due to rotation of the cylinder with a constant speed. An exact solution of the governing equations for momentum and energy are obtained in the form of Bessel functions. A finite difference implicit scheme was used in the numerical solution to solve the governing equations of convection flow and mass transfer. The velocity, concentration and temperature distributions were obtained with and without the magnetic field. The results show that for different values of the Hartmann number, the velocity and concentration between the two cylinders decreases as the Hartmann number increases. On the other hand, the Hartmann number does not affect the temperature. Also, it is found that by increasing the Hartmann number, the Nusselt and Sherwood numbers decreases.
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