The Effect of a Magnetic Field on the Melting of Gallium in a Rectangular Cavity (original) (raw)
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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.
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.
Journal of Thermal Engineering, 2021
In the present numerical study, the effect of an external horizontal magnetic field on the natural convection of an electrically conducting molten metal (gallium) inside a vertical cylindrical crucible has been investigated. The effect of the external magnetic field is evaluated on the flow pattern and also the temperature field of molten gallium in the mold with an aspect ratio of A=1.0 and a radii ratio of λ=3.0. A series of simulations are carried out for Hartmann numbers of 0, 22.5, 112, and 167 and Rayleigh numbers of 104, 105, and 106. The obtained results show that for a given Rayleigh number, increasing the Hartmann number suppresses convection flows in all directions with different intensities. Moreover, it was found that the employed horizontal magnetic field leads to vanishing the axisymmetric pattern of flow structures. This is due to the formation of Roberts and Hartmann layers near the walls parallel (0° and 180°) and normal (90° and 270°) to the magnetic field, respec...
MHD natural convection phase-change heat transfer in a cavity: analysis of the magnetic field effect
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2017
suspend the convective mechanisms. However, high magnetic fields induce more uniform temperature gradients. Therefore, using a strong magnetic field can have a significant impact on the melting control process of electrically-conducting materials. Keywords Phase-change materials • Magnetic field • Natural convection • Cavity List of symbols A mush Mushy-zone constant (Carman-Koseny equation constant) B 0 Magnetic induction C Specific heat (J/kg K) c 1-c 4 Coefficients of the basis C p Specific heat in constant pressure (J/kg K) g Gravity (m/s 2) Ha Hartmann number k Thermal conductivity (W/m K) L Latent heat of fusion (J/kg) L x Length x-direction (m) L y Length y-direction (m) Nu Average Nusselt number P Pressure (Pa) Pr Prandtl number Ra Rayleigh number Re Reynolds number S Enclosure inclination angle S(T) Carman-Koseny equation (source term) Ste Stefan number T Temperature (K) t Time (s) T f Melting temperature (K) u Velocity in the x-direction (m/s) v Velocity in the y-direction (m/s
Applied and Computational Mechanics, 2020
The roll of melting heat transfer on magnetohydrodynamic natural convection in a square enclosure with heating of bottom wall is examined numerically in this article. The dimensionless governing partial differential equations are transformed into vorticity and stream function formulation and then solved using the finite difference method (FDM). The effects of thermal Rayleigh number (Ra), melting parameter (M) and Hartmann number (Ha) are graphically illustrated. As melting parameter and Rayleigh number increase, the rate of fluid flow and temperature gradients also increase. And in the presence of magnetic field, the temperature gradient reduces and hence, the conduction mechanism is dominated for larger Ha. Greater heat transfer rate is observed in the case of uniform heating compared with non-uniform case. The average Nusselt number reduces with increasing magnetic parameter in the both cases of heating of bottom wall.
Effect of Uniform Magnetic Field on Melting at Various Rayleigh Numbers
Emerging Science Journal, 2019
Melting phenomena occurs in various industrial applications, such as metal castings of turbine blades, environmental engineering, PCM-based thermal storage devices, etc. During the design of these devices, they are designed for efficient heat transfer rate. To improve the heat transfer rate, understanding of the important flow processes during the melting (and solidification) is necessary. An objective of the present work is to study the effect of natural convection and magnetic field on interface morphology and thereby on melting rate. In this work, therefore, an effect of uniform transverse magnetic field on the melting inside a cavity, filled initially with solid gallium, at various Rayleigh numbers (Ra=3×105, 6×105, and 9×105) is presented. A 2D unsteady numerical simulation, with the enthalpy-porosity formulation, is performed using ANSYS-Fluent. The magnetic field is characterized by the Hartmann number (Ha) and the results are shown for the Ha = 0, 30 and 50. The horizontal w...
Numerical simulation of magnetic control of heat transfer in thermal convection
International Journal of Heat and Fluid Flow, 2004
We report on numerical study of effects of orientation and distribution of an external magnetic field on the reorganization of convective structures and heat transfer in thermal convection in electrically conductive fluids. The simulations were performed using a transient RANS (T-RANS) approach in which the large-scale deterministic structures are numerically resolved in time and space and the unresolved contribution is modelled using an algebraic stress-flux three-equation subscale model. For low Prandtl (Pr) fluids the subscale model was extended to include Pr-dependent molecular dissipation of heat flux. The method was first validated in natural convection in a side-heated cubical enclosure subjected to magnetic fields of different orientation, strength and penetration depth, showing good agreement with the previous benchmark studies. Subsequently, a series of simulations was performed of turbulent Rayleigh-B enard convection subjected to different magnetic fields over a range of Rayleigh (Ra) and Hartmann (Ha) numbers. The computed Nusselt number showed good agreement with the available experimental results. Numerical visualization of instantaneous flow patterns showed dramatic differences in the convective structures and local heat transfer for different orientation of the magnetic field with respect to the gravitation vector. A gradual, step-like increase in the magnetic strength revealed an interesting outcome of the ''competition'' between the buoyancy and the Lorentz forces, leading first to chaotic transition and eventually to laminarization. For specific ranges of Ha, it was found that a local magnetic field confined to the wall boundary layer along the thermally active walls provides almost equal effects as the homogeneous field over the whole flow, indicating an interesting possibility for controlling thermal convection and associated heat transfer.
Effect of a Magnetic Field on Buoyancy-Driven Convection in Differentially Heated Square Cavity
IEEE Transactions on Magnetics, 2009
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.
Magnetohydrodynamic convection in molten gallium
Journal of Fluid Mechanics, 1999
We present the results of an experimental and numerical study of the effects of a steady magnetic field on sidewall convection in molten gallium. The magnetic field is applied in a direction which is orthogonal to the main flow which reduces the convection and good agreement is found for the scaling of this effect with the relevant parameters. Moreover, qualitatively similar changes in the structure of the bulk of the flow are observed in the experiment and the numerical simulations. In particular, the flow is restricted to two dimensions by the magnetic field, but it remains different to that found in two-dimensional free convection calculations. We also show that oscillations found at even greater temperature gradients can be suppressed by the magnetic field. † Present address