scholarly journals Axisymmetric Natural Convection of Liquid Metal in an Annular Enclosure under the Influence of Azimuthal Magnetic Field

Energies ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 2896 ◽  
Author(s):  
Takuya Masuda ◽  
Toshio Tagawa
Keyword(s):  
Magnetic Field ◽  
Natural Convection ◽  
Liquid Metal ◽  
Stream Function ◽  
Average Nusselt Number ◽  
Hartmann Number ◽  
Vertical Wall ◽  
Cross Sectional ◽  
Contour Map ◽  
Azimuthal Magnetic Field

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 number. The average Nusselt number was decreased in proportion to the square of the Hartmann number in the high Hartmann number regime.

Enhancement of Heat Transfer Rate by Application of a Static Magnetic Field During Natural Convection of Liquid Metal in a Cube

1997 ◽  
Vol 119 (2) ◽  
pp. 265-271 ◽  
Author(s):  
T. Tagawa ◽  
H. Ozoe
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Natural Convection ◽  
Liquid Metal ◽  
Average Nusselt Number ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Heated Wall ◽  
Horizontal Magnetic Field ◽  
Cubical Enclosure

Natural convection of liquid metal in a cubical enclosure under an external magnetic field was investigated by three-dimensional numerical analyses. The system parameters were Ra = 105 and 106, Pr = 0.025, and Ha = 0–1000. One vertical wall of the cubical enclosure was heated, and the opposing vertical wall was cooled, both isothermally; the other four walls were thermally insulated. A uniform horizontal magnetic field was applied parallel to the heated and cooled walls. At Ra = 105 and Ha = 50, the average Nusselt number on the heated wall attained almost the maximum value and was greater than that at Ha = 0. The velocity vectors along the vertical walls, and those along the horizontal planes, were rectified in a two-dimensional way at Ha = 50 or over, and the average Nusselt number decreased gradually for higher values of the Hartmann number. Similar characteristics were obtained at Ra = 106. The agreement with our earlier experiments was moderately good.

scholarly journals CuO–Water Nanofluid Magnetohydrodynamic Natural Convection inside a Sinusoidal Annulus in Presence of Melting Heat Transfer

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
M. Sheikholeslami ◽  
R. Ellahi ◽  
C. Fetecau
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Melting Heat ◽  
Melting Heat Transfer ◽  
Limiting Case ◽  
Good Agreement ◽  
Melting Parameter

Impact of nanofluid natural convection due to magnetic field in existence of melting heat transfer is simulated using CVFEM in this research. KKL model is taken into account to obtain properties of CuO–H2O nanofluid. Roles of melting parameter (δ), CuO–H2O volume fraction (ϕ), Hartmann number (Ha), and Rayleigh (Ra) number are depicted in outputs. Results depict that temperature gradient improves with rise of Rayleigh number and melting parameter. Nusselt number detracts with rise of Ha. At the end, a comparison as a limiting case of the considered problem with the existing studies is made and found in good agreement.

Natural Convection in a Partitioned Vertical Enclosure Heated With a Uniform Heat Flux

2006 ◽  
Vol 129 (6) ◽  
pp. 717-726 ◽  
Author(s):  
Kamil Kahveci
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Thermal Resistance ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Finite Thickness ◽  
Vertical Wall ◽  
Uniform Heat Flux ◽  
Uniform Heat

This numerical study looks at laminar natural convection in an enclosure divided by a partition with a finite thickness and conductivity. The enclosure is assumed to be heated using a uniform heat flux on a vertical wall, and cooled to a constant temperature on the opposite wall. The governing equations in the vorticity-stream function formulation are solved by employing a polynomial-based differential quadrature method. The results show that the presence of a vertical partition has a considerable effect on the circulation intensity, and therefore, the heat transfer characteristics across the enclosure. The average Nusselt number decreases with an increase of the distance between the hot wall and the partition. With a decrease in the thermal resistance of the partition, the average Nusselt number shows an increasing trend and a peak point is detected. If the thermal resistance of the partition further declines, the average Nusselt number begins to decrease asymptotically to a constant value. The partition thickness has little effect on the average Nusselt number.

Rayleigh–Bénard instability in a vertical cylinder with a vertical magnetic field

2002 ◽  
Vol 469 ◽  
pp. 189-207 ◽  
Author(s):  
B. C. HOUCHENS ◽  
L. MARTIN WITKOWSKI ◽  
J. S. WALKER
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Numerical Solution ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Hartmann Number ◽  
Critical Rayleigh Number ◽  
Vertical Wall ◽  
Vertical Cylinder ◽  
Vertical Magnetic Field

This paper presents two linear stability analyses for an electrically conducting liquid contained in a vertical cylinder with a thermally insulated vertical wall and with isothermal top and bottom walls. There is a steady uniform vertical magnetic field. The first linear stability analysis involves a hybrid approach which combines an analytical solution for the Hartmann layers adjacent to the top and bottom walls with a numerical solution for the rest of the liquid domain. The second linear stability analysis involves an asymptotic solution for large values of the Hartmann number. Numerically accurate predictions of the critical Rayleigh number can be obtained for Hartmann numbers from zero to infinity with the two solutions presented here and a previous numerical solution which gives accurate results for small values of the Hartmann number.

A Differential Quadrature Solution of MHD Natural Convection in an Inclined Enclosure With a Partition

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Kamil Kahveci ◽  
Semiha Öztuna
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Inclination Angle ◽  
Hartmann Number ◽  
Differential Quadrature ◽  
Flow And Heat Transfer ◽  
Inclined Enclosure ◽  
Vorticity Generation

Magnetohydrodynamics natural convection in an inclined enclosure with a partition is studied numerically using a differential quadrature method. Governing equations for the fluid flow and heat transfer are solved for the Rayleigh number varying from 104 to 106, the Prandtl numbers (0.1, 1, and 10), four different Hartmann numbers (0, 25, 50, and 100), the inclination angle ranging from 0degto90deg, and the magnetic field with the x and y directions. The results show that the convective flow weakens considerably with increasing magnetic field strength, and the x-directional magnetic field is more effective in reducing the convection intensity. As the inclination angle increases, multicellular flows begin to develop on both sides of the enclosure for higher values of the Hartmann number if the enclosure is under the x-directional magnetic field. The vorticity generation intensity increases with increase of Rayleigh number. On the other hand, increasing Hartmann number has a negative effect on vorticity generation. With an increase in the inclination angle, the intensity of vorticity generation is observed to shift to top left corners and bottom right corners. Vorticity generation loops in each region of enclosure form due to multicelluar flow for an x-directional magnetic field when the inclination angle is increased further. In addition, depending on the boundary layer developed, the vorticity value on the hot wall increases first sharply with increasing y and then begins to decrease gradually. For the high Rayleigh numbers, the average Nusselt number shows an increasing trend as the inclination angle increases and a peak value is detected. Beyond the peak point, the foregoing trend reverses to decrease with the further increase of the inclination angle. The results also show that the Prandtl number has only a marginal effect on the flow and heat transfer.

scholarly journals Spin-Up from Rest of a Liquid Metal with Deformable Free Surface in a Cylinder under the Influence of a Uniform Axial Magnetic Field

Fluids ◽  
2021 ◽  
Vol 6 (12) ◽  
pp. 438
Author(s):  
Toshio Tagawa ◽  
Kewei Song
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Liquid Metal ◽  
Hartmann Number ◽  
Viscosity Ratio ◽  
Axial Magnetic Field ◽  
Density Ratio ◽  
Striking Difference ◽  
Gas Phases ◽  
Component Velocity

Spin-up from rest of a liquid metal having deformable free surface in the presence of a uniform axial magnetic field is numerically studied. Both liquid and gas phases in a vertically mounted cylinder are assumed to be an incompressible, immiscible, Newtonian fluid. Since the viscous dissipation and the Joule heating are neglected, thermal convection due to buoyancy and thermocapillary effects is not taken into account. The effects of Ekman number and Hartmann number were computed with fixing the Froude number of 1.5, the density ratio of 800, and the viscosity ratio of 50. The evolutions of the free surface, three-component velocity field, and electric current density are portrayed using the level-set method and HSMAC method. When a uniform axial magnetic field is imposed, the azimuthal momentum is transferred from the rotating bottom wall to the core region directly through the Hartmann layer. This is the most striking difference from spin-up of the nonmagnetic case.

scholarly journals Effect of the Direction of Uniform Horizontal Magnetic Field on the Linear Stability of Natural Convection in a Long Vertical Rectangular Enclosure

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1689
Author(s):  
Toshio Tagawa
Keyword(s):  
Magnetic Field ◽  
Natural Convection ◽  
Temperature Gradient ◽  
Linear Stability ◽  
Applied Magnetic Field ◽  
Hartmann Number ◽  
Horizontal Magnetic Field ◽  
Direction Parallel ◽  
Vertical Side ◽  
Rectangular Enclosure

The effect of the direction of external horizontal magnetic fields on the linear stability of natural convection of liquid metal in an infinitely long vertical rectangular enclosure is numerically studied. A vertical side wall is heated and the opposing vertical wall is cooled both isothermally, whereas the other two vertical walls are adiabatic. A uniform horizontal magnetic field is applied either in the direction parallel or perpendicular to the temperature gradient. In this study, the height of the enclosure is so long as to neglect the top and bottom effects where returning flow takes place, and thus the basic flow is assumed to be a parallel flow and the temperature field is in heat conduction state. The Prandtl number is limited to the value of 0.025 and horizontal cross-section is square. The natural convection is monotonously stabilized as increase in the Hartmann number when the applied magnetic field is parallel to the temperature gradient. However, when the applied magnetic field is perpendicular to the temperature gradient, it is once destabilized at a certain low Hartmann number, but it is stabilized at high Hartmann numbers.

Convective Heat Transfer Utilizing Magnetic Nanoparticles in the Presence of a Sloping Magnetic Field Inside a Square Enclosure

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
Latifa M. Al-Balushi ◽  
M. M. Rahman
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Nusselt Number ◽  
Magnetic Nanoparticles ◽  
Shear Rate ◽  
Average Nusselt Number ◽  
Hartmann Number ◽  
The Other ◽  
Square Enclosure ◽  
Thermal Boundary Conditions

Unsteady natural convection flow and heat transfer utilizing magnetic nanoparticles in the presence of a sloping magnetic field inside a square enclosure are simulated numerically following nonhomogeneous dynamic model. Four different thermal boundary conditions: constant, parabolic in space, sinusoidally in space, and time for the bottom hot wall are considered. The top wall of the enclosure is cold while the vertical walls are thermally insulated. Galerkin weighted residual finite element method is used to solve the governing nondimensional partial differential equations. For simulations, 12 types of nanofluids consisting magnetite (Fe3O4), cobalt ferrite (CoFe2O4), Mn–Zn ferrite (Mn–ZnFe2O4), and silicon dioxide (SiO2) nanoparticles along with water, engine oil, and kerosene as base fluids are used. The effects of the important model parameters such as Hartmann number, magnetic field sloping angle, and thermal Rayleigh number on the flow fields are investigated. The results show that the average Nusselt number, shear rate, as well as the nanofluid velocity decreases as the Hartmann number intensifies. Moreover, the rate of heat transfer in nanofluid exaggerates with the increase of the thermal Rayleigh number and the magnetic field sloping angle. Sinusoidally varied in space thermal boundary condition at the bottom wall provides the highest average Nusselt number and the shear rate compared to the other types of thermal boundary conditions studied here. For this case, the highest average Nusselt number is obtained for the Mn–ZnFe2O4–Ke nanofluid. On the other hand, Fe3O4–H2O nanofluid delivers the highest shear rate compared to the other premeditated nanofluids.

Numerical Investigation of Natural Convection in a Square Enclosure with a Baffle Mounted on Vertical Wall

2015 ◽  
Vol 813-814 ◽  
pp. 748-753 ◽  
Author(s):  
N. Nagasubramanian ◽  
M.R. Thansekhar ◽  
M. Venkatesan ◽  
K. Ramanathan
Keyword(s):  
Natural Convection ◽  
Numerical Investigation ◽  
Average Nusselt Number ◽  
Vertical Wall ◽  
Temperature Fields ◽  
Cold Wall ◽  
Primary Vortex ◽  
Square Enclosure ◽  
Flow And Heat Transfer ◽  
Laminar Natural Convection

Results from numerical investigation of laminar natural convection inside a differentially heated square enclosure with a thin baffle attached to the cold wall are reported. The effect of the baffles on the flow and temperature fields were analyzed for baffle lengths equal to 20, 35 and 50 percent of the width of the enclosure, attached at three locations for Ra = 104, 105, 106 and Pr = 0.707. The presence of a baffle on the cold right wall affects the strength of the clockwise rotating primary vortex. Reduced flow and heat transfer are observed. Longer the baffle more pronounced the effect on the flow field. Secondary convection cells are seen between the baffle and the bottom wall for certain cases. Reduction in average Nusselt Number is observed on the cold wall with the baffle than the hot wall.

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