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.

Natural Convection of Mercury in a Magnetic Field parallel to the Gravity

1979 ◽  
Vol 101 (2) ◽  
pp. 227-232 ◽  
Author(s):  
M. Seki ◽  
H. Kawamura ◽  
K. Sanokawa
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Natural Convection ◽  
Vertical Wall ◽  
Heated Wall ◽  
Gravity Vector ◽  
Stagnation Region ◽  
Numerical Studies ◽  
Calculated Velocity ◽  
The Magnetic Field

Experimental and numerical studies were carried out on the natural convection of mercury in a rectangular container heated from a vertical wall. A magnetic field was applied parallel to the gravity vector and to the heated wall. Experimental results showed that the magnetic field decreased the Nusselt number considerably in the low region of the Grashof number. The effect of the parallel field was found to be less than that for a field normal to the gravity vector, but it is still not negligible. Numerical results on the Nusselt number were found to predict approximately the experimental ones. Calculated velocity profiles displayed noticeable changes due to the application of the magnetic field. A broad stagnation region was formed in the core of the container.

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.

Effect of Periodic Imposed Heat Flux on Three-Dimensional Natural Convection in a Partially Heated Cubical Enclosure

2016 ◽  
Vol 831 ◽  
pp. 83-91
Author(s):  
Lahoucine Belarche ◽  
Btissam Abourida
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Study ◽  
Control Volume ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Maximum Temperature ◽  
Cubical Enclosure ◽  
Simplec Algorithm ◽  
Volume Method

The three-dimensional numerical study of natural convection in a cubical enclosure, discretely heated, was carried out in this study. Two heating square sections, similar to the integrated electronic components, are placed on the vertical wall of the enclosure. The imposed heating fluxes vary sinusoidally with time, in phase and in opposition of phase. The temperature of the opposite vertical wall is maintained at a cold uniform temperature and the other walls are adiabatic. The governing equations are solved using Control volume method by SIMPLEC algorithm. The sections dimension ε = D / H and the Rayleigh number Ra were fixed respectively at 0,35 and 106. The average heat transfer and the maximum temperature on the active portions will be examined for a given set of the governing parameters, namely the amplitude of the variable temperatures a and their period τp. The obtained results show significant changes in terms of heat transfer, by proper choice of the heating mode and the governing parameters.

Numerical Calculation of Three-Dimensional Turbulent Natural Convection in a Cubical Enclosure Using a Two-Equation Model for Turbulence

1986 ◽  
Vol 108 (4) ◽  
pp. 806-813 ◽  
Author(s):  
H. Ozoe ◽  
A. Mouri ◽  
M. Hiramitsu ◽  
S. W. Churchill ◽  
N. Lior
Keyword(s):  
Natural Convection ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Spiral Flow ◽  
Vertical Side ◽  
Turbulent Natural Convection ◽  
Cubical Enclosure ◽  
Side Walls

This paper presents a model and numerical results for turbulent natural convection in a cubical enclosure heated from below, cooled on a portion of one vertical side wall and insulated on all other surfaces. Three-dimensional balances were derived for material, energy, and the three components of momentum, as well as for the turbulent kinetic energy k and the rate of dissipation of turbulent kinetic energy ε. The constants used in the model were the same as those used by Fraikin et al. for two-dimensional convection in a channel. Illustrative transient calculations were carried out for Ra = 106 and 107 and Pr = 0.7. Both the dominant component of the vector potential and the Nusselt number were found to converge to a steady state. Isothermal lines and velocity vectors for vertical cross sections normal to the cooled wall indicated three-dimensional effects near the side walls. A top view of the velocity vectors revealed a downward spiral flow near the side walls along the cooled vertical wall. A weak spiral flow was also found along the side walls near the wall opposing the partially cooled one. The highest values of the eddy diffusivity were 2.6 and 5.8 times the molecular kinematic viscosity for Ra = 106 and 107, respectively. A coaxial double spiral movement, similar to that previously reported for laminar natural convection, was found for the time-averaged flow field. This computing scheme is expected to be applicable to other thermal boundary conditions.

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.

Enhanced Heat Transfer Rate Measured for Natural Convection in Liquid Gallium in a Cubical Enclosure Under a Static Magnetic Field

1998 ◽  
Vol 120 (4) ◽  
pp. 1027-1032 ◽  
Author(s):  
Toshio Tagawa ◽  
Hiroyuki Ozoe
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Heated Wall ◽  
Electric Heater ◽  
Liquid Gallium ◽  
Cubical Enclosure ◽  
Moderate Magnetic Field

The heat transfer rate of natural convection in liquid gallium in a cubical enclosure was measured experimentally under an external magnetic field applied horizontally and parallel to the vertical heated wall and the opposing cooled wall and the opposing cooled wall of the enclosure. One vertical wall was heated with an electric heater and the opposing wall was cooled isothermally with running water. Experiments were conducted in the range of modified Rayleigh number from 1.85 × 106 to 4.76 × 106 and of Hartmann number from 0 to 573. The average Nusselt number was measured and found to increase when a moderate magnetic field was applied, but to decrease under a stronger magnetic field. This result means that the heat transfer rate has a maximum value at a certain moderate magnetic field, which supports our previous numerical analyses.

scholarly journals Natural convection flow in a square cavity with internal heat generation and a flush mounted heater on a side wall

2011 ◽  
Vol 7 (2) ◽  
pp. 37-50 ◽  
Author(s):  
Md. Mustafizur Rahman ◽  
M. Arif Hasan Mamun ◽  
M. Masum Billah ◽  
Saidur Rahman
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Heat Generation ◽  
Vertical Wall ◽  
Heated Wall ◽  
Convection Flow ◽  
Square Cavity ◽  
Natural Convection Flow ◽  
Heater Length

In this study natural convection flow in a square cavity with heat generating fluid and a finite size heater on the vertical wall have been investigated numerically. To change the heat transfer in the cavity, a heater is placed at different locations on the right vertical wall of the cavity, while the left wall is considered to be cold. In addition, the top and bottom horizontal walls are considered to be adiabatic and the cavity is assumed to be filled with a Bousinessq fluid having a Prandtl number of 0.72. The governing mass, momentum and energy equations along with boundary conditions are expressed in a normalized primitive variables formulation. Finite Element Method is used in solution of the normalized governing equations. The parameters leading the problem are the Rayleigh number, location of the heater, length of the heater and heat generation. To observe the effects of the mentioned parameters on natural convection in the cavity, we considered various values of heater locations, heater length and heat generation parameter for different values of Ra varying in the range 102 to 105. Results are presented in terms of streamlines, isotherms, average Nusselt number at the hot wall and average fluid temperature in the cavity for the mentioned parameters. The results showed that the flow and thermal fields through streamlines and isotherms as well as the rate of heat transfer from the heated wall in terms of Nusselt number are strongly dependent on the length and locations of the heater as well as heat generating parameter.DOI: 10.3329/jname.v7i2.3292 

scholarly journals The effect of an external magnetic field on the entropy generation in three-dimensional natural convection

2010 ◽  
Vol 14 (2) ◽  
pp. 341-352 ◽  
Author(s):  
Lioua Kolsi ◽  
Awatef Abidi ◽  
Naceur Borjini ◽  
Ben Aïssia
Keyword(s):  
Magnetic Field ◽  
Natural Convection ◽  
External Magnetic Field ◽  
Liquid Metal ◽  
Entropy Generation ◽  
Numerical Study ◽  
Three Dimensional ◽  
Laminar Natural Convection ◽  
The Magnetic Field

A 3-D original numerical study of entropy generation in the case of liquid metal laminar natural convection in a differentially heated cubic cavity and in the presence of an external magnetic field orthogonal to the isothermal walls is carried out. The effect of this field on the various types of irreversibilities is analyzed. It was observed that in the presence of a magnetic field the generated entropy is distributed on the entire cavity and that the magnetic field limits the 3-D character of the distribution of the generated entropy.

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