Effects of a Magnetic Field on Natural Convection in a Toroidal Channel

1962 ◽  
Vol 29 (3) ◽  
pp. 559-567 ◽  
Author(s):  
Paul Concus
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Hartmann Number ◽  
Convective Motion ◽  
Liquid Sodium ◽  
Fixed Temperature ◽  
Horizontal Magnetic Field ◽  
Thermally Conducting ◽  
Solid Block

The problem of the natural convection of an electrically and thermally conducting fluid within a long, narrow, vertical toroidial channel centered in a large block of an electrically and thermally conducting solid is analyzed. A uniform horizontal magnetic field is applied to the fluid, and the bottom of the solid block is maintained at a higher fixed temperature than the top. The laminar, steady-state, single-cell convective motion of the fluid is considered and an approximate solution is found for the heat-transfer rate between the bottom and top surfaces of the block in the limiting cases of small and large Hartmann number. A numerical example is given for liquid sodium in which the application of a magnetic field of a few hundred gauss is shown to reduce the rate of heat transfer significantly.

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.

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 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.

scholarly journals Heat transfer augmentation of magnetohydrodynamics natural convection in L-shaped cavities utilizing nanofluids

2012 ◽  
Vol 16 (2) ◽  
pp. 489-501 ◽  
Author(s):  
Ehsan Sourtiji ◽  
Seyed Hosseinizadeh
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Flow Field ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
The Magnetic Field

A numerical study of natural convection heat transfer through an alumina-water nanofluid inside L-shaped cavities in the presence of an external magnetic field is performed. The study has been carried out for a wide range of important parame?ters such as Rayleigh number, Hartmann number, aspect ratio of the cavity and solid volume fraction of the nanofluid. The influence of the nanoparticle, buoyancy force and the magnetic field on the flow and temperature fields have been plotted and discussed. The results show that after a critical Rayleigh number depending on the aspect ratio, the heat transfer in the cavity rises abruptly due to some significant changes in flow field. It is also found that the heat transfer enhances in the presence of the nanoparticles and increases with solid volume fraction of the nanofluid. In addition, the performance of the nanofluid utilization is more effective at high Ray?leigh numbers. The influence of the magnetic field has been also studied and de?duced that it has a remarkable effect on the heat transfer and flow field in the cavity that as the Hartmann number increases the overall Nusselt number is significantly decreased specially at high Rayleigh numbers.

Numerical simulation of natural convection within wavy square enclosure filled with nanofluid under magnetic field using EFGM with parallel algorithm

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Surabhi Nishad ◽  
Sapna Jain ◽  
Rama Bhargava
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Inclination Angle ◽  
Transfer Rate ◽  
Hartmann Number ◽  
Content Type ◽  
The Magnetic Field ◽  
Field Inclination

Purpose This paper aims to study the flow and heat transfer inside a wavy enclosure filled with Cu-water nanofluid under magnetic field effect by parallel implemented meshfree approach. Design/methodology/approach The simulation has been carried out for a two-dimensional model with steady, laminar and incompressible flow of the nanofluid filled inside wavy enclosure in which one of the walls is sinusoidal such that the amplitude (A = 0.15) and number of undulations (n = 2) are fixed. A uniform magnetic field B0 has been applied at an inclination angle γ. The governing equations for the transport phenomena have been solved numerically by implementing element-free Galerkin method (EFGM) with the sequential as well as parallel approach. The effect of various parameters, namely, nanoparticle volume fraction (φ), Rayleigh number (Ra), Hartmann number (Ha) and magnetic field inclination angle (γ) has been studied on the natural convection flow of nanofluid. Findings The results are obtained in terms of average Nusselt number calculated at the cold wavy wall, streamlines and isotherms. It has been observed that the increasing value of Rayleigh number results in increased heat transfer rate while the Hartmann number retards the fluid motion. On the other hand, the magnetic field inclination angle gives rise to the heat transfer rate up to its critical value. Above this value, the heat transfer rate starts to decrease. Originality/value The implementation of the magnetic field and its inclination has provided very interesting results on heat and fluid flow which can be used in the drug delivery where nanofluids are used in many physiological problems. Another important novelty of the paper is that meshfree method (EFGM) has been used here because the domain is irregular. The results have been found to be very satisfactory. In addition, parallelization of the scheme (which has not been implemented earlier in such problems) improves the computational efficiency.

scholarly journals Turbulent natural convection heat transfer in a square cavity with nanofluids in presence of inclined magnetic field

2021 ◽  
pp. 326-326
Author(s):  
Mohamed El Hattab ◽  
Zakaria Lafdaili
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Orientation Angle ◽  
Inclined Magnetic Field ◽  
Square Cavity ◽  
Turbulent Natural Convection

In this paper, we present a numerical study of turbulent natural convection in a square cavity differentially heated and filled with nanofluid and subjected to an inclined magnetic field. The standard k-? model was used as the turbulence model. The transport equations were discretized by the finite volume method using the SIMPLE algorithm. The influence of the Rayleigh number, the Hartmann number, the orientation angle of the applied magnetic field, the type of nanoparticles as well as the volume fraction of nanoparticles, on the hydrodynamic and thermal characteristics of the nanofluid was illustrated and discussed in terms of streamlines, isotherms and mean Nusselt number. The results obtained show that the heat transfer rate increases with increasing Rayleigh number and orientation angle of the magnetic field but it decreases with increasing Hartmann number. In addition, heat transfer improves with increasing volume fraction and with the use of Al2O3 nanoparticles.

Numerical Investigation of Magneto-Natural Heat Transfer in Nanofluid Filled Inclined Enclosure

2020 ◽  
Vol 9 (2) ◽  
pp. 98-105
Author(s):  
L. Eljamali ◽  
R. Sehaqui
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Hartmann Number ◽  
Temperature Profiles ◽  
Governing Equations ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Inclined Enclosure ◽  
Vertical Walls

This paper examines the natural convection in an inclined enclosure that is filled with a water-copper nanofluid and influenced by a magnetic field applied normal to the plane of the cavity. The horizontal walls are assumed to be insulated while the side vertical walls of the cavity are heated differentially. The governing equations are re-formulated in functions of stream function and vorticity. The resulting boundary value problem is solved numerically using an ADI method (alternating direction implicit). A variety of plots showing the velocity and temperature profiles and the influence of Hartmann number as well as Rayleigh number on the streamlines and isotherms are shown.

Lattice Boltzmann Simulation of Magnetic Field Effect on Natural Convection of Power-Law Nanofluids in Rectangular Enclosures

2017 ◽  
Vol 9 (5) ◽  
pp. 1094-1110
Author(s):  
Lei Wang ◽  
Zhenhua Chai ◽  
Baochang Shi
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Power Law ◽  
Lattice Boltzmann ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Power Law Index

AbstractIn this paper, the magnetic field effects on natural convection of power-law nanofluids in rectangular enclosures are investigated numerically with the lattice Boltzmann method. The fluid in the cavity is a water-based nanofluid containing Cu nanoparticles and the investigations are carried out for different governing parameters including Hartmann number (0.0≤Ha≤20.0), Rayleigh number (104≤Ra≤106), power-law index (0.5≤n≤1.0), nanopartical volume fraction (0.0≤ϕ≤0.1) and aspect ratio (0.125≤AR≤8.0). The results reveal that the flow oscillations can be suppressed effectively by imposing an external magnetic field and the augmentation of Hartmann number and power-law index generally decreases the heat transfer rate. Additionally, it is observed that the average Nusselt number is increased with the increase of Rayleigh number and nanoparticle volume fraction. Moreover, the present results also indicate that there is a critical value for aspect ratio at which the impact on heat transfer is the most pronounced.

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