Numerical Simulation of Thermomagnetic Convection of Air in a Porous Square Enclosure Under a Magnetic Quadrupole Field
Jiang Changwei
Zhong Hui
Feng Wei
Zen Junyong
Zhu Qiangming
The thermomagnetic convection of air in a twodimensional porous square enclosure under a magnetic quadrupole field is numerically investigated. The Scalar Magnetic Potential Method is used to calculate the magnetic field. A generalized model, which includes a Brinkman term, a Forcheimmer term, and a nonlinear convective term, is used to solve the momentum. The flow and temperature fields for the air thermomagnetic convection are presented and the local and average Nusselt numbers on the walls are calculated and compared. The results show that the magnetic field intensity, the Darcy number and the Rayleigh number have a significant effect on the flow field and heat transfer in a porous square enclosure.
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Enhancements or suppressions of the convection
phenomena and improvement of heat and mass transfer continue to
be an active research area, due to their significance for both
fundamental interests and engineering applications, such as
solar receivers, cooling of electronic devices, solidification
of materials and so on. There are many methods of
enhancements or suppressions of the convection phenomena, for
example by placing fins on the heated wall, exerting electric
and magnetic fields, etc. [1, 2].
Recently, magnetic force has received more attention in
the field of metallic materials, and less in the field of
nonmetallic materials. With the development of a
superconducting magnet providing strong magnetic induction of 10 Tesla
or more in recent years, the suppression or enhancement
of the natural convection of the paramagnetic fluids like
oxygen gas and air by a magnetic field has become an
interesting research topic investigated by many researchers.
Many research works about magnetically induced natural
convection have followed [3]. The effect of the magnetic
buoyancy force on the convection of the paramagnetic
fluids was first reported by Braithwaite et al. [4]. They used the
magnetic field both to enhance and suppress the Rayleigh
Benard convection in a solution of gadolinium-nitrate in a
shallow layer heated from below and cooled from above and
showed that the effect depends on the relative orientation
of the magnetic force and the temperature gradient.
Carruthers and Wolfe [5] studied the thermomagnetic
convection of oxygen gas in a rectangular container with thermal
and magnetic field gradients theoretically and
experimentally, and found that magnetic buoyancy force canceled out
the influence of gravitational buoyancy force when the
rectangular enclosure heated from one vertical wall and cooled
from opposing wall was located in horizontal magnetic field
with vertical magnetic field gradient, and horizontal
magnetic field could enhance and suppress the RayleighBenard
convection when the rectangular enclosure heated from
below and cooled from above was located with the same mode.
Shigemitsus group [6] derived a model equation for
magnetic convection using a method similar to the Boussinesq
approximation and studied natural convection of
paramagnetic, diamagnetic and electrically conducting fluids in a
cubic enclosure with thermal and magnetic field gradients
at different thermal boundaries numerically and
experimentally. Tagawa and co-workers [7] studied natural convection
of paramagnetic and diamagnetic fluids in a cylinder under
gradient magnetic field at different thermal boundaries
numerically and experimentally and found that the magnetic
body due to gradient magnetic field could be used to
control heat transfer rate of paramagnetic and diamagnetic
fluids. Bednarz and co-workers [8] studied natural convection
of paramagnetic fluids in a cubic enclosure under magnetic
field by an electric coil numerically and experimentally and
analyzed the effect of inclined angle of electric coil, location
of electric coil, Ra number, number on heat transfer rate
of paramagnetic fluids.
The above studies are concerned with the effect of
magnetic force on natural convection of paramagnetic fluids.
However, almost no attention has been paid to the combined
effects of magnetic and gravitational forces on the natural
convection of paramagnetic fluids in porous medium.
Natural convection in an enclosure filled with a paramagnetic
or diamagnetic fluid-saturated porous medium under strong
magnetic field was numerically investigated by Wang et al.
[9, 10]. Considering the effect of Darcy number, Rayleigh
number and number, the results of numerical
investigation showed that the magnetic force has a significant effect
on the flow field and heat transfer in a paramagnetic or
diamagnetic fluid-saturated porous medium. The application of
strong magnetic field on porous medium may be found in
the field of medical treatment, metallurgy, materials
processing, combustion. There may be plenty of applications in the
near future in the field of engineering operations. Thus, the
study of the effect of magnetic force on natural convection
in porous media is important (...truncated)