Numerical Simulation of Thermomagnetic Convection of Air in a Porous Square Enclosure Under a Magnetic Quadrupole Field

Journal of Superconductivity and Novel Magnetism, Jul 2013

The thermomagnetic convection of air in a two-dimensional 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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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. - 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)


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Jiang Changwei, Zhong Hui, Feng Wei, Zen Junyong, Zhu Qiangming. Numerical Simulation of Thermomagnetic Convection of Air in a Porous Square Enclosure Under a Magnetic Quadrupole Field, Journal of Superconductivity and Novel Magnetism, 2013, pp. 519-525, Volume 27, Issue 2, DOI: 10.1007/s10948-013-2298-x