Magneto-convection inside a tilted enclosure
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DOI: 10.1134/S0869864320030063
Magneto-convection inside a tilted enclosure 1
M. Pirmohammadi and A. Salehi-Shabestari
2
1
Pardis Branch, Islamic Azad University, Pardis, Iran
2
Niroo Research Institute, Tehran, Iran
E-mail: [email protected] (Received May 3, 2018; revised July 31, 2018; accepted for publication August 1, 2018; further refined April 21, 2020) In this study, laminar magneto-convection flow of a viscous fluid in an inclined enclosure is considered. The temperature gradient is applied on two opposing walls while the other two walls are maintained adiabatic. In order to solve the governing non-linear differential equations, an in-house developed code based on the finite volume method is utilized. The fluid of interest is molten sodium whose thermal and electrical properties such as heat capacity, thermal and electrical conductivity are temperature dependent. Representative results illustrating the effects of the enclosure inclination angle on the contour maps of the streamlines and temperature are reported and discussed. In addition, results for the midsection velocity profile and the average Nusselt number at the hot wall of the enclosure are presented and discussed for various inclination angles and Hartmann numbers. It is observed that for Hartmann number of 600, an increase in the inclination angle leads to the growth of the number of vortices in the enclosure. Keywords: magneto-convection flow, inclination angle, Rayleigh number, Hartmann number, Nusselt number.
Introduction Laminar natural-convection flow in enclosures has significant applications in many engineering areas including cooling of electronic equipment, solar energy collection, and crystal growth in liquids and has been investigated by a number of researchers. It is well known that unavoidable hydrodynamic motion can be damped by applying a magnetic field. Investigations of heat transfer for melt flows under crystal growth conditions help one to qualify the critical operating parameters of crystal growth. In general, the homogeneity and quality of single crystals grown from doped semiconductor melts is of interest to the manufacturers of electronic chips. Hence, there has been increased interest in the flows of electrically conducting fluids in cavities subjected to external magnetic field. When the fluid is electrically conducting and exposed to a magnetic field the Lorentz force is also active and interacts with the buoyancy force, both governing the flow and temperature fields. Implementation of an external magnetic field has increasing applications in material manufacturing industry as a control mechanism since the Lorentz force suppresses the convection currents by reducing the velocities. Study and thorough understanding of the momentum and heat transfer in such a process is important for the better control and improving
M. Pirmohammadi and A. Salehi-Shabestari, 2020
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M. Pirmohammadi and A. Salehi-Shabestari
the quality of the manufactured products. In the work [1], an analytical solution was propose
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