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ISSN Online: 2377-424X

ISBN Print: 978-1-56700-421-2

International Heat Transfer Conference 15
August, 10-15, 2014, Kyoto, Japan

3D Numerical Simulation of Buoyancy Driven Flow in a Cubical Enclosure with Different Wall Conductivities

Get access (open in a dialog) DOI: 10.1615/IHTC15.pls.009138
pages 6435-6443

Resumo

The buoyancy driven flow of a liquid metal in a cubical enclosure is numerical simulated for relatively high Hartmann numbers (Ha = 2000 - 5000). One vertical wall of the enclosure is heated, while its opposite wall is cooled and the other (four) walls are thermally insulated. All walls of the enclosure are assumed to be electrically conducting. The direction of the magnetic field, B0, is in the Z-direction (orthogonal to the temperature gradient ΔT) in one case, and in the X-direction (parallel to the temperature gradient) in another. The Navier Stokes, continuity and energy equations are solved along with the quasi-static approximation of Maxwell equations using ANUPRAVAHA, a finite-volume solver developed in-house by the same research group. A wall function treatment is used to circumvent the requirement of numerical resolution of the Hartmann layers. Conjugate thermal and electromagnetic distributions are considered for flow-wall coupling. Numerical simulations are carried out to study the effect of Z and X directional magnetic fields on convective motion (and Nusselt Number) for a Rayleigh number, Ra, of 104 and Prandtl number, Pr = 0.01, for Hartmann numbers, Ha = 2000, 3000 and 5000. The results show that X-directional magnetic field has a pronounced effect on the Nusselt number relative to the Z-directional magnetic field. For each Hartmann number, the effect of different values of wall conductivity (Cw = 0.1, 1.0, 10, and 100) on Nusselt number is also studied. Results show that that an increase in applied magnetic field decreases the flow velocity and Nusselt number, also changing the flow structure. An increase in wall conductivity from 0.1 to 100 decreases convective motion and the average Nusselt number.