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# DRBEM Solution of MHD Flow with Magnetic Induction and Heat Transfer

B. Pekmen1,2, M. Tezer-Sezgin2,3
Department of Mathematics, Atılım University, 06836, Ankara, Turkey.
Institute of Applied Mathematics, Middle East Technical University, 06800, Ankara, Turkey.
Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey.

Computer Modeling in Engineering & Sciences 2015, 105(3), 183-207. https://doi.org/10.3970/cmes.2015.105.183

### Abstract

This study proposes the dual reciprocity boundary element (DRBEM) solution for full magnetohydrodynamics (MHD) equations in a lid-driven square cavity. MHD equations are coupled with the heat transfer equation by means of the Boussinesq approximation. Induced magnetic field is also taken into consideration. The governing equations in terms of stream function, temperature, induced magnetic field components, and vorticity are solved employing DRBEM in space together with the implicit backward Euler formula for the time derivatives. The use of DRBEM with linear boundary elements which is a boundary discretization method enables one to obtain small sized linear systems. This makes the whole procedure computationally efficient and cheap. The results are depicted with respect to varying physical parameters such as Prandtl (0:005 ≤ Pr ≤ 1), Reynolds (100 ≤ Re ≤ 2500), magnetic Reynolds (1 ≤ Rem ≤ 100), Hartmann (10 ≤ Ha ≤ 100) and Rayleigh (10 ≤ Ra ≤ 106) numbers for discussing the effect of each parameter on the flow and temperature behaviors of the fluid. It is found that an increase in Ha slows down the fluid motion and heat transfer becomes conductive. Centered square blockage causes secondary flows on its left and right even for small Re. Strong temperature gradients occur around the blockage and near the moving lid for increasing values of Ra.

### Keywords

MHD, convection, DRBEM, heat transfer

Pekmen, B., Tezer-Sezgin, M. (2015). DRBEM Solution of MHD Flow with Magnetic Induction and Heat Transfer. CMES-Computer Modeling in Engineering & Sciences, 105(3), 183–207.

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