The BEM Solutions of MHD Flow and Heat Transfer in a Rectangular Duct with Temperature Dependent Viscosity
Keywords:
BEM, DRBEM, MHD duct flow, variable viscosity.Abstract
The steady, laminar, fully developed magnetohydrodynamic (MHD) flow of an incompressible, electrically conducting fluid with temperature dependent viscosity is studied in a rectangular duct together with its heat transfer. Although the induced magnetic field is neglected due to the small Reynolds number, the Hall effect, viscous and Joule dissipations are taken into consideration. The momentum and the energy equations are solved iteratively. Firstly, the momentum equation is solved by using the boundary element method with a parametrix since the diffusion term contains variable viscosity parameter depending on the temperature exponentially. Next, the momentum equation is also solved by using the dual reciprocity boundary element method (DRBEM) for comparison. The energy equation is solved by using the DRBEM keeping all the terms containing the velocity as inhomogeneity. The temperature and the velocity behaviours are examined for several values of Hartmann number, dimensionless viscosity parameter, Brinkmann number and the Hall parameter. As Hartmann number is increasing, the velocity magnitude drops which is a well known property of the MHD duct flow. Increasing viscosity parameter reduces both the flow and the temperature magnitudes whereas the increase in the Hall parameter accelerates the flow and increases the fluid temperature.
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