The application of BEM to MHD flow and heat transfer in a rectangular duct with temperature dependent viscosity

The steady, laminar, fully developed 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 equation for the pipe-axis velocity and the energy equation are solved iteratively. Firstly, the momentum equation is solved by using the boundary element method (BEM) with a parametrix (Levi function) since the diffusion term contains variable viscosity parameter depending on the temperature exponentially. Then, the energy equation is solved by using the dual reciprocity boundary element method (DRBEM). The temperature and the velocity behaviours are examined for several values of Hartmann number 0 ≤ Ha ≤ 10, dimensionless viscosity parameter B = 0,1,2, Brinkmann number Br = 0,1,2 and the Hall parameter m = 0,3,8. As Ha is increasing, the velocity magnitude drops which is a well known property of the MHD duct flow. Increasing B reduces both the flow and the temperature magnitudes whereas the increase in the Hall parameter accelerates the flow and increases the fluid temperature