RBF-DQ Solution of Natural Convection under the Effect of a Magnetic Field in a Tilted Cavity

In this study, radial basis function based differential quadrature (RBF-DQ) method is applied to the natural convection in an inclined unit square cavity under the effect of an applied magnetic field in different angles. The stream function-vorticity form of the dimensionless governing equations are concentrated on. The change in different Hartmann numbers, Rayleigh numbers and inclination angles of the cavity is investigated both in terms of streamlines, isotherms, vorticity contours and the average Nusselt number through the heated wall. The increase in Hartmann number causes heat transfer to be conductive due to the Lorentz force, and therefore the inclination angle of the cavity loses its effect. A remarkable effect of the inclination angle on heat transfer for is presented. The proposed method is a global method and provides to use small number of grid points as a result of DQ method.

Keywords:

Radial basis functions , Differential quadrature method , Natural convection , Tilted cavity