Effect of magnetic field on natural convection flow in a liquid gallium filled square cavity for linearly heated side wall(s)

A numerical study is presented for natural convection flow of electrically conducting liquid gallium in a square cavity. In the cavity, the bottom wall is uniformly heated and the left vertical wall is linearly heated whereas the right vertical wall is linearly heated or cooled while the top wall kept thermally insulated. A uniform magnetic field inclined at an angle ϕ with respect to horizontal plane is externally imposed. Penalty finite element method with bi-quadratic rectangular elements is used to solve the non-dimensional governing equations. Numerical results are presented for wide range of Hartmann number (Ha   = 0–100) with inclined angles (ϕ=0,π/2)(ϕ=0,π/2) for high Rayleigh number Ra = 105 in terms of stream functions and isotherm contours, local and average Nusselt number. The results shows that the magnetic field with inclined angle has effects on the flow and heat transfer rates in the cavity. It is also found that the average Nusselt number decreases non-linearly by increasing Hartmann number for any inclined angle.