Numerical investigation of natural convection in a rectangular cavity under different directions of uniform magnetic field

Natural convection flows of an electrically conducting fluid under a uniform magnetic field at different angles θ with respect to horizontal plane are investigated numerically in rectangular cavities. A new compact finite difference algorithm, involving a second-order compact scheme for the streamfunction-velocity (ψ − u) form of Navier–Stokes equations and a fourth-order compact scheme for the energy equation, is employed to solve the steady-state laminar magnetohydrodynamic (MHD) natural convection problems. Numerical simulations are carried out in a wide range of Rayleigh number (Ra) and Hartmann number (Ha) at the Prandtl number Pr = 0.025. The computed results show that the heat transfer is not only determined by the strength of the magnetic field, but also influenced by the inclination angle. Especially, when the aspect ratio (A) is less or more than 1, it is found that the inclination angle plays a great role on flow and heat transfer.