This paper numerically investigates the effect of the transverse magnetic field on flow field patterns and heat transfer processes in a tilted square cavity. The horizontal walls of the enclosure are assumed to be insulated while the vertical walls are kept isothermal. The power law control volume approach is developed to solve the conservation equations at Prandtl number of 0.71. Validation tests with existing data demonstrate the ability of the present scheme to produce accurate results. The effects of Grashof number, enclosure inclination angle, and Hartmann number are also investigated. The study covers the range of the Hartmann number from 0 to 100, the enclosure inclination angle from 0° to ‐90° with Grashof number of 104 and 106. The effect of the magnetic field is found to suppress the convection currents and heat transfer inside the cavity. This effect is significant for low inclination angles and high Grashof numbers. Additionally, it is noted that there is no variation of average Nusselt number with respect to inclination angle for high Hartmann number.

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A fast false implicit transient scheme FITS is developed to predict the two-dimensional steady-state solutions of buoyancy-assisted laminar internal flows. This new scheme uses the control volume based on power law technique in conjugation with the alternating direction implicit (ADI) and the successive grid refinement (SGR) procedures to solve the transient vorticity and energy transport equations. The ADI procedure allows the power law, which gives an excellent approximation to the exact 1-D solution, to be applied locally in one-dimensional sense for each sweep in the co-ordinates' directions. This in turn increased the solution accuracy and hence permits the use of a larger time increment. As a result a remarkable increase in the convergence rate to steady-state is achieved. The final solution is obtained by successively refining the grid as the solution advances in time. The efficiency of FITS is verified by comparing the present predictions with three steady-state benchmark solutions: natural convection of a heat generating fluid in a rectangular enclosure, natural convection inside a cavity with two isothermal walls, and a vertical buoyancyassisted laminar backward-facing step flow.KEY WORDS Buoyancy-assisted laminar internal flows False implicit transient scheme Steady-state solutions

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