A finite difference simulation on free convection in tilted enclosures of low aspect ratio

Two dimensional laminar free convection across a tilted rectangular enclosure of aspect ratio 0.5 is analyzed in a finite difference simulation. The constant property vorticity, energy and stream function equations are solved in elliptic form using second order conservative approximations in a relaxation iterative scheme coupled with a fast Fourier transform algorithm. The primary flow is found to be unicellular, with boundary-layer character increasing with Rayleigh number, Prandtl number and tilt angle greater than 0 deg (heating from above). Convection is shown to be sharply suppressed at tilt angles less than 0 deg, with a maximum Nusselt number at angles between 5 and 35 deg, shifting to lower values with increasing Rayleigh number. The highest average Nusselt numbers are obtained with isothermal connecting walls, while the lowest are obtained with perfectly conducting connecting walls with adiabatic walls producing intermediate values.