Abstract This paper presents numerical results for buoyancy driven flow and heat transfer in a two-dimensional, micropolar fluid filled enclosure. A rectangular enclosure is heated and cooled on the end walls while the other two sides are insulated. Parametric heat transfer calculations have been performed by the cubic spline collocation method. A series of Rayleigh numbers and aspect ratios of the enclosure are presented. The effect of inclination and various material parameters on the rate of heat transfer was discussed. The maximum heat transfer has been found for an inclined angle close to 41° at aspect ratio 1.75 to 0.75. The critical aspect ratio varies with the vortex viscosity.