Centrifugally forced convection, mixed and natural convection are numerically studied in a short vertical annulus with a heated and rotating inner cylinder. The cooled outer cylinder is at rest and the hortizontal endplates are assumed adiabatic. The effect of a non-Newtonian shear thinning viscosity modeled by the Carreau-shifted constitutive equation is examined. Computations were performed for different values of the flow index and Weissenberg number with the Prandtl number based on the zero-shear-rate viscosity, the radius ratio and the ratio of height to gap spacing are kept fixed. The results show that the shear thinning effect decreases the friction factor at the rotating cylinder and increases the heat transfer through the annular gap. it is also shown that the reduction in apparent viscosity may produce oscillatory flows, especially for centrifugally forced convection. (C) 2000 Elsevier Science B.V. All rights reserved.