The laminar, axisymmetric flow of a rotating Boussinesq generalized Newtonian fluid contained within a concentric spherical annulus is investigated for the case where the outer spherical shell is kept at a higher temperature than the inner one. Inner and outer spheres can rotate at different angular velocities. The penalty Galerkin finite element method has been extended to non-Newtonian viscous flows. A Carreau constitutive relationship is used. Results are presented for a spherical gap of radii ratio 0.5, Reynolds number 0 less than or equal to Re less than or equal to 7000, Rayleigh number Ra = 0,2 x 10(5) (isothermal and non-isothermal flows), Deborah number 0 less than or equal to De less than or equal to 10, ratio of the rate of rotation of outer to inner sphere 0 less than or equal to xi less than or equal to 0.03, ＇＇power law＇＇ exponent 0.5 less than or equal to n less than or equal to 1.3 and Prandtl number Pr = 0.7,7. The influence of shear-thinning and shear-thickening fluid properties and heat transfer on the vortex breakdown bubble in the space of the physical characteristic parameters is examined.