A two-dimensional time-dependent numerical model of convection in a cylindrical annulus is described. Model results are presented and compared with similar models in planar geometry. In curvilinear geometry the upper (outer) boundary has a larger surface area than does the lower (inner) boundary. This result in an asymmetry between the upper and lower thermal boundary layers which is not found in planar geometry. A boundary layer argument is developed for curvilinear geometry which accounts for differences in model predictions between the curvilinear and planar models. It is found that in cylindrical geometry the effects of curvature on Nusselt numbers, mean temperature, relative thickness of the innear and outer thermal boundary layers, and temperature drops across the thermal boundary layers can all be parameterized in terms of the fraction f of the inner to outer radii of the cylindrical bounding surfaces. ¿American Geophysical Union 1993