Numerical techniques have been used to study natural convection in a fluid subjected to axial rotation. Axisymmetrical flows were studied in two different geometries for a variety of rotational speeds. For case I(R1 = 1.0, R2 = 2.5, H = 3.0), the computed flow patterns were qualitatively compared with those which would be expected from the basic rules of physics, and good agreement was obtained. Rotational speeds between&OHgr; = 0,and&OHgr; = 20were studied for a Grashoff number of 3000. Increased rotational speed was found to decrease the over‐all heat transfer rate. For case II(R1 = 1.0, R2 = 4.0, H = 1.0), rotational speeds of&OHgr; = 0.0to&OHgr; = 40.0were studied at a Grashoff number of 400. At low rotational speeds, a single convection cell was found, however, at higher rotational speeds, the single cell became unstable, and changed to a two‐celled pattern. This transition resulted in a slight increase in the over‐all heat transfer rate.