Heat transfer by laminar flow from a rotating sphere

Summary

The heat transfer problem for the flow of an incompressible viscous, heat-conducting fluid, due to uniform rotation about a diameter of a sphere, which is kept at a constant temperature, has been solved with viscous dissipation included. Due to inflow at the poles the cooler liquid is drawn from infinity towards the rotating sphere and this causes a lowering of the temperature there. After flowing in the boundary layer of the sphere the liquid gets heated up and causes a rise in temperature near the equator. Numerical results are given in case of water (Prandtl number σ=5), and it is found that the isothermals are surfaces of revolution flattened at the poles and elongated near the equator. The thermal and the velocity boundary layers turn out to be of the same order of magnitude.