On the relation between Nusselt and Péclet number in high Péclet number convective heat transfer

For the steady forced convection cooling of an isothermal spherical object in an axially symmetric incompressible fluid flow at high Péclet numbers, where the heat transport occurs mainly in a thin thermal boundary layer near the surface of the object, the relation: Nu∝Pe1/2Nu∝Pe1/2 or Nu∝Pe1/3Nu∝Pe1/3 between the Nusselt number and the Péclet number is generally found. In this paper we investigate for the general case of a 3-dimensional object immersed in a 3-d incompressible fluid flow the connection between these two characteristic numbers and obtain a similar relation: Nu ∝ Pe1/k+2Nu ∝ Pe1/k+2 with integer values k≥0k≥0 , where k depends only on the boundary conditions of the fluid flow field at the surface of the object.