Almost all convection calculations hinge on the ability to choose the correct Nusselt number correlation. The Nusselt number is defined as
where h is the convective heat transfer coefficient, Lchr is the appropriate characteristic length and k is the fluid thermal conductivity.
The physical interpretation of Nusselt number is the enhancement of heat transfer due to convection over conduction alone. If Nu=1, then, than your fluid is stationary and all heat transfer is by conduction. With Nu>1, the fluid motion enhances heat transfer by advection.
The Nusselt number is of paramount importance because it contains the heat transfer coefficient information. Indeed, one interpretation of Nusselt number is simply that of dimesionless heat transfer coefficient. In simplest terms, Nu is simply a dimensionless ehat transfer coefficient.