Is it possible to consider natural convection as a case of forced convection with zero velocity? When calculating the Nusselt number we have to use Reynolds number if there is forced convection, while Grashof number is used in case of natural convection. I was wondering if and why could be a big mistake to compute the Nusselt number considering only the Reynolds formulation, using zero velocity if there is natural convection.
 A: Probably all of the real-world convective heat transfer equations are empirical in nature, because most of them involve turbulence, and physicists don't yet know how to mathematically model turbulence.  As such, using one convective heat transfer equation to model convective heat transfer for a phenomenon for which it was not formulated, probably means that you are applying your convective heat transfer equation to a regime for which data either wasn't taken, was somewhat lacking, or completely failed because it doesn't account for either laminar flow or turbulent flow.  Unless you can find published data which uses your equation in the way that you intend to use it, consider the probability of having an unknown amount of error in your result.
A: What David White said - plus the fact that Re is the ratio of inertial force to viscous force and Gr is the ratio of buoyancy to viscous force, but inertial force and buoyancy are very different things physically, even though they are both "forces".
Aside from measuring "how much volume of fluid" is involved in the process and its viscosity, Gr depends on the coefficient of thermal expansion of the fluid and the temperature difference between different parts of it. Re depends on the fluid's density and velocity. There is nothing much in common between those properties.
