Nusselt number is the ratio of the resistance to conductive transport to that of convective transport.  Thus, Re number plays a role but so does Pr (Ra is also a function of Pr) which is the ratio of the momentum diffusion to thermal diffusion.  The question can only be answered depending on the geometry and whether it is a flow over an object or through a conduit. Also you need to consider whether it is developing flow or fully developed flow.  Your conditions seem to indicate a range from laminar to turbulent region.  In the laminar region the Nusselt number is a constant under fully developed conditions and is dependent on the geometry

Regards

http://en.wikipedia.org/wiki/Nusselt_number

There exists numerous correlations between dimensionless characteristic numbers such as Nu, Re, Ra, Pr ...

The kind of correlations and the coefficients involved strongly depend on the geometry of the problem considered.

Maybe you could give us some more details ?

Look for Sheremet's studies. He investigate conjugate heat transfer and analize influence of average Nusselt number from Ra, Re etc

Nusselt number is the ratio of the resistance to conductive transport to that of convective transport.  Thus, Re number plays a role but so does Pr (Ra is also a function of Pr) which is the ratio of the momentum diffusion to thermal diffusion.  The question can only be answered depending on the geometry and whether it is a flow over an object or through a conduit. Also you need to consider whether it is developing flow or fully developed flow.  Your conditions seem to indicate a range from laminar to turbulent region.  In the laminar region the Nusselt number is a constant under fully developed conditions and is dependent on the geometry

There exists different empirical correlations based on geometries between Nusselt number (Nu),  Reynolds number(Re), Prandtl number (Pr) and the Rayleigh Number (Ra) depending upon how the fluid is initiated. The average Nu is a function of Ra and Pr for a free (natural) convection problem and is a function of Re and Pr for a forced convection problem.

Free or natural convection: A natural process such as the buoyancy effect (variations in density induces the velocity field) causes the fluid motion.

Forced convection: An external source such as a pump or a fan is used to force the fluid to flow over or within a geometry.

Take a look at what is written in Wikipedia: http://en.wikipedia.org/wiki/Nusselt_number

In my experience, many times you use these correlations (between Nu and Re number) in order to calibrate/evaluate or check different numerical models in problems involving turbulent flows and natural/forced heat transfer. For complex problems, in general and depending on the problem to study, these correlations are obtained from experiments (e.g., heat transfer in impinging jets or double glazed facanes buildings).....These correlations help to put in order a lot of experimental results, in a compact way and then using those data to compare the obtained numerical results. You can check the theory to obtain these non-dimensional number in White's book, 'viscous flow', for example.