If you are dealing with transient convection, I would imagine that a numerical solution is necessary. If you have access to a CFD package, it would be relatively simple to build a few models and run them with varying Reynolds numbers. You could try doing the numerics by "hand" (self programmed) but that would get quite complicated. That would involv building a node network, setting up the Navier-Stokes equations at each node, boundary and initial conditions, and using which ever numerical method you believe would be accurate to propagate through your model.