[EMC2]

Boundary layer thickness - is proportional to flow rate and is also affected by the surface. Both the flow regimine (laminar vs turbulent) and pipe size affect the heat transfer coefficient (film coefficient h).

For a purely laminar flow, the film coefficient h is inversely proportional to the hydraulic pipe diameter. Double this diameter and you halve the film coefficient. The larger the diameter, the worse off you are regarding heat transfer.

The greater the turbulence (and the less laminar) the flow, the higher the film coefficient h is, and thus the better the heat transfer. Turbulence greatly aids heat transfer

Based strictly on pipe/channel size (NO structural parametrics such as surface roughness to alter the flow regime one way or the other), yes there is a ratio. What you're really talking about here is the Reynolds number Re. The equation is:

Re = ( D * p * v ) / u

where D is the hydraulic pipe diameter, p is the fluid's density, v is the fluid's mean velocity, and u is the fluid's dynamic viscosity. (say that fast 3 times) Note that they hydraulic pipe diameter is NOT the diameter of the pipe. Flows with Reynolds numbers below ~2300 are considered to be laminar.

Also, turns in a pipe increase local turbulence (but increase pressure drop, although not at the same rate).

<edit: big fingers + speed = typos>