The heat transfer across the tubes of heat exchangers is limited by the
'boundary layer' on each side. This is a thin layer of water/fluid next to
the tube wall that doesn't move as fast as the rest of the fluid. With
turbulent flow in the tubes, this thin layer has a parabolic profil as you
move from the bulk fluid, into the layer and finally touching the wall.
The heat transfer coefficient through this layer is a function of the
thermal conductivity of the fluid, the visocity of the fluid, and the bulk
velocity of the fluid.
*IN GENERAL*, the higher the fluid velocity, the thinner the layer and the
better the heat transfer. The limits on fluid velocity though are too much
erosion of the tubing and cost of pumping power to achieve high velocities.
Most industrial heat exchangers for water strive for speeds of 5 to 7 feet
per second. Less than this and heat transfer suffers, more than this and
erosion and pumping costs rise sharply with not much better heat transfer.
There are of course several experimental surface finishes that have been
tried in order to break up this laminar layer. Scored rings, 'dimples' on
the tube wall and spiral inserts to 'spin' the water in the tube come to
mind. But plain tubes are still quite common for a variety of reasons (cost
and cleanability being two).
AFAIK there is no 'first principles' formulation for this. All the work in
this area is empirical from test beds and industry experience (i.e.