I mentioned forced flow in my previous message affecting h because I was thinking of transition from laminar to turbulent flow, and this would be where the characteristic length, determined from the Reynolds numbers applies for your geometry, so yes that would be a macro geometry parameter. But I was not considering viscous friction even in natural convection that the Grashof number characterizes. But even this is really a forced flow from the bouyant force. And there are other fluid characterizations that is going to affect h over the surface. I'm sorry, but I have been focusing on the Mechanical field for over 20 years, and have forgotten a lot of this basic fluid analysis stuff, because I haven't had to worry about this for a while.
But the convection BC specified in Mechanical is a simple load/BC. The h you specify is a constant over the surface, so you can use the average over the entire surface. If you need to get real accurate for heat transfer to the fluid, you can run a fluid solver such as Fluent or CFX, and transfer those results to a structrual analysis by linking the Solution cell of the Fluent/CFX system to the Setup cell of the structural system.
This will allow you an accurate heat transfer coefficent and fluid bulk temperature at all points (and times) on the surface you choose for your imported convection load/BC.