Onset of fully developed flow in a channel

[sanka]

Suppose we have a case of laminar flow in a channel. For a case of constant flow rate, at some point downstream of the channel inlet, the hydrodynamic and thermal boundary layers will merge and simultaneously developing flow will transition to full-developed flow (not necessarily at the same time). At this point the Nusselt number will be constant.

HOWEVER, am I correct in saying that if the flow rate is increased, the onset of fully-developed flow will occur at some point earlier in the channel than it did for the lower flow rate case? My reasoning for this is that at the higher flow rate, the velocity increases and the momentum diffuses quicker through the boundary layer, causing it to merge earlier in the channel? By the same reasoning, heat will diffuse quicker thorugh the thermal BL, causing it to merge earlier.

This was always my understanding but I was just reading a paper relating Nusselt No. to Reynolds No., which shows the fully developed region occurring at the lower flow rates and the developing region at the higher flow rates.

Thanks in advance for any help

 

[boneh3ad]

Is this paper you are reading discussing Newtonian fluids?

 

[sanka]

Yep, it is.

It's okay though, I've managed to figure it out myself. For laminar flow, the onset of fully developed flow occurs at the lower Reynolds numbers because viscous forces tend to dominate and this leads to a thicker BL, causing it to merge earlier in channels/pipes. As the Re No. is increased (but still staying Laminar), the inertial forces take over and the region where viscous effects are important (the BL) is less. Thus, boundary layers do not merge as early in the channel and the transition to fully-developed flow occurs further downstream.