  We investigate to what degree the steady laminar flow in typical micro- and
mini-channels with offset strip fin arrays can be described as developed on a
macro-scale level, in the presence of channel entrance and side-wall effects.
Hereto, the extent of the developed and quasi-developed flow regions in such
channels is determined through large-scale numerical flow simulations. It is
observed that the onset point of developed flow increases linearly with the
Reynolds number and channel width, but remains small relative to the total
channel length. Further, we find that the local macro-scale pressure gradient
and closure force for the (double) volume-averaged Navier-Stokes equations are
adequately modeled by a developed friction factor correlation, as typical
discrepancies are below 15% in both the developed and developing flow region.
We show that these findings can be attributed to the eigenvalues and mode
amplitudes which characterize the quasi-developed flow in the entrance region
of the channel. Finally, we discuss the influence of the channel side walls on
the flow periodicity, the mass flow rate, as well as the macro-scale velocity
profile, which we capture by a displacement factor and slip length coefficient.
Our findings are supported by extensive numerical data for fin height-to-length
ratios up to 1, fin pitch-to-length ratios up to 0.5, and channel aspect ratios
between 1/5 and 1/17, covering Reynolds numbers from 28 to 1224.

Fluid Dynamics