  In this work, the friction factor for steady periodically developed flow
through micro-and mini-channels with periodic arrays of offset strip fins is
analyzed. The friction factor is studied numerically on a unit cell of the
array for Reynolds numbers ranging from 1 to 600, and fin height-to-length
ratios below 1. It is shown that the friction factor correlations from the
literature, which primarily focus on larger conventional offset strip fin
geometries in the transitional flow regime, do not predict the correct trends
for laminar flow in micro-and mini-channels. Therefore, a new friction factor
correlation for micro-and mini-channels with offset strip fin arrays is
constructed from an extensive set of numerical simulations through a
least-squares fitting procedure. The suitability of this new correlation is
further supported by means of the Bayesian approach for parameter estimation
and model validation. The correlation predicts an inversely linear relationship
between the friction factor and the Reynolds number, in accordance with our
observation that a strong inertia regime prevails over nearly the entire range
of investigated Reynolds numbers. Yet, through a more detailed analysis, also
the presence of a weak inertia regime and a transitional regime is identified,
and the transitions from the strong inertia regime are quantified by means of
two critical Reynolds numbers. Finally, the new correlation also incorporates
the asymptotic trends that are observed for each geometrical parameter of the
offset strip fin array, and whose origins are discussed from a physical
perspective.
