Abstract
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.
Highlights
Over the last two decades, considerable research has been devoted to flow through micro- and mini-channels with a periodic array of solid fin structures (Refs. 1–4)
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 minichannels
Through a more detailed analysis, 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
Summary
Over the last two decades, considerable research has been devoted to flow through micro- and mini-channels with a periodic array of solid fin structures (Refs. 1–4). It was based on experimental pressure drop measurements for nine different types of heat transfer surfaces, all consisting of periodic fin arrays, of which only three were offset strip fin geometries (Ref. 27) As it can be seen from the range of Reynolds numbers and fin height-to-length ratios, the experimental data in Manson’s study are limited to flow regimes beyond the transition toward vortex shedding and to larger conventional fin geometries. In this work, the friction factor for the steady laminar flow regime inside offset strip fin arrays is re-investigated numerically and correlated with respect to the geometrical fin parameters for microand mini-channel applications (h=l < 1) In these applications, the flow is expected to become periodically developed after a short distance from the inlet (Ref. 35). Its accuracy is evaluated with respect to our own data as well as the experimental data from the literature
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