Nusselt number for steady periodically developed heat transfer in micro- and mini-channels with arrays of offset strip fins subject to a uniform heat flux

• Published in: International journal of heat and mass transfer Vol. 195; p. 123145
• Main Authors: Vangeffelen, A., Buckinx, G., De Servi, C., Vetrano, M.R., Baelmans, M.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2022
• Subjects: Bayesian inference; Correlation; Nusselt number; Offset strip fin; Periodically developed heat transfer; Unit cell; Correlation; Unit cell; Nusselt number; Periodically developed heat transfer; Bayesian inference; Offset strip fin
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2022.123145

•The available Nusselt number correlations exhibit discrepancies of 40% to 90%.•New Nusselt number correlations for air and water predict our 2282 simulations with 4% accuracy.•The Nusselt number increases linearly with the Reynolds number due to strong flow inertia.•The spatial independence of the adopted Nusselt number is contrasted with the Nusselt numbers from the literature. In this work, the Nusselt number is examined for periodically developed heat transfer in micro- and mini-channels with arrays of offset strip fins, subject to a constant heat flux. The Nusselt number is defined on the basis of a heat transfer coefficient which represents the spatially constant macro-scale temperature difference between the fluid and solid during conjugate heat transfer. Its values are determined numerically on a single unit cell of the array for Reynolds numbers between 1 and 600 and fin height-to-length ratios below 1. Two combinations of the Prandtl number and the thermal conductivity ratio are selected, corresponding to air and water. It is shown that the Nusselt number correlations from the literature mainly apply to air in the transitional flow regime in larger conventional channels if the wall temperature remains uniform. As a result, they do not correctly capture the observed trends for the Nusselt number in micro- and mini-channels subject to a constant heat flux. Therefore, new Nusselt number correlations, obtained through a least-squares fitting of 2282 numerical simulations, are presented for air and water. The suitability of these correlations is assessed via the Bayesian approach for parameter estimation and model validation. The correlations respect the observed asymptotic trends and limits of the Nusselt number for all the geometrical parameters of the offset strip fins. In addition, they predict a linear dependence of the Nusselt number on the Reynolds number, in good agreement with the data from this work. Nevertheless, a detailed analysis reveals a more complex scaling of the Nusselt number with the Reynolds number, closely related to the underlying flow regimes, particularly the weak and strong inertia regimes. Finally, through 62 additional simulations, the influence of the material properties on the Nusselt number is illustrated and compared to the available literature.