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In the present work, we examine to what degree the heat transfer can be described as developed on a macro-scale level in typical micro- and mini-channels with offset strip fin arrays subject to a uniform heat flux, considering flow entrance and side-wall effects. Full-scale numerical heat transfer simulations are conducted to determine the extent of the developed macro-scale heat transfer region within the arrays. We find that the onset point of developed heat transfer increases linearly with the P\'eclet number and channel width. However, the thermal development lengths remain limited relative to the overall channel length. Therefore, the local macro-scale heat transfer coefficient can be modeled by developed Nusselt number correlations with discrepancies below 25% in both the developed and developing heat transfer regions. We observe that quasi-developed heat transfer prevails over nearly the entire entrance region of the channel and significantly contributes to the main heat transfer characteristics, particularly the eigenvalues and amplitudes of the dominant temperature modes. Additionally, we analyze the impact of channel side walls on the temperature field's periodicity and the macro-scale temperature profile, which we characterize through an effective heat transfer coefficient. Our comprehensive numerical data covers various fin height-to-length ratios up to 1, fin pitch-to-length ratios up to 0.5, and channel aspect ratios ranging from 1/5 to 1/17, encompassing Reynolds numbers from 28 to 1224. Two sets of Prandtl number and thermal conductivity ratio are investigated, corresponding to the combinations of copper/air, and copper/water., Comment: 61 pages, 19 figures

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., Comment: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Physics of Fluids 33, 103610 (2021) and may be found at https://pubs.aip.org/aip/pof/article/35/7/073611/2903243/Developed-and-quasi-developed-macro-scale-flow-in . 47 pages, 25 figures

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. 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., Comment: This article may be downloaded for personal use only. Any other use requires prior permission of the author and Elsevier Publishing. This article appeared in International Journal of Heat and Mass Transfer 195, 123145 (2022) and may be found at https://www.sciencedirect.com/science/article/pii/S0017931022006160; 63 pages, 21 figures, 3 tables

Existing energy balance models, which estimate maximum droplet spreading, insufficiently capture the droplet spreading from low to high Weber and Reynolds numbers and contact angles. This is mainly due to the simplified definition of the viscous dissipation term and incomplete modeling of the maximum spreading time. In this particular research, droplet impact on a smooth sapphire surface is studied for seven glycerol concentrations between 0% - 100%, and 294 data points are acquired using high-speed photography. Fluid properties such as density, surface tension, and viscosity are also measured. For the first time according to the authors' knowledge, we incorporate the fluid viscosity in the modeling of the maximum spreading time based on the recorded data. We also estimate the characteristic velocity of the viscous dissipation term in the energy balance equation. These viscosity-based characteristic scales help to formulate a more comprehensive maximum droplet spreading model. Thanks to this improvement, our model successfully fits the data available in the literature for various fluids and surfaces compared to the existing models.

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., Comment: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Physics of Fluids 33, 103610 (2021) and may be found at https://aip.scitation.org/doi/abs/10.1063/5.0067652 49 pages, 18 figures, 3 tables

Even a small fraction of nanoparticles in fluids affects the splashing behavior of a droplet upon impact on a smooth surface. Nanofluid drop impact onto a smooth sapphire substrate is experimentally investigated over wide ranges of Reynolds ($10^2<\mathrm{Re}<10^4$) and Weber ($50<\mathrm{We}<500$) numbers for three nanofluid mass concentrations (0.01%, 0.1%, 1%) using high-speed photography. Nanofluids are prepared by diluting a commercial Al$_2$O$_3$-water nanofluid in aqueous glycerol solutions without dispersants. In total, 30 samples are prepared and 1799 data points are acquired. Every sample is experimentally characterized prior to droplet impact measurements in terms of stability, density, viscosity, and surface tension to demonstrate the observed outcomes on the We-Re maps. Each droplet impact condition is repeated at least 3 times to ensure good repeatability. The non-monotonic behavior of the spreading-to-splashing transition remains the same for nanofluids. However, nanofluids influence this boundary by promoting splashing at low Reynolds numbers. We explain this behavior by increased lamella spreading speed and lift during the lamella spreading stage. Finally, we develop an empirical correlation which describes the splashing threshold dependency on nanoparticle concentration for the first time., Comment: Supplementary Information included