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The flow in channels of microdevices is usually in the developing regime. Three-dimensional laminar flow characteristics of a nanofluid in microchannel plate fin heat sinks are investigated numerically in this paper. Deionized water and Al2O3–water nanofluid are employed as the cooling fluid in our work. The effects of the Reynolds number (100 < Re < 1000), channel aspect ratio (0 < ε < 1), and nanoparticle volume fraction (0.5% < Φ < 5%) on pressure drop and entropy generation in microchannel plate fin heat sinks are examined in detail. Herein, the general expression of the entropy generation rate considering entrance effects is developed. The results revealed that the frictional entropy generation and pressure drop increase as nanoparticle volume fraction and Reynolds number increase, while decrease as the channel aspect ratio increases. When the nanoparticle volume fraction increases from 0 to 3% at Re = 500, the pressure drop of microchannel plate fin heat sinks with ε = 0.5 increases by 9%. It is demonstrated that the effect of the entrance region is crucial for evaluating the performance of microchannel plate fin heat sinks. The study may shed some light on the design and optimization of microchannel heat sinks.

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Developing a three-dimensional laminar flow in the entrance region of rectangular microchannels has been investigated in this paper. When the hydrodynamic development length is the same magnitude as the microchannel length, entrance effects have to be taken into account, especially in relatively short ducts. Simultaneously, there are a variety of non-continuum or rarefaction effects, such as velocity slip and temperature jump. The available data in the literature appearing on this issue is quite limited, the available study is the semi-theoretical approximate model to predict pressure drop of developing slip flow in rectangular microchannels with different aspect ratios. In this paper, we apply the lattice Boltzmann equation method (LBE) to investigate the developing slip flow through a rectangular microchannel. The effects of the Reynolds number (1 < Re < 1000), channel aspect ratio (0 < ε < 1), and Knudsen number (0.001 < Kn < 0.1) on the dimensionless hydrodynamic entrance length, and the apparent friction factor, and Reynolds number product, are examined in detail. The numerical solution of LBM can recover excellent agreement with the available data in the literature, which proves its accuracy in capturing fundamental fluid characteristics in the slip-flow regime.

The entrance region constitutes a considerable fraction of the channel length in miniaturized devices. Laminar slip flow in microchannel plate fin heat sinks under hydrodynamically developing conditions is investigated semi-analytically and numerically in this paper. The semi-analytical model for the pressure drop of microchannel plate fin heat sinks is obtained by solving the momentum equation with the first-order velocity slip boundary conditions at the channel walls. The simple pressure drop model utilizes fundamental solutions from fluid dynamics to predict its constitutive components. The accuracy of the model is examined using computational fluid dynamics (CFD) simulations and the experimental and numerical data available in the literature. The model can be applied to either apparent liquid slip over hydrophobic and superhydrophobic surfaces or gas slip flow in microchannel heat sinks. The developed model has an accuracy of 92 percent for slip flow in microchannel plate fin heat sinks. The developed model may be used to predict the pressure drop of slip flow in microchannel plate fin heat sinks for minimizing the effort and expense of experiments, especially in the design and optimization of microchannel plate fin heat sinks.