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Developing slip-flow and heat transfer in trapezoidal microchannels. (English) Zbl 1153.80326

Summary: Simultaneously developing velocity and temperature fields in the slip-flow regime are investigated numerically in trapezoidal microchannels with constant wall temperatures. A wide range of channel aspect ratios (\(0.25 \leqslant\alpha\leqslant 2\)) and side angles (\(30^\circ \leqslant \phi \leqslant 90^\circ\)) are considered in the Reynolds number range \(0.1 \leqslant Re \leqslant 10\). A control-volume based numerical method is used to solve the Navier-Stokes and energy equations with velocity-slip and temperature-jump at the walls. As characterized by the Knudsen number (\(Kn \leqslant 0.1)\), the effects of rarefaction on the key flow features are examined in detail. Major reductions in the friction and heat transfer coefficients are observed in the entrance region due to large amounts of velocity-slip and temperature-jump. In the fully developed region, the friction coefficient decreases strongly both with increasing \(Kn\) and aspect ratio but has a weaker dependence on the side angle. The heat transfer coefficient also decreases strongly with increasing rarefaction and aspect ratio; however, as the aspect ratio increases, its sensitivity to \(Kn\) decreases. Practical engineering correlations are also provided for fully developed flow friction and heat transfer coefficients.

MSC:

80A20 Heat and mass transfer, heat flow (MSC2010)
76D05 Navier-Stokes equations for incompressible viscous fluids
76M12 Finite volume methods applied to problems in fluid mechanics
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