Developing slip-flow and heat transfer in trapezoidal microchannels

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 ⩽ α ⩽ 2) and side angles (30° ⩽ ϕ ⩽ 90°) are considered in the Reynolds number range 0.1 ⩽ Re ⩽ 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 ⩽ 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.