Laminar flow and heat transfer in the entrance region of elliptical minichannels

Abstract

Three-dimensional laminar flow and convective heat transfer for T, H1 and H2 thermal boundary conditions at the entrance region in elliptical minichannels have been investigated numerically. The effects of Reynolds number (25 ≤ Re ≤ 2000) and aspect ratio (0.2 ≤ ε ≤ 1) on the friction coefficient, Nusselt number and the entrance length are examined in detail. The results demonstrate that the apparent friction factor and Reynolds number product and the local Nusselt number are both weak function of the cross-sectional geometry but quite sensitive to Reynolds number at the entrance region. The entrance lengths, including the hydrodynamic and the thermal entrance lengths, are both decreasing functions of Reynolds number and aspect ratio. In the entrance region, the velocity overshoots near the wall results in strong pressure gradient and the temperature distribution is almost the same for H1 and H2 conditions. The local maximum of the pressure first arises at the end of major semi-axis and thereafter moves towards the channels core as the fluid flows in the axial direction. When close to the fully developed region, the inhomogeneous cross-sectional temperature field in H2 boundary condition deteriorates the heat transfer performance especially for the elliptical minichannel with small aspect ratios. General correlations are proposed for the first time for the apparent friction coefficients, as well as the entrance lengths for elliptical channels.