Thermally Developing Flow and Heat Transfer in Elliptical Minichannels with Constant Wall Temperature

Laminar convective heat transfer of elliptical minichannels is investigated for hydrodynamically fully developed but thermal developing flow with no-slip condition. A three-dimensional numerical model is developed in different elliptical geometries with the aspect ratio varying from 0.2 to 1. The effect of Reynolds number (25 ≤ Re ≤ 2000) on the local Nusselt number is examined in detail. The results indicate that the local Nusselt number is a decreasing function of Reynolds number and it is sensitive to Reynolds number especially for Re less than 250. The effect of aspect ratio on local Nusselt number is small when compared with the effect of Reynolds number on local Nusselt number. The local Nusselt number is independent of cross-section geometry at the inlet. The maximum effect of aspect ratio on local Nusselt number arises at the transition section rather than the fully developed region. However, the non-dimensional thermal entrance length is a monotonic decreasing concave function of aspect ratio but a weak function of Reynolds number. Correlations for the local Nusselt number and the thermal developing length for elliptical channels are developed with good accuracy, which may provide guidance for design and optimization of elliptical minichannel heat sinks.