Effect of obstacle shape on flow and heat transfer in a partially heated channel: A finite element study

This paper numerically investigates the influence of the shape of the obstacle on the fluid flow and heat transfer in a partially heated rectangular channel. We consider four geometries with the same area, square, circular, elliptical and equilateral triangular, under the same flow and thermal conditions. The dimensionless governing equations are solved by finite element method for a fixed Reynolds number ( Re = 20 ) and Prandtl number ( Pr = 0.71 ). The effect of obstacle shape and orientation on fluid flow and heat transfer are assessed by analyzing velocity contours, isotherms, drag coefficient, lift coefficient, average Nusselt number and total heat transfer rate. The results show that the triangular obstacle induces the highest drag and the poorest heat transfer, whereas the circular obstacle has the best thermal performance when compared to the surface-averaged Nusselt number. However, the total heat transfer rate is maximum for the triangular obstacle due to its large perimeter. Hence it is a trade-off between surface efficiency and global thermal exchange. The elliptical obstacle provides the best compromise between drag reduction and thermal performance. A performance index P I = N u a v g / C D at β = 0 ° is introduced to quantify this trade-off, with the elliptical obstacle yielding the highest P I ≈ 0.0705 . The equal-area comparative study confirms that the obstacle geometry has a significant effect on the wake development, drag features and heat transfer performance and thus is important for optimal design of compact heat exchangers and thermal management systems for electronic devices.