A comprehensive study on the power-law fluid flow around and through a porous cylinder with different aspect ratios

This paper presents a numerical investigation of power-law fluid flow past and through elliptical porous cylinder, considering heat transfer effects. The study covers a wide range of parameters, including Reynolds number, power-law index, cylinder aspect ratio and Darcy number. The wake pattern, streamline distribution, drag coefficient, pressure distribution, and Nusselt number are analyzed comprehensively for various cases. Within the investigated parameter range, four distinct vortices are observed: an external vortex separated from the cylinder, an external vortex attached to the cylinder, a boundary vortex partially inside and outside the cylinder, and an internal vortex entirely inside the cylinder. The occurrence of the external and separated vortex is limited to AR = 0.2 and =10−3 , while the internal and boundary vortices are exclusively observed at AR = 2.0. Additionally, increasing the aspect ratio of the elliptical cylinder results in shorter vortices at a given Reynolds and Darcy number. For example, at Re = 40 and Da=10−4, vortex lengths decrease from 5 to 0.6 with increasing aspect ratio from 0.2 to 2. Furthermore, by decreasing aspect ratio, the drag coefficient generally increases and the Nusselt number decreases from 0.2 to 1, but this trend reverses as the aspect ratio rises from 1 to 2.