Free convective flow of Ostwald-de Waele fluid in a Π-shaped cavity with heated strip and lateral wall cooling

This paper studies the free convection of Ostwald-de Waele fluid in a Π-shaped chamber with a Π-shaped heated strip at the lower mid-section. The upper wall and the remaining sections of the lower wall are thermally insulated, while the lateral walls are maintained at a low temperature. The primary objective is to identify the optimal power-law index ( n ) and the geometric configurations of the strip that yield enhanced heat transfer. Furthermore, the impact of Rayleigh number ( Ra ) on the thermal performance of the cavity in that optimum condition is to be investigated. The Galerkin finite element approach has been employed to resolve the governing equations and auxiliary conditions. Within the study, the power-law index of the Ostwald-de Waele fluid has been systematically varied (0.6 ≤  n  ≤ 1.4). At the same time, the variations in the non-dimensional height (0.1 ≤  ζ  ≤ 0.5) and width (0.1 ≤  ε  ≤ 0.3) of the heated strip have been explored. The results show improved thermal performance with a growth in Rayleigh number, particularly when n  < 1. The average Nussetl number for n  = 0.6 at Ra  = 10 6 is approximately 14 % higher than for n  = 1.4. The findings further indicate an increment of 35 % in the heat transfer rate when the height of the strip decreases from 0.5 to 0.1. This investigation provides valuable insights into the natural convection phenomena of Ostwald-de Waele fluid in complex geometries, paving the way for advanced thermal management techniques in various engineering applications.