Exploration of Ostwald-de Waele non-Newtonian nanofluid subject to Lorentz force, and entropy optimization in a corrugated porous medium enclosure: Galerkin finite element analysis

In this work, we combine the rheological and nanofluidic properties of the fluid in a hermetically sealed chamber. The work was accomplished digitally using Galerkin finite element technique. The work aims to know the effect of these complex properties of the fluid on the quality of thermal activity of the type of free convection. The fluid of this study is composed of a complex fluid with viscosity added to a proportion of nanoparticles. As for the room, it has ripples on the walls and an elliptical obstacle in the middle. The thermal transfer studied here takes place between the hot elliptical obstacle and the cold walls of the room. based on this proposition, the issues studied here are: undulation number (N = 1, 2, 3, and 4); Power – law index (n = 0.8, 1, 1.2, and 1.4); Darcy number (Da = 10^-2, 10^-3, 10^-4, and 10^-5); Rayleigh number (Ra = 10³, 10⁴, 10⁵, and 10⁶); Hartmann number (Ha = 0, 25, 50, and 100); and the rotational angle of elliptic cylinder (γ = 0, 30, 60, and 90°). The finding shows that the Nusselt number (Nu), is augmented when these parameters increase: Da (for all values of Ra) and γ (large Ra). At the height's Ra number (1 0 ⁶) it was observed that increasing the Ha number and Da number reduced Nu by 18 % and 65 %, respectively. While Nu was enhanced by 129 % when increasing Da number at Ra = 10⁶.