Computational analysis of power-law fluids for convective heat transfer in permeable enclosures using Darcy effects

Natural convection is a complex environmental phenomenon that typically occurs in engineering settings in porous structures. Shear thinning or shear thickening fluids are characteristics of power-law fluids, which are non-Newtonian in nature and find wide-ranging uses in various industrial processes. Non-Newtonian fluid flow in porous media is a difficult problem with important consequences for energy systems and heat transfer. In this paper, convective heat transmission in permeable enclosures will be thoroughly examined. The main goal is to comprehend the intricate interaction between the buoyancy-induced convection intensity, the porosity of the casing, and the fluid's power-law rheology as indicated by the Rayleigh number. The objective is to comprehend the underlying mechanisms and identify the ideal conditions for improving heat transfer processes.The problem's governing equations for a scientific investigation are predicated on the concepts of heat transport and fluid dynamics. The fluid flow and thermal behavior are represented using the energy equation, the Boussinesq approximation, and the Navier-Stokes equations. The continuity equation in a porous media represents the conservation of mass. Finite Element Analysis is the numerical method that is suggested for this challenging topic since it enables a comprehensive examination of the situation. The results of the investigation support several important conclusions. The power-law index directly impacts heat transmission patterns. A higher Rayleigh number indicates increased buoyancy-induced convection, which increases the heat transfer rates inside the shell. The porosity of the medium significantly affects temperature gradients and flow distribution, and it is most noticeable when permeability is present. The findings show how, in the context of porous media, these parameters have complicated relationships with one another.