Numerical analysis of permeability and Darcy effect in heat transfer of pyramid-shaped structure

In this work, a numerical investigation is conducted to examine the complex interplay of permeability, Darcy effect, and heat transfer within pyramid-shaped structures. The present study is intended to fully understand the influence of heat dissipation and the flow characteristics inside such geometries under different conditions. Advanced Computational method is employed to investigate the impact of the Darcy effect and different pyramid permeability on heat transfer mechanisms, revealing the intrinsic relationship between these parameters. The equations governing this research are based on fluid mechanics and heat transfer principles. The Navier-Stokes equation, energy equation, and Boussinesq approximation are used to represent fluid movement and temperature behavior. The continuity equation is used to account for mass conservation in the porous medium. The finite element numerical method is used in this research. In this work, another discussion to ponder is the correlation between heat transport characteristics and kinetic energy profiles subjected to a change in Rayleigh number concerning the pyramid-shaped geometry. The results lie in the guidance for streamlining the cooling mechanisms of pyramid-like conformations for the contributions of the role that permeability plays in designs that correlate to the behavior of flows involving the fluid of concern in a methodical directory making for their statistical elucidation and add to their growth to improve the architectural sensible designs and performance wherever they appear in an engineering atmosphere. Some of the major findings of this research include fundamental insight into optimizing heat dissipation in pyramid-shaped structures, which will have a broad impact on applications and emerging fields, such as architectural design, new classes of smart materials engineering, and thermal management systems. This study investigates the role of its volumetric permeability variations, the Darcy effect, and how their interplay impacts fluid flow and heat transfer in pyramid-shaped structures. This research paper takes a new and refined angle to the complexities of natural convective heat transfer in permeable enclosures with inlets and outlets. Significantly, the FEM technique enhances optimal heat transfer techniques within these containers that are useful in engineering solutions for various functions. This adds to the knowledge-based concept of efficient and sustainable heat transfer and fluid dynamic