On Thermal Convection Effect due to Fluid-Blocks of Varying Shapes Embedded in a Porous Medium

Abstract

This paper investigates the effect of natural convection heat transfer and fluid flow due to variations in the shape of fluid blocks embedded within a differentially heated porous enclosure. Such configurations are significant in thermal and engineering applications, including nuclear power plants, building insulation, and thermal management systems. To address design and geometric constraints, three common fluid-block shapes-Ťtriangular, square, and hexagonal-Ťare analyzed. Using the Darcy flow model for the porous medium, simulations are conducted to evaluate the stream function, temperature distribution, and Nusselt number across a range of parameters: block size ($0.05\le B\le 0.25$), conductivity ratio ($0.5\le \kappa \le 10$), triangular block position ($X,Y$), Rayleigh number ($10^3\le Ra\le 10^5$), Darcy number ($10^{-3}\le Da\le 10^{-1}$), and Prandtl number ($0.1\le Pr\le 100$). Key findings reveal that block size and position significantly impact convection heat transfer: for instance, a centrally positioned large hexagonal block reduces the average Nusselt number by up to 70%, while triangular blocks near the enclosure corners enhance heat transfer by 25%–30%. These results have practical implications for optimizing thermal management designs in porous systems, highlighting the importance of fluid-block geometry and positioning in controlling heat transfer.