Natural convection of nanofluid flow in a porous enclosure with isothermal heated plate: A Tiwari and Das nanofluid model

· Analysis of natural convection in porous enclosures with Cu-water nanofluids. · Numerical evaluation of Rayleigh and Darcy numbers on thermal performance. · Study of plate configurations: horizontal, inclined, and vertical. · Optimization insights for heat transfer applications in engineering. Nanofluids have garnered significant research interest due to their superior thermal properties, which enhance heat transfer efficiency in various engineering applications. In particular, studying buoyancy-driven nanofluid flow in enclosures with permeable media is crucial for optimizing thermal management systems. However, limited studies have explored the impact of different heated plate orientations on thermofluidic behavior within a permeable medium. The present study numerically investigates the buoyancy-driven flow of Cu-water nanofluid in a square enclosure containing a centrally positioned heated plate immersed in a permeable medium. The objective is to analyze the effects of different plate configurations—(Case I) horizontal, (Case II) inclined, and (Case III) vertical—on thermal distribution and fluid flow dynamics. The enclosure consists of two opposing cold walls and two adiabatic walls, with gravitational effects acting vertically downward. The Tiwari and Das nanofluid model is employed to capture the thermal behavior and flow characteristics. The governing partial differential equations are converted into their dimensionless form and solved using the vorticity-stream function formulation with the finite difference method. The research fills a gap in understanding how plate orientation influences heat transfer and flow characteristics in nanofluid-permeable systems. Computational results demonstrate that increasing the Rayleigh number (10 3 < Ra < 10 6 ) and Darcy number (10 −4 < Da < 10 −1 ) significantly enhances convective heat transfer and accelerates fluid motion. Additionally, the nanofluid volume fraction (Φ) plays a crucial role in improving thermal performance. The results reveal that increasing the Rayleigh number from 10 3 to 10 6 enhances the average Nusselt number by approximately 357% to 425%, significantly improving the heat transfer rate. Similarly, as the Darcy number increases from 10 −4 to 10 −1 , the heat transfer rate rises by 167% to 188%, depending on the plate orientation. Among the analyzed cases, the inclined plate configuration exhibits superior heat transfer enhancement due to optimized buoyancy-driven flow patterns. The findings of this study have practical applications in thermal energy storage, cooling of electronic devices, solar collectors, and advanced heat exchanger designs. Understanding the interplay between plate orientation, permeability, and nanofluid properties can aid in the development of more efficient thermal management systems across various industrial sectors.