The natural convection within enclosures along with entropy generation minimization plays a crucial role in various applications, particularly when they involve the utilization of nanofluids and porous media. This phe- nomenon plays a crucial role in enhancing heat transfer, fluid flow, and overall system performance. By un- derstanding and optimizing the natural convection and entropy generation processes, it becomes possible to improve the efficiency and effectiveness of various thermal management systems, such as heat exchangers, electronic cooling systems, and renewable energy devices. Moreover, the integration of nanofluids and porous media introduces additional complexities and opportunities for enhancing heat transfer and fluid flow charac- teristics within enclosures. The current study investigates entropy generation (Sgen) and natural convection in a Z-staggered cavity filled with a porous media filled with a TiO2-water nanofluid. The symmetrical enclosures with dimensions of 0.6 L × 0.5 L are considered, and the media contain a porous material saturated with TiO2- water nanofluid. The wavy left and right vertical walls of the staggered enclosure were maintained hot and cold at temperatures (Th) and (Tc), respectively. All the straight horizontal walls were considered insulated and impermeable. The fundamental equations are solved using the Galerkin Finite Element Method (GFEM), and the results are described in detail. The key result was that raising the Rayleigh number (Ra) and nanoparticle volume fraction increased heat transmission. Specifically, increasing the Rayleigh number from (Ra = 105) to (Ra = 106) leads in an 80% increase in heat transfer. However, as the density of the nanofluid increases, the highest values of streamlines decrease. Decreasing the Darcy number (Da) educed the maximum values of the streamlines and average Nusselt number (Nu). Additionally, increasing the heat generation factor ( λ ) from ( λ= 0) to ( λ= 5) de- creases the Nusselt number by 30%. Furthermore, the most effective streamline value was achieved at an inclination angle ( γ ) of 60. Introduction Natural convection (N.C.) inside enclosures has attracted a signifi- cant amount of interest due to its many practical applications. Solar collectors are one of these applications [1]. Based on the studies and review articles, there are various enclosure shapes, such as square and rectangular enclosures, with the highest number of publications [2,3]. Other enclosure shapes include triangular, rhombus, parallelogrammic, tr

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