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This study aims to investigate entropy generation through natural convection and examine heat transfer properties within a partially heated and cooled enclosure influenced by an angled magnetic field. The enclosure, subjected to consistent heat production or absorption, contains a porous medium saturated with a hybrid nanofluid blend of Cu-Fe₃O₄ and MoS₂-Fe₃O₄.

The temperature and velocity equations are converted to a dimensionless form using suitable non-dimensional quantities, adhering to the imposed constraints. To solve these transformed dimensionless equations, the finite-difference method, based on the MAC (Marker and Cell) technique, is used. Comprehensive numerical simulations address various control parameters, including nanoparticle volume fraction, Rayleigh number, heat source or sink, Darcy number, Hartmann number and slit position. The results are illustrated through streamlines, isotherms, average Nusselt numbers and entropy generation plots, offering a clear visualization of the impact of these parameters across different scenarios.

Results obtained show that the Cu-Fe₃O₄hybrid nanofluid exhibits higher entropy generation than the MoS₂-Fe₃O₄ hybrid nanofluid when comparing them at a Rayleigh number of 10⁶ and a Darcy number of 10^–1. The MoS₂ hybrid nanofluid demonstrates a low permeability, as evidenced by an average Darcy number of 10^–3, in comparison to the Cu hybrid nanofluid. The isothermal contours for a Rayleigh number of 10⁴are positioned parallel to the vertical walls. Additionally, the quantity of each isotherm contour adjacent to the hot wall is being monitored. The Cu and MoS₂ nanoparticles exhibit the highest average entropy generation at a Rayleigh number of 10⁵ and a Darcy number of 10^–1, respectively. When a uniform heat sink is present, the temperature gradient in the central part of the cavity decreases. In contrast, the absence of a heat source or sink leads to a more intense temperature distribution within the cavity. This differs significantly from the scenario where a uniform heat sink regulates the temperature.

The originality of this study is to examine the generation of entropy in natural convection within a partially heated and cooled enclosure that contains hybrid nanofluids. Partially heated corners are essential for optimizing heat transfer in a wide range of industrial applications. This enhancement is achieved by increasing the surface area, which improves convective heat transfer. These diverse applications encompass fields such as chemical engineering, mechanical engineering, surface research, energy production and heat recovery processes. Researchers have been working on improving the precision of heated and cold corners using various methods, such as numerical, experimental and analytical approaches. These efforts aim to enhance the broad utility of these corners further.

Thermal energy storage systems use thermal energy to elevate the temperature of a storage substance, enabling the release of energy during a discharge cycle. The storage or retrieval of energy occurs through the heating or cooling of either a liquid or a solid, without undergoing a phase change, within a sensible heat storage system. In a sensible packed bed thermal energy storage system, the structure comprises porous media that form the packed solid material, while fluid occupies the voids. Thus, a cavity, partially filled with a fluid layer and partially with a saturated porous layer, has become important in the investigation of natural convection heat transfer, carrying significant relevance within thermal energy storage systems. Motivated by these insights, the current investigation delves into the convection heat transfer driven by buoyancy and entropy generation within a partially porous cavity that is differentially heated, vertically layered and filled with a hybrid nanofluid.

The investigation encompasses two distinct scenarios. In the first instance, the porous layer is positioned next to the heated wall, while the opposite region consists of a fluid layer. In the second case, the layers switch places, with the fluid layer adjacent to the heated wall. The system of equations for fluid and porous media, along with appropriate initial and boundary conditions, is addressed using the finite difference method. The Tiwari–Das model is used in this investigation, and the viscosity and thermal conductivity are determined using correlations specific to spherical nanoparticles.

Comprehensive numerical simulations have been performed, considering controlling factors such as the Darcy number, nanoparticle volume fraction, Rayleigh number, bottom slit position and Hartmann number. The visual representation of the numerical findings includes streamlines, isotherms and entropy lines, as well as plots illustrating average entropy generation and the average Nusselt number. These representations aim to provide insight into the influence of these parameters across a spectrum of scenarios.

The computational outcomes indicate that with an increase in the Darcy number, the addition of 2.5% magnetite nanoparticles to the GO nanofluid results in an enhanced heat transfer rate, showing increases of 0.567% in Case 1 and 3.894% in Case 2. Compared with Case 2, Case 1 exhibits a 59.90% enhancement in heat transfer within the enclosure. Positioning the porous layer next to the partially cooled wall significantly boosts the average total entropy production, showing a substantial increase of 11.36% at an elevated Rayleigh number value. Positioning the hot slit near the bottom wall leads to a reduction in total entropy generation by 33.20% compared to its placement at the center and by 33.32% in comparison to its proximity to the top wall.