Combined thermal radiation and buoyancy-driven conjugate natural convection in an inclined porous enclosure filled with Carreau fluid

This investigation aims to determine the most effective heat transfer mechanism in an inclined enclosure by varying the inclination angle, position, and size of the heat sink and source. It also seeks to explain the fluid behavior and the interaction between thermal radiation and natural convection by examining how different factors influence momentum, fluid dynamics, and heat transfer characteristics. The finite volume method is employed in the present study to investigate steady, laminar, combined thermal radiation and buoyancy-driven conjugate natural convection heat transfer of a Carreau fluid saturated within a fully porous, inclined square enclosure tilted from [Formula: see text] to [Formula: see text] in [Formula: see text] increments. The enclosure includes a partially active heat sink and heat source. This analysis was conducted by varying the heat source length as [Formula: see text], 0.4, 0.6, 0.8, and 1, and the heat sink length as [Formula: see text], 0.4, 0.6, 0.8 and 1, across several arrangement locations over wide ranges of Carreau flow indexes ([Formula: see text]), Prandtl numbers ([Formula: see text]), thermal radiation parameters ([Formula: see text]), and medium porosities ([Formula: see text]) at a Rayleigh number [Formula: see text]. The Darcy–Brinkman model was adopted to model the flow within the porous metal foam using the local thermal nonequilibrium (LTNE) approach to represent energy transfer between the working fluid and the porous matrix. The simulation considered fixed values of the Darcy number [Formula: see text], solid-fluid interface heat transfer parameter [Formula: see text], and porous thermal conductivity ratio [Formula: see text]. The results of this parametric investigation indicated that the heat transfer mechanism within the enclosure was primarily influenced by the positioning and dimensions of the heat sink and heat source, as well as by the rheological properties and thermal radiation. The middle–middle arrangement resulted in the highest heat transfer rate, while the left–left arrangement produced the lowest. The Nusselt number of both the fluid and the solid matrix significantly increased with an increase in the heat sink length and a decrease in the heat source length. The optimal inclination angle for heat transfer was found to be [Formula: see text], whereas an angle of [Formula: see text] led to the lowest heat transfer. Additionally, increasing thermal radiation and porosity improved the average Nusselt number, especially at higher levels of radiation.