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This study investigates the utilization of a trapezoidal cavity with a corrugated bottom wall containing a Carreau hybrid nanofluid composed of water, aluminum, and copper nanoparticles. A heated, rotating cylinder is placed at the center of the enclosure in the presence of an external magnetic field. The impact of Forchheimer and Brinkman porous medium models on the hybrid nanofluid is examined. Three different inlet–outlet placement configurations are considered to investigate their influence on heat transfer. The governing equations for fluid flow and heat transfer are solved numerically. Through simulations, a range of flow-controlling variables is systematically adjusted, including the Darcy number, Reynolds number, Hartmann number, nanoparticle volume fraction, undulation on the hot bottom wall, power law index, and rotational speed of the inner heated cylinder. The results demonstrate that the hybrid nanofluid and rotating cylinder significantly enhance heat transfer within the trapezoidal cavity. Higher values of the Darcy number, Reynolds number, and nanoparticle volume fraction lead to increased heat transfer rates. The placement configuration of the inlet and outlet ports also affects heat transfer performance, with the bottom-top configuration yielding the best results. Furthermore, a comparative analysis of flow profiles and heat distribution is conducted using the multiple expression programing technique. The proposed model accurately predicts the flow and heat transfer characteristics in the trapezoidal cavity, as validated through comparison with provided data sets. [ABSTRACT FROM AUTHOR]

This article investigates the fluid dynamics and heat transfer properties in a trapezoidal enclosure containing a heated cylindrical object. It involves the interaction of multiple physical processes such as the magnetic field, thermal radiation, porous materials, and aqueous copper oxide nanoparticles. The governing partial differential equations are analyzed numerically through the continuous Galerkin finite element algorithm. The analysis takes into account various physical parameter factors, including the Richardson number (0 – 5) , the Hartmann number (5 − 40) , the Darcy number (0.001 − 0.1) , thermal radiation parameter (0.5 − 2) , and nanoparticle volume concentration (0.01 − 0.1). The physical mechanism of thermal and mass transfer in the enclosure caused by various factors is fully explored. In addition, the multiple expression programming (MEP) technique is implemented to report a comparative analysis of flow profiles and thermal distribution. The findings demonstrated that at low Ri, the primary flow within the cavity is driven by the shear friction generated by the moving walls. The growing importance of radiative heat transfer reduces the effectiveness of convective heat transfer, resulting in a decline in the average Nusselt number with R. The heat transfer rate rises up to 27.7% as ϕ augments; however, its value declines by 9.37% against Ha. The expected results obtained by the MEP approach are very consistent with the numerical ones. There is no doubt that the new MEP concept provides a valuable tool for researchers to predict the heat transfer behavior of any data set in cavities of different shapes. It is expected to provide new idea for the development of efficient cooling systems and the improvement of energy efficiency in various engineering applications. [ABSTRACT FROM AUTHOR]