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.
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