Development of Nusselt number correlation for iso flux sphere in 90°-bent rectangular duct flow

Compact designs in engineering devices such as refrigeration systems often require heated components installed within corners of flow paths. While extensive Nusselt number correlations exist for a heated sphere in straight flows, curvature and flow path features in such configurations can significantly affect heat transfer, making conventional correlations potentially inaccurate. As a result, one of the most common curvatures is the 90° bend, yet the effect of 90°-bent rectangular ducts on sphere heat transfer remains largely unexplored. This study addresses this gap by numerically developing Nusselt number correlations for a heated sphere in 90°-bent duct flows using three-dimensional CFD simulations. Simulations were conducted at various dimensionless sphere-to-vertical gap distances (0.1 ≤ r v ≤ 0.9), sphere-to-horizontal gap distances (0.1 ≤ r h ≤ 0.9), Reynolds numbers (1000 ≤ R e s ≤ 5000), and Prandtl numbers (0.71 ≤ Pr ≤ 1) considering both buoyancy and radiation effects to develop a comprehensive correlation. Results reveal a significant increase in average Nusselt numbers in bent ducts compared to straight flows, with mixed convection and radiation influencing heat transfer by up to 3.5 % and 30.7 % at Ri = 0.25, respectively. A detailed parametric study was performed based on the major parameters r h , r v , Re s , and Pr to analyze flow structure and heat transfer behavior under varying conditions. New correlations for the Nusselt number and friction factor are proposed for practical applications and compared to straight-flow correlations using the thermal performance factor (TPF), which can be 60 % higher at lower Reynolds and gradually decreases at higher Reynolds numbers.