Enhanced thermal performance and entropy management in a Y-shaped cavity with an inner rectangular Vertical Wall: A computational study with sensitivity analysis using response surface methodology

Natural convection (NC) and heat transfer (HT) in complex geometries are critical for optimizing thermal systems, including electronic cooling and energy-efficient designs. Our research aims to analyze the effect of the Rayleigh number (Ra) under different rectangular vertical wall (RVW) thermal boundary conditions on HT efficiency and entropy generation (E_gen). The Finite Element Method is used to solve the governing equations. Key parameters include Ra = 10³ to 10⁶, Prandtl number (Pr = 7.0), and various RVW configurations. Results reveal that an increase in Ra enhances both the average Nusselt number (Nu_avg) and E_gen while reducing the Bejan number (Be), indicating intensified flow and higher viscous dissipation. At Ra = 10⁶, the heated RVW shows only a 4.61 % higher Nu_avg than the cold RVW, but results in 88.36 % higher E_gen and a 42.25 % lower Be, suggesting a dominance of viscous effects. Sensitivity analysis shows that Ra is the most influential factor on Nu_avg, while RVW height (h) has a moderate and width (w) a weak positive influence. This study provides critical insights into the design of thermally efficient systems, highlighting the significant roles of RVW thermal conditions and Ra in balancing HT performance and E_gen within a Y-shaped enclosure.

To ensure the accuracy of our simulation, we conducted qualitative validation using other published studies and quantitative validation, achieving an error margin below 1 %.