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ABSTRACT Natural convection (NC) and heat transfer (HT) are significant in engineering, particularly in thermal management systems. This study analyzes the thermal behavior and entropy generation ( E gen ) within a “⊥”‐shaped cavity with a rectangular vertical wall (RVW). The inclusion of RVW in a “⊥”‐shaped cavity with a square wall below, demonstrating complexity and improvements. This study explores the interaction between thermal gradients, buoyancy‐driven flow, and the impact of the RVW. This study aims to analyze the influence of the Rayleigh number ( Ra ) on HT performance, flow characteristics, E gen , and also the impact of the RVW. It further assesses environmental efficiency using the Ecological Coefficient Performance (ECOP) that identifies thermally optimal configurations by demonstrating a balance between enhanced HT and thermodynamic irreversibility. Additionally, this study investigates Response Surface Methodology (RSM) to evaluate the sensitivity analysis for finding which parameter mostly affects the average Nusselt number ( Nu avg ) and demonstrates the predictions of the Nu avg with RSM and Artificial Neural Network (ANN). The current analysis employs the finite element method to explore the NC and HT in a “⊥”‐shaped cavity with a square heated wall below using COMSOL Multiphysics software 6.3. The flow is considered to be two‐dimensional, laminar, incompressible, and steady state in nature. A grid independence test confirms numerical reliability. For numerical validation, the calculated results are compared with the findings from earlier published studies to verify accuracy and reliability. Key parameters, Rayleigh numbers (10 3 ≤ Ra ≤ 10 6 ) and Prandtl number ( Pr ), are fixed at 0.71 (air). Dimensionless parameters, including Nu avg , E gen , and Be avg , are calculated to assess HT and quantify optimal configuration. Nu avg and E gen increase with increasing Ra , but Be avg decreases in both cases. The shape and position of the RVW significantly enhanced the HT. The inclusion of RVW gives 78.60% higher Nu avg and 61.61% higher E gen than without RVW at Ra = 10 6 . According to the ECOP, for a lower Ra , case‐1 (without RVW) is more efficient than case‐2 (with RVW), but when the Ra increases, case‐2 (with RVW) becomes more efficient. Sensitivity analysis demonstrates that Nu avg is mostly influenced by Ra , then by the height of the RVW, and slightly by the width of the RVW. With a limited data set, the RSM model with lower mean squared error demonstrates superior predictive accuracy and reliability compared with the ANN model. This study provides useful insights for designing better thermal systems, which shows how the RVW and Ra play key roles in balancing HT and E gen inside the cavity.