Coupled fluid-thermal analysis of a square chamber with a wavy top wall and an internal solid elliptical/circular block

• Natural convection in a square enclosure is studied for thermal performance. • Effects of obstacle shape and wavy top wall (amplitude, frequency) are analyzed. • Vertical ellipse-shaped obstacle shows better performance than other shapes. • Top wall waviness has minimal effect compared to elliptical obstacle shape. This study investigates the thermal performance of the conjugate free convective flow of air within a square enclosure containing a heat-conducting obstacle at the center, either elliptical or circular-shaped, and a wavy cold top wall. Variations in both the corrugation frequency and amplitude of the wavy top wall, along with adjustments to the shape of the central obstacle, are systematically examined to identify the optimal thermal performance of the system. Governing Navier-Stokes and energy equations are solved using the finite element method. Initially, three different obstacle shapes, namely horizontal ellipse, vertical ellipse, and circle, are considered to assess the influence of the obstacle’s geometrical orientation, while maintaining fixed corrugation frequency and amplitude. Later, three values of dimensionless corrugation amplitude ( A = 0.02, 0.03, and 0.04) and corrugation frequency ( f = 7, 9, and 11) are taken to determine their effects on heat transfer efficiency and entropy generation. A comprehensive analysis is conducted, evaluating various performance indicators, including average fluid temperature, average Nusselt number, total entropy generation, and the ecological coefficient of performance. Notably, the study prioritizes achieving enhanced heat transfer while minimizing entropy generation. The results reveal that the optimal configuration offering the highest heat transfer effectiveness with the lowest entropy generation is obtained when a vertical elliptical obstacle is employed, evidenced by the consistently highest value of ECOP for flows with varying Ra . This favorable outcome is most evident with a corrugation amplitude of A = 0.04 and a corrugation frequency of f = 11, while all other parameters are kept constant.