Entropy generation in conjugate mixed convection of a rough cylindrical surface confined within a square chamber under internal heat generation

• A novel conjugate mixed convection model with a rough-walled cylinder and internal heat generation in a lid-driven cavity. • Analyzes the influence of roughness shapes (circular, triangular, square) to assess their thermal and flow impacts. • Investigates cylinder placement effects on thermal performance under varying flow conditions. • Identifies optimal configuration based on Nusselt number, entropy generation, drag, ECOP , and system effectiveness. This study investigates conjugate mixed convection in a lid-driven cavity containing a rough-walled cylinder with internal heat generation. Three roughness geometries (circular, triangular, square) and different cylinder placements are considered, with the working fluid modeled as a water-ethylene glycol mixture undergoing laminar flow (10 3 ≤ Gr ≤ 10 5 , 31.62 ≤ Re ≤ 316.23, 0.1 ≤ Ri ≤ 10). The dynamics of fluid motion and thermal distribution within the solid cylinder and the cavity are dictated by two-dimensional Navier-Stokes and energy equations, which are numerically resolved through the finite element approach. The current study reveals that a circular-shaped rough cylinder positioned at the center of the cavity yields better optimization through ECOP and effectiveness when there is no internal heat generation. With the internal heat generation, thermal transport drops around 10 % at a high Re, whereas the ECOP drops around 70 % for the entire range of parameters. Hence, the other parameter should be optimized to mitigate this adverse situation when the system involves heat generation.