Journal of Advances in Mathematics and Computer Science

This research presents a numerical investigation of conjugate magnetohydrodynamic (MHD) free convective flow of Cu–H₂O nanofluid within a top-corrugated trapezoidal cavity containing multiple internal heat-generating objects of different geometries square, star, and triangular. The study is conducted under steady-state, laminar, incompressible conditions using COMSOL Multiphysics to explore the effects of Rayleigh number (Ra), Hartmann number (Ha), cavity inclination angle (λ), and obstacle shape on thermal and flow behavior. Key performance indicators such as Nusselt number, entropy generation, thermal performance criterion (TPC), and average fluid temperature are analyzed to assess system efficiency. Results reveal that square-shaped obstacles provide the highest heat transfer rate and lowest entropy generation across all tested conditions. An inclination angle of 20° offers optimum fluid circulation and temperature distribution, leading to enhanced thermal performance. The presence of a magnetic field (Ha = 50) moderates’ convection by suppressing flow strength, especially at high Ra. Comparative evaluations confirm that the combination of square obstacles and a 20° cavity inclination yields the most thermodynamically efficient configuration. This study provides valuable insights for optimizing MHD nanofluid systems in engineering applications such as electronic cooling, solar collectors, and advanced energy systems.