<p>The investigation of steady, incompressible, laminar mixed convective fluid flow within two different types of trapezoidal enclosures filled with saturated water and study explores how the power-law index governs buoyancy-driven heat transfer in a porous trapezoidal cavity filled with non-Newtonian fluids. Unlike Newtonian fluids, non-Newtonian fluids exhibit flow behavior that directly depends on the power-law index, which characterizes their shear-dependent viscosity. We formulate the governing equations in terms of the stream function and temperature and solve them using a validated, in-house MATLAB solver. Embedding a porous matrix within a trapezoidal enclosure creates intricate interactions between convective currents and conductive resistance. By performing numerical simulations across a range of Rayleigh numbers (Ra = 10² to 2 × 10³) and boundary conditions, we systematically assess how variations in the power-law index alter local velocity fields, temperature distributions and overall heat-transfer rates. Our results reveal that increasing the power-law index strengthens convective flow and raises the average Nusselt number, whereas decreasing the index shifts the balance toward diffusion-dominated transport. These findings offer practical guidance for enhancing thermal management in industrial systems that employ both Newtonian and non-Newtonian fluids within porous structures. The study presents new empirical correlations linking Nu, Ra and power law co-efficients offering a practical tool for engineering design. Unlike previous works that focused primarily on Newtonian fluids or simplified geometries, this work provides a detailed analysis of non-Newtonian effects in realistic porous enclosures. These results contribute to a deeper understanding of convective mechanisms in complex therm-ofluid systems and offer guidance for optimizing thermal performance in engineering applications.</p>