Coupled effects of radiation, magnetic field, and hybrid nanofluids on mixed convection in a skewed cavity: A numerical and statistical approach

Magnetohydrodynamic (MHD) mixed convection with nanofluids in various cavity configurations has been extensively investigated due to its wide range of engineering applications. However, studies focusing on MHD mixed convection with radiative flow using hybrid nanofluids within a skewed cavity remain scarce. Addressing the gap of the combined influence of skewed cavity, radiation, and hybrid nanoparticle dispersion on flow with heat transfer properties, this study presents a quantitative analysis of magnetohydrodynamic (MHD) radiative mixed convection with Water-based Cu–Al₂O₃ hybrid nanofluid in a skewed lid-driven cavity using response surface-based sensitivity analysis. The two-dimensional governing equations are formulated with associated boundary conditions, and solved using the Galerkin weighted residual finite element technique. The key parameters, including the Hartmann number (Ha), Richardson number (Ri), nanoparticle volume fraction (ϕ), and radiation parameter (Rd), are systematically varied to inspect their influence on flow and thermal properties. A Central Composite Design (CCD) within the response surface methodology (RSM) framework is used to quantify the sensitivity of the average Nusselt number (Nuₐᵥ) to each parameter. Results indicated that increasing ϕ (0.015→0.020, 0.020→0.025, and 0.025→0.030) enhances Nuₐᵥ by approximately 2.74%, 1.70%, and 1.19%, respectively. Increasing Ri significantly improves heat transfer, with Nuₐᵥ rising by about 40.69%, 40.38%, and 14.93% over the ranges Ri = 0.1→1, 1→5, and 5→10, respectively. In contrast, increasing Ha reduces Nuₐᵥ by 4.22%, 8.55%, and 11.59% (for Ha = 0→10→25→50), while increasing Rd decreases Nuₐᵥ by 37.51%, 18.73%, and 20.87% (for Rd = 0→2.5→5→10). Optimal thermal performance occurs at ϕ = 0.03, Ri = 10, Ha = 0, and Rd = 0, with a maximum Nuₐᵥ of 13.413. Sensitivity analysis identifies ϕ as the most influential parameter, followed by Ri, while Ha and Rd negatively affect heat transfer.