Double-diffusive optimization in hybrid nanofluid convection using response surface method

Double-diffusive mixed convection in lid-driven cavities has been widely studied. However, the use of Al₂O₃–Cu/H₂O hybrid nanofluids in H-shaped enclosures are crucial for compact heat exchangers and micro-cooling systems which remains largely unexplored despite their superior thermal and convective properties. Moreover, the sensitivity of governing input parameters, a critical aspect for optimizing thermal-fluid performance has not been systematically addressed in previous studies. To address the gaps, this study focuses on the sensitivity analysis of mixed convection heat and mass transfer within a lid-driven H-shaped cavity, filled with hybrid nanofluid and featuring partially heated and concentrated walls. The primary objective is to study the influence of key dimensionless factors Ri, Re , and Le on the thermal and mass transfer performance of the system. A statistical method using response surface methodology (RSM) was implemented, with numerical simulations based on the Galerkin weighted residual FEM to solve the governing partial differential equations. The findings demonstrate that both the average heat transfer rate ( Nu ) and the average mass transfer rate ( Sh ) show a positive sensitivity to Ri and Re , however an inverse correlation was noted with Le . Furthermore, the sensitivity analysis indicates that Nu increases with the rise in Ri and Re but decreases with Le , while Sh increases with all three factors. The average heat transfer rate indicates a 12.02% increase as the nanoparticle volume fraction ( ϕ ) increases from 1% to 4%, while a decrease of 11.25% is noted when Le rises from 0.01 to 5. The statistical assessment of the model shows high R ² values (98.52% for Nu and 95.13% for Sh ), confirming the model’s suitability for forecasting these response functions. This study offers significant insights for optimizing heat and mass transfer processes in hybrid nanofluid applications.