Optimization of dynamic response characteristics in aluminum-alloy nanofluid flow: insights from temporal stability and sensitivity analyses

Purpose The behavior of nanofluid flows over shrinking surfaces is known to exhibit dual solutions and complex stability characteristics, yet limited attention has been given to how these flow responses can be optimized with respect to key physical parameters. This study aims to address this gap by examining the linear stability, sensitivity and optimized performance of AA7075-water nanofluid flow over an exponentially shrinking sheet under the combined effects of an inclined magnetic field, thermal radiation and Joule heating. Design/methodology/approach The governing boundary layer equations are transformed into nonlinear ordinary differential equations using similarity variables. These equations are solved numerically using the bvp4c solver in MATLAB to capture both primary and secondary solution branches. Linear stability analysis is then applied to determine which solution is physically stable. Response surface methodology is used to obtain optimal parameter combinations that simultaneously minimize skin friction and maximize the Nusselt number (Nu). To further evaluate how the responses vary with changes in magnetic parameter, nanoparticle volume fraction and magnetic field inclination, a detailed sensitivity analysis is performed. Findings The study reveals that dual solutions occur only within specific ranges of suction and shrinking parameters. Increasing suction and magnetic intensity enhances flow stability by shifting the bifurcation point, thereby delaying separation. Stability analysis confirms that the first solution branch is stable, while the second is unstable. Sensitivity results show that the skin friction coefficient increases with the magnetic parameter, nanoparticle concentration and inclination angle, whereas the Nu increases predominantly with the magnetic parameter. Optimization results identify conditions that yield minimal skin friction and maximal heat transfer, achieving an overall desirability of 62.8%. Originality/value This work combines linear stability, sensitivity analysis and response optimization into a single framework for AA7075-water nanofluid flows, an area that has received limited prior attention. The results offer clear insight into how controllable physical parameters affect both flow stability and thermal performance. The study presents a practical and comprehensive approach that supports designing advanced heat transfer systems using metallic nanofluids.