Linear stability and parametric optimization of AA7075 nanofluid flow over an exponentially shrinking sheet under inclined magnetic field and thermal effects

Abstract

This study investigates the linear temporal stability analysis of forced convection in water-based AA7075 nanofluid over an exponentially shrinking sheet, incorporating the effects of inclined magnetic field, Joule heating, and thermal radiation. Unlike previous studies that primarily focus on stability analysis, this research also explores the sensitivity of response functions. The governing ordinary differential equations, obtained via similarity transformations, are solved using MATLAB’s bvp4c solver. A parametric study is conducted over a range of physical parameters including magnetic parameter $\left(M\right)$, inclination angle $\left(\gamma \right)$, suction parameter $\left(S\right)$, shrinking parameter $\left(\lambda \right)$, AA7075 nanoparticle volume fraction $\left(\varphi \right)$, radiation parameter $\left(R\right)$, and Joule heating parameter $\left(J\right)$. The analysis reveals multiple solutions for certain parameter ranges and a saddle–node bifurcation is observed. Further, stability analysis confirms that only the first solution branch is stable and physically reliable. Increasing $M,S$, and $\gamma$ delays boundary layer separation. In the first solution, the gradient of velocity at the wall, represented by the skin friction coefficient, increases by 10.76%, 8.19%, and 8.23% with increasing magnetic parameter $\left(M\right)$, suction parameter $\left(S\right)$, and inclination angle $\left(\gamma \right)$, respectively. The incorporation of AA7075 nanoparticles into the base fluid results in a 48.28% enhancement in the temperature gradient at the wall, reflected through the Nusselt number, in the first (stable) solution. Additionally, the Joule heating $\left(J\right)$ and thermal radiation $\left(R\right)$ parameters contribute to an increase in the wall temperature gradient by 13.7% and 11.9%, respectively, indicating improved thermal transport efficiency. Sensitivity analysis using Response Surface Methodology (RSM) identifies nanoparticle volume fraction as the most influential parameter, with a desirability index of 63.9% yielding optimal values of drag coefficient (2.20139) and Nusselt number (13.6657). The results are validated against limiting cases from the existing literature and show excellent agreement. These findings provide significant insights for enhancing heat transfer and flow control in practical applications such as automotive cooling systems, fabrication processes, and energy devices.