Sensitivity of activation energy and thermal radiation in dihydrogen oxide based nanofluid performance in PTSC

This study investigates the flow characteristics and thermal performance of $A{l}_2{O}_3/H_{2}O$ nanofluid across a curved, stretchable sheet for application in parabolic trough solar collectors (PTSC). Nanofluids, mostly water-based, enhance heat transfer efficiency in solar energy systems. This work investigates the effects of activation energy, thermal radiation, and chemical reactions on the performance of nanofluids, which is critical for optimizing sustainable energy technologies. Heat transfer is modeled by incorporating curvature, viscous forces, radial pressure gradients, thermal radiation, and chemical reactions. This work's novelty lies in conducting a sensitivity analysis to test which parameters are most sensitive to the combined effects of activation energy, thermal radiation, and chemical reaction rate, a key factor in the space environment. The Koo–Kleinstreuer–Li (KKL) model accounts for the interaction of nanoparticles in effective thermal conductivity and viscosity. Using similarity transformations, the governing equations for momentum, energy, and nanoparticle concentration are transformed into ordinary differential equations (ODEs) and solved using the BVP4C MATLAB scheme. The results, illustrated graphically, show that increasing curvature $\left(\Lambda \right)$ and activation energy $\left(E\right)$ improve the concentration profile, while chemical reaction rate $\left(\kappa \right)$ and Schmidt number $\left(Sc\right)$ decrease it. The temperature profile increases with higher radiation parameters $\left(Rd\right)$ and Biot number $\left(Bi\right)$. Response surface methodology (RSM) evaluate the impact of input parameters $(0.1\le E\le 1.3$, $0.1\le Rd\le 1.4$, and $0.1\le \kappa \le 0.8)$ on system performance. Analysis of variance (ANOVA) using RSM quantifies the impact of parameters on energy efficiency, with $R^2=95.80\%$ and $Adj{R}^2=92.10\%$ for the Nusselt number $\left(Nu\right)$, confirming the high reliability. Sensitivity analysis shows that $Nu$ is very sensitive to $\kappa$, moderately sensitive to $Rd$, and less sensitive to $E$. The residual plots confirm the correlations. These results offer ideas for optimizing nanofluid-based thermal systems, improving energy efficiency and stability in PTSC.