This study investigates the numerical analysis of curvature-dependent symmetric channel walls filled with porous media, focusing on various flow characteristics using Artificial Neural Networks optimized with the Levenberg–Marquardt Backpropagation Scheme (ANNs-BLMS). The analysis explores the Electrically Conducting Peristaltic Propulsion of Carreau–Yasuda Ternary Hybrid Nanofluids (ECPPCY-THNFs) propagating through sinusoidal wave trains within a curved conduit. To streamline the analysis, the governing equations have been simplified under specific assumptions of lubrication theory. The simplified governing equations are solved using Adam and three-stage Lobatto IIIa formula numerical techniques to generate a dataset spanning the curvature-dependent channel walls, covering four cases and nine scenarios of ECPPCY-THNFs. This dataset encompasses four cases and nine scenarios of ECPPCY-THNFs, with a step size of 0.02. As a result, the domain is divided into 131 grid points for velocity and temperature profiles and 71 grid points for rates of heat transfer analysis. The dataset is divided into three parts: 10% for training, 10% for testing, and 80% for validation. To apply the proposed methodology, the dataset is constructed by varying the Hartmann number, flow rate, Darcy number, curvature parameter, and radiation parameter. Subsequently, an artificial intelligence-based algorithm is employed to derive solution expressions for various flow fields and to analyze the dataset. The results are presented through detailed tabular and graphical illustrations. Heat transfer analysis is performed using the proposed model, and the findings are validated through multiple techniques, including error histograms, regression plots, mean square error (MSE), time series analysis, error autocorrelation, and state transition. A comparative study between two numerical methods and Artificial Intelligence (AI)-generated predictions is also undertaken. The results obtained using the AI-based ANN-BLMS framework confirm the reliability and accuracy of the proposed methodology in effectively solving the ECPPCY-THNFs. The results demonstrate that the curvature parameter has a considerable effect on the mechanical and thermal aspects of the flow, and therefore, it must be incorporated into the modeling of flows through curved channels. Additionally, the flow rate of 7.5 is the critical value, representing the minimum required to sustain fluid flow in a curved channel. When the curvature parameter is below this critical value, an increase in the curvature results in a decrease in the temperature profile. However, when the curvature parameter exceeds the critical value, the temperature profile shows the opposite trend. Furthermore, the velocity of ternary hybrid nanofluids show concave-up shapes for flow rates (Θ) values greater than 7.5 and concave-down shapes for flow rates values less than 7.5. The highest and lowest velocities occur near the center of the curved channel for Θ>7.5 and Θ<7.5, respectively. Moreover, the coefficient of determination values, used as performance indicators, are found to be unity (1.000) for the ANN model. The MSE values and error histogram values for the heat transfer rates are 2.8467 × 10−11 and −3.05 × 10−7, respectively.

The modern world is utilizing solar thermal radiation and nanotechnology to advance new technologies. Nanofluids have a significant influence on the performance of solar thermal systems by enhancing their ability to heat transfer. Solar energy, which is primarily derived from the sun, is applied in numerous technologies such as photovoltaic cells, solar-powered vehicles, solar panels, street lighting, solar thermal aircraft, and water-pumping systems. Keeping such applications in mind, researchers are exploring how nanotechnology can enhance solar thermal radiation to improve aircraft flight efficiency. Hence, this study aims to contribute effectively to the field of solar aviation by utilizing advanced nanotechnology. Given the drawbacks of traditional energy sources, solar power emerged as a solution to the need for reliable, cost-effective, and environmentally friendly renewable energy. Therefore, this research is carried out through the development of a mathematical model that mimics the flow and thermal properties of a parabolic trough surface collector (PTSC) attached to the wing of a solar aircraft. The main objective of this investigation is to analyze magnetized tetra-hybrid Williamson nanofluid (NF) flowing through an aircraft wing's internal PTSC concerning flow properties, temperature distribution, surface friction, entropy generation, and heat transfer. The governing equations are transformed into ordinary differential equations with suitable non-similarity transformations and then tackled numerically via the Bvp4c function in MATLAB. Furthermore, Artificial Neural Networks (ANNs), Response Surface Methodology (RSM), and stability analysis are employed to enhance the heat transfer and surface friction performance of the proposed tetra-hybrid Williamson NF flow. To achieve this, the magnetic number, radiation parameter, and porosity parameter are selected for conducting RSM, ANN, and stability analysis to improve heat transfer and surface friction. The results indicate that tetra-hybrid NFs (TTHNFs) exhibit superior thermal transfer compared to NFs, hybrid nanofluids (HNFs), and ternary nanofluids. As solar radiation and magnetic field parameters improve, the wing performance of airplanes is enhanced in heat transfer situations. Therefore, this study provides important information for improving solar-powered aircraft thermal management and cutting-edge nanotechnology. Additionally, the magnetic, solar radiation, and porosity parameters decrease entropy generation, while the porosity parameter reduces surface friction. Sensitivity analysis performed using RSM indicates that drag force is positively influenced by the porosity parameter, while heat transfer is positively influenced by the magnetic parameter. Finally, the statistical analysis of surface friction and thermal transport in the current model, along with the testing methods, shows high R2, predicted R2, and adjusted R2 values (99.99%, 99.99%, and 99.96%, and 99.99%, 99.99%, and 99.99%) for the response function, demonstrating that this model is well suited for predicting both drag force and heat transfer. The heat transfer performance was evaluated for NFs, HNFs, ternary hybrid (THNFs), and tetra-hybrid nanofluids under magnetic, radiation, and porosity parameters. Compared to the NFs, HNFs improved heat transfer by approximately 8%–9%, THNFs by 18%–20%, and TTHNFs by 41%–45% across all parameters. These enhancements show a clear trend of increasing thermal performance with the addition of more types of nanoparticles. Additionally, the reliability of the proposed ANN model is validated by assessing its precision, accuracy, and convergence using error histograms, performance plots, and fitness curves for heat transfer and surface friction.