Hybrid FEM-neural network approach to radiative slip flow of TiO\(_2\)–SiO\(_2\) nanofluid over stretching surfaces

We study the thermal performance and chemical reactive flow of a hybrid nanofluid over a stretching sheet heat generation. Titanium oxide (TiO\(_{2}\)) and silicon dioxide (SiO\(_{2}\)) combine to form a hybrid nanofluid, which is an improper fluid with water, Eg\((50\,{:}\,50)\) as a general fluid. Using a suitable similarity variable, the constitutive partial differential equations are converted into a system of connected nonlinear ordinary differential equations. The resulting equations are then solved numerically using the efficient finite element analysis method with the help of Mathematica 10.4 software and, for better results, with the Neural Network Levenberg–Marquardt method in MATLAB R2017b. The present study can be useful in precision engineering and nanotechnology tasks such as developing microfluidic devices and biomedical apparatuses where nanofluid flow control is crucial. The model assists in understanding fluid dynamics for complex cooling systems, particularly in industries where efficient heat transfer is essential, such as electronics and aerospace. Surface tension plays a major role in determining the uniformity and quality of thin films, and therefore it can also be advantageous in coating technologies and material processing. Our results reveal that increasing the volume fraction parameters \(\phi_1\) and \(\phi_2\) results in a thicker thermal boundary layer in both steady and unsteady states. Higher values of \(\phi_1\) and \(\phi_2\) enhance the \(\phi_1\) velocity profile while reducing the \(\phi_2\) velocity profile for both steady and unsteady states of TiO\(_2\)/SiO\(_2\)–water/Eg\((50\,{:}\,50)\) hybrid nanofluid. The results show that thermal conductivity performance of the hybrid nanofluid model is efficient compared with a single nanofluid.