Comparative analysis of thermally radiative parabolic surface with heat generation to investigate the Williamson hybrid nanofluid flow via artificial neural network

Many investigations have focused on typical configurations such as flat or cylindrical surfaces. However, the scrutiny of hydrothermal characteristics over the parabolic domain adds a unique dimension owing to its extensive application in solar thermal systems, energy systems, and power plants to improve cooling efficiency, biomedical applications, environmental and renewable energy utilization, and the automotive and aerospace industries. In addition, increasing the thermal efficiency of working rheological liquids over parabolic surfaces with the induction of hybridized nanocomposites makes this problem more relatable to realistically occurring phenomena, and provides accurate data for the execution of simulations in diversified engineering problems. This pagination inspects the increase in the thermal efficiency of ethylene glycol, which expresses the attributes of shear thinning and thickening materials characterized by the Williamson model with the induction of hybridized nanoparticles composed of MoS₂ and graphene. The effectiveness of magnetization in the transversal direction to the flow is also assessed. The significance of the radiative energy and heat source is also articulated. By utilizing conservation laws, the mathematical modeling is manipulated in the sense of a partial differential system, and later transformed into a dimensionless differential setup through transformations. Numerical simulations are performed to resolve governing coupled differential system by employing Runge–Kutta procedure with conversion into initial value form. The shooting procedure is implemented to provide initial guesses for the boundary conditions. The prediction of quantities against the parameters is made through the Levenberg–Marquardt back-propagated scheme, and upshots for trained, tested, and validated data are drawn. The evaluation of the network is analyzed using mean square error and regression analysis. The results are visualized in graphical and tabular manner to interpret their behavior. A decrease in the velocity distribution is perceived by dispersing hybrid nanoparticles, whereas contrary aspect is perceived for the drag coefficient. The numerical outcomes for friction factor and Nusselt number are enumerated in a tabulated manner. Nusselt number increases up to 53% when radiation impacts are present, while elevates up to 47% when heat generation phenomenon is present.