Machine learning estimation of heat and mass transfer attributes of thermal radiative Williamson nanofluid flow via nonlinear stretchable surface

Abstract

Nanomaterials exhibit remarkable thermal properties and have promising utilization in areas such as thermal energy transmission, biopharmaceuticals, the food industry, solar power generation and electric cooling systems. The significant applications of nanoparticles inspired the development of a mathematical model to analyze mass and heat transfer in magnetically influenced Williamson nanoliquid flow across an exponentially extendable surface by incorporating physical factors of Brownian motion and thermophoresis effects along with Arrhenius activation energy and convective boundary constraints. The fundamental equations describing the mathematical structure are designed in the sense of a highly nonlinear coupled partial differential setup. A set of similar variables is utilized to transmute the differential setup into a non-dimensional ordinary system. The attained ODEs are resolved with the implementation of a shooting algorithm in conjunction with the RK-4 technique. Afterwards, a machine learning algorithm based on the backpropagated Leven-berg Marquardt paradigm is also utilized to forecast the numerical outcomes of the quantities of engineering. The impact of relevant flow factors on the associated flow distributions and the quantities of engineering interest are presented via graphical and tabular format. The numerical outcomes signify that momentum distribution dominates by inducing mono nanoparticles as compared to hybrid particles. Enhancement in thermal distribution is perceived by intensifying Brownian motion and thermophoresis effects, whereas contrary aspects are observed for associated flux. In addition, the trained ANN models shows that the best validation performance of Model-A is 1.15e-5 that happens at 565 epochs, while the best validation performance for Model-B is 3.38e-5 at 641 epochs. Small estimations guarantee that model training completed properly. Nusselt number elevates by 29 % for mono and 25 % for hybrid nanoliquid flow when $\left(Rd\right)$ varies from 0.2 to 0.6, while depreciates up to 1.5 % by elevating $\left(Nt\right)\text{.}$