Thermal insights into magnetized ternary nanofluid flow: a novel paradigm integrating graph-neural network and Keller-box approach

Developing an efficient heat transfer liquid remains to be a significant challenge for industries, since traditional fluids are inadequate for optimal cooling and heating. However, ternary nanofluids, characterised by their superior thermal characteristics, provide a feasible solution to this issue, but their complex behaviour presents considerable modelling challenges. To address this problem, we proposed a machine learning (ML)-based numerical approach to investigate the parameters affecting the heat and mass transfer of a magnetised ternary nanofluid across Darcy porous media on a stretched sheet. Chemical reaction, magnetic field and thermal radiation were also considered, leading to enhanced heat transfer due to superior thermal conductivity. We present an innovative hybrid methodology that employs graph neural networks (GNN) and a modified finite difference approach to enhance numerical modelling capabilities. We used the similarity scaling to transform the governing partial differential equations (PDEs) into a set of ordinary differential equations (ODEs). As the permeability parameter rises, both normal and streamline velocity distributions diminish, whereas the temperature increases. The hybrid GNN-numerical method effectively correlates with solutions for a complex thermal-fluid system with R2>0.99. GNN algorithm correctly forecast results with an average RMSE of 10−6 and MAE of 10−6. Radiation and magnetic variables augment the thermal distribution of the ternary nanofluid flow. Proposed hybrid algorithm present an efficient framework for optimising ternary nanofluid dynamics in porous media, applicable to enhanced oil recovery, solar thermal systems, and advanced cooling for electronics.