This research examines the dynamics of heat transfer while highlighting the crucial role of Fourier heat flux concerning the thermodynamic and hydrodynamic characteristics of ternary hybrid nanofluids (HNFs) traversing a disk. The physical model and flow configuration were thoroughly analyzed under the influences of various parameters. The major equations that characterize the flow dynamics are formulated as partial differential equations (PDEs). By utilizing appropriate correspondence variables, the system of PDEs was altered keen on ordinary differential equations (ODEs). The coordination of coupled nonlinear equations is resolved arithmetically utilizing the “bvp4c function in MATLAB.” The influence of the principal appropriate factors on the radial speed, axial speed, and warmth is illustrated realistically. Ultimately, a table is constructed to demonstrate the interrelationships of numerous perilous issues on the Skin friction and Nusselt number. It was observed that an enhancement in the attractive constraint significantly diminishes the speed outline, attributable to the Lorentz influence caused by the applied attractive subject. Additionally, an enhancement in thermal transfer was observed as a consequence of an increase in thermal radiation.

This investigation explores the magnetohydrodynamic (MHD) free convective heat and mass transfer characteristics of a ternary nanofluid traversing an exponentially accelerated inclined plate within a porous medium. The theoretical framework integrates the complexities of internal heat generation/absorption and fluctuating wall temperatures. Analytical solutions were rigorously derived utilizing the Laplace transform technique, while a sophisticated Artificial Neural Network (ANN) was implemented to forecast and corroborate these mathematical outcomes. Heat Transfer (Nusselt Number) evaluated against the interplay of the Prandtl number, thermal radiation parameters, and temporal progression. Mass Transfer (Sherwood Number) analyzed as a function of magnetic permeability, the Schmidt number, and time. Thermal Enhancement findings indicate that an augmentation in the nanofluid volume fraction significantly bolsters thermal conductivity, thereby elevating the temperature profile. The proposed Levenberg-Marquardt Algorithm-based Backpropagation Artificial Neural Network (LMA BANN) demonstrated exceptional predictive fidelity. The model achieved a precision threshold exceeding 99.9% for the Nusselt number and near-perfect accuracy for the Sherwood number. These results are substantiated by negligible Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Mean Absolute Error (MAE) values, coupled with correlation coefficients (R) nearing unity, signifying a robust alignment between the analytical and predicted datasets.