This study aims to provide a thorough mathematical simulation of the effects of heat radiation and thermocapillarity on the time-dependent flow of couple stress ternary hybrid nanofluid across a stretching parallel surface in magneto-hydrodynamics. The ternary hybrid nanofluid consists of Ag, TiO2, Al2O3 nanoparticles dispersed within a base fluid, blood, enhancing its thermal performance. The governing partial differential equations are converted into a system of nonlinear ordinary differential equations by applying the proper similarity transformations to model the flow’s unstable behavior. After that, the Homotopy Analysis Method is used to solve these equations semi-analytically. The intricate interactions between radiative heat transport, thermocapillary forces induced by surface tension gradients, Lorentz force from the applied magnetic field, and couple stress effects are all captured in the simulation. The influence of main dimensionless parameters, including the magnetic parameter, couple stress parameter, nanoparticle volume fractions, dimensionless film thickness, unsteady parameter, thermal radiation parameter and Eckert number, on velocity profile, temperature profile, skin friction and Nusselt number in the form of graphs. According to the results, radiation improves the properties of heat transmission, whereas thermocapillarity dramatically changes the flow and thermal boundary layers. Furthermore, the fluid velocity is suppressed by the occurrence of magnetic fields and couple stress, providing information about possible control mechanisms in thermal management systems. The results’ graphical and tabular representations demonstrate how sensitive the temperature and velocity fields are to the physical parameters at play. These findings offer significant new insights into thermal management technologies and energy systems that employ complex nanofluid compositions.

This manuscript delineates a thorough study on the heat and mass transfer phenomenon of the Williamson fluid flow embedded with a tetra-hybrid nanofluid evaluating a wide range of considered and physical effects such as magnetohydrodynamics (MHD), porous medium, radiative heat flux, Joule heating, Soret and Dufour effects, and a Stefan blowing parameter at the boundary, and the rest. A tetra-hybrid nanofluid containing nanofluid gold (Au), silver (Ag), titanium dioxide (TiO₂), and aluminium oxide (Al₂O₃) is used for the improvement of significant thermal and mass transport characteristics. In the back, the demand for efficient thermal systems relates to sets with multiple, integrated transport mechanisms; however, the synergistic transport mechanisms have been largely unexplored, and the coupled hybrid advanced dimensions nanofluids have been unexplored in terms of their combined influences on these parameters. The core target was to examine the active relationships within the physical dynamics parameters while also evaluating the relative increases in the velocity, temperature, and concentration. This paper employs a robust computational approach to the study by solving the governing systems of non-linear ordinary differential equations using an appropriate method of similarity transformation and subsequent numerical techniques. The integration of artificial neural network (ANN) models within this spectrum for the first time, with predictions and optimization set for the outputs, adds a new dimension to this work. The data show that incorporating Soret and Dufour effects, along with the tetra-hybrid nanoparticles, markedly increases the Nusselt and Sherwood numbers, indicating improved heat and mass transfer rates. Furthermore, streamline plots are created to illustrate alterations in the flow structure induced by the Soret and Dufour parameters. This research makes valuable contributions to the development of refined cooling technologies, particularly in energy, chemical, and other process-oriented industries, highlighting the practical utility and innovation potential of the synergistic application of artificial neural networks alongside sophisticated nanofluid models.