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.

The novel concept of hybrid nanofluids (HNFs) captivated scientists and researchers due to its remarkable thermal conductivities, which led to improved thermal performance. There are several applications for these fluids in the fields of technology and industry. A third-grade Williamson-Casson HNF model for magnetohydrodynamics over an exponentially stretched surface in a DF permeable medium is presented in this work. It covers the impacts of viscous dissipation (VD) as well as the analysis of heat and mass transfer (HMT). The established governing PDEs for momentum, energy, and concentration transfer are transformed into a collection of nonlinear ODEs using similarity transformations (ST). These transformed equations are solved using semi-numerical methods called HAM. It investigates how velocity field (VF), temperature field (TF), and concentration field (CF) are affected by changes in critical parameters such as thermal conductivity, third-grade fluid parameter, DF number, magnetic field (MF) strength, Williamson and Casson fluid parameters, and nanoparticle volume fractions (VLFs). The results show that the presence of an HNF increases thermal conductivity, which improves heat transfer efficiency. Additionally, VD and third-grade fluid characteristics significantly impact fluid flow and energy transfer. The recent research offers important new information for practical applications in thermal engineering systems, biofluid mechanics, and polymer processing.