This study presents a ternary hybrid nanofluid model exhibiting superior thermal performance as compared to conventional fluids. The ternary hybrid nanofluid is formulated by suspending alumina Al2O3, silicon dioxide (SiO2), and Titanium dioxide (TiO2) nanoparticles in blood, and its flow is model using non-Newtonian Maxwell model. Furthermore, the combined effects of nonlinear thermal radiation and space-based heat source are incorporated. The system of ordinary differential equations (ODEs), which is obtained via the use of similarity transformations, is solved numerically by the bvp4c technique in MATLAB. The impact of different physical parameters are displayed through Figures and Tables. Results show that amplifying the magnetic field, porosity, and Maxwell parameters diminishes the velocity of ternary and hybrid nanofluid. The skin friction enhances 10% and 3.1% for magnetic parameter and Maxwell fluid parameter respectively. The elevated numbers of radiation, space-dependent heat source and thermal Biot number amplify the temperature distribution. Nusselt number of ternary hybrid nanofluid improves 2.3% for thermal radiation, 1% for heat source, 1.2% for temperature difference parameter and 3% for Biot number.