Ternary nanofluid flow over a stretching surface with nanoparticles shapes effect under transverse magnetic field using Runge Kutta Fehlberg method

• Flow problem is analyzed of nanoparticle morphology on the behavior of TiO 2 (titanium dioxide) Al 2 O 3 (aluminum oxide)-copper (Cu) nanofluids and non-Newtonian viscoplastic SA based. • The transverse magnetic field affects the sheet that is expanding or shrinking is considered. • Numerical treatment is accomplished by using the Runge-Kutta algorithm. • Alumina-based nanofluids exhibit a decrease in viscosity without a corresponding decrease in thermal conductivity. This study investigates sodium alginate (SA)-based nanofluids, highlighting their thermophysical properties and potential advantages over conventional heat transfer fluids. It examines the influence of nanoparticle morphology on TiO₂, Al₂O₃-Cu nanofluids, and non-Newtonian viscoplastic SA-based fluids under a transverse magnetic field. Four nanoparticle shapes—cylinders, bricks, blades, and platelets—are considered. Nonlinear PDEs are transformed into ODEs and solved numerically using the Runge–Kutta–Fehlberg method in MAPLE. Results show that temperature decreases with a higher Prandtl number but increases with the Eckert number and viscoplastic parameter. The velocity profile decreases for all Cu nanoparticle shapes but rises with a more significant stretching surface parameter. Alumina-based nanofluids reduce viscosity without lowering thermal conductivity. These findings benefit applications in electronic cooling, biomedical hyperthermia, and manufacturing processes.