The present research analyzes the properties of a Casson ternary nanofluid over a stretching sheet with Thomson and Troian slip conditions, taking into consideration the influences of electromagnetohydrodynamic (EMHD). The ternary nanofluid comprises three different nanoparticles, which include titanium dioxide (TiO2), copper (Cu), and silver (Ag), all being suspended in oil, which is the base fluid. They are involved because of their good thermal conductivity and chemical stability, and AgCuTiO2 /Oil nanofluid is a composite of copper, titanium oxide, and oil. Hence, carrying out the said procedure, the ternary nanofluid becomes AgCuTiO2/Oil. The sheet is, however, thought to be stretching vertically while the flow is determined by the effect of the gravity force through the free convention. Moreover, the phenomena of EMHD, porous medium, thermal slip, thermal radiation, Joule heating, and heat source/sink are included to make the energy equation more real-life. This leads to a set of partial differential equations (PDEs) based mathematical models transformed into ordinary differential equations (ODEs)-appropriate similarity transformation. The Runge–Kutta–Fehlberg (RKF-45) method solves the given ordinary differential system. According to the research’s findings, the temperature of the ternary Casson nanofluid rises when the suspension of silver, copper, and titanium dioxide nanoparticles increases, and the velocity of flow for merely silver and copper decreases when the density decreases. This causes the flow rate to be constricted through the velocity slip condition, at the same time as the nanofluid’s temperature increases.
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