This study explores the impact of ternary hybrid nanofluid and velocity slip on the Non-Newtonian fluid flow between two nonparallel plates. Additional influence of an applied magnetic field is considered with Casson fluid (Blood) as a base fluid. Both analytic and numerical techniques are employed to comprehensively analyze the system’s behavior under these combined effects. The governing partial differential equations (PDEs) governing continuity and momentum are simplified into a system of ordinary differential equations (ODEs) through similarity transformations. To obtain an explicit series solution for the resulting problem, we employ the Duan Rach approach (DRA). Subsequently, we conduct a thorough analysis of the solution’s convergence to ensure its reliability and accuracy. The same problem is also solved by using the Runge-Kutta-Fehlberg 4th–5th order approach featuring shooting technique and an excellent agreement is observed between the two sets of results. A comparison was made between the results obtained from this investigation in particular cases and the results obtained via the HAM-based Mathematica package for validation. Influence of various parameters of practical importance on the velocity and temperature profiles is studied and portrayed graphically. Values of skin friction coefficient are tabulated by assigning different values to various emerging parameters. It is found that the velocity slip parameter has a positive value in a converging channel, it implies that there is a slip between the fluid and the channel wall, and the slip velocity is directed in the same direction as the flow. Hence velocity increases. Also, results obtained reveal that for positive value of β + velocity gets high in converging case and lower velocity can be seen in diverging geometry. Same behavior is seen for β − .