A. Al‐Zubaidi, Musharafa Saleem, S. Saleem
ABSTRACT This study investigates the unsteady two‐dimensional Heimenz flow of a Casson fluid over a semi‐infinite Riga horizontal plate, considering leading‐edge accretion and ablation effects. A ternary hybrid nanofluid model is used, where sodium alginate (SA) serves as the base Casson fluid containing titanium oxide, copper, and silver nanoparticles. The effects of Stefan blowing on microorganism transport, Newtonian heating, nonlinear thermal radiation, activation energy, non‐uniform heat source/sink, and Soret (thermal‐diffusion) effects are examined to analyze momentum, heat, mass, and motile organism transfers in the boundary layer under stagnation‐point conditions. The governing partial differential equations (PDEs) are transformed into dimensionless nonlinear ordinary differential equations (ODEs) using an appropriate nondimensionalization technique and solved numerically via the bvp4c method in MATLAB. Validation against existing literature confirms the accuracy of the solutions. The results show that increasing the Casson fluid parameter reduces velocity due to enhanced Newtonian‐like behavior, while stagnation‐point flow, non‐uniform heating, Soret effects, and electromagnetic forcing from the Riga surface significantly influence the thermal, nanoparticle, and microorganism distributions in the boundary layer. Increasing the leading‐edge parameter slows down the fluid but strengthens temperature and nanoparticle/microorganism accumulation near the wall. Higher activation energy enhances velocity, temperature, and nanoparticle concentration while slightly reducing microorganism density. The Stefan blowing parameter adds mass to the boundary layer, enriching nanoparticles and microorganisms, whereas suction or injection controls the local flow and boundary thickness. Notably, the modified Hartmann number from the Riga surface propels the fluid, increasing velocity and heat transfer.