Role of stability analysis and waste discharge concentration of ternary hybrid nanofluid in a non-Newtonian model with slip boundary conditions

Investigating the effects of waste discharge on nanofluids using a non-Newtonian fluid model is vital for enhancing heat and mass transfer performance in engineering systems, such as cooling systems in power plants, oil, and gas drilling operations, and wastewater treatment facilities, while simultaneously mitigating the environmental impact of pollutant diffusion in these industrial processes. Therefore, this study examines the effects of porous medium, thermal radiation, magnetic effect, and external pollutants in a water-based ternary hybrid nanofluid flow within the context of the Reiner-Philippoff fluid model. The suitable similarity transformations are utilized to transform the partial differential equations (PDEs) into ordinary differential equations (ODEs). The resulting set of ODEs are solved numerically to find the solutions using the function bvp4c available in MATLAB software. The ternary hybrid nanofluid (Ag-Cu-TiO 2 ) significantly enhances heat and mass transfer rates by about 42.72 % and 2.53 % compared to water (H 2 O) at around 4.36 % and 0.60 % relative to the hybrid nanofluid (Ag-TiO 2 ), respectively. In pollutant-free conditions, the heat and mass transfer of ternary hybrid nanofluid (Ag-Cu-TiO2) progresses up to 0.34 % and 0.26 %, respectively, compared to H 2 O. Meanwhile, for hybrid nanofluid (Ag-TiO2), it develops by about 0.24 % and 0.31 %, respectively. This indicates that the impact of the external pollutants significantly delays mass transfer but increases the concentration field and destabilizes the flow near the shrinking sheet. Trio slip parameters reduce shear stress, heat, and mass transfer rates, while the mixed convection parameter enhances the skin friction coefficient in the assisting flow and diminishes it in the opposing flow. The magnetic parameter enlarges shear stress with the help of the Lorentz force but thermal radiation increases the heat transfer rate while reducing surface drag. Additionally, nanoparticle volume fractions and the porous medium elevate shear stress and heat transfer rate. This research provides insights into optimizing nanofluids in pollutant-laden environments, with potential applications in industrial processes involving heat exchangers and pollution control. The datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request.