Mathematical modeling on colloidal mixture of Casson Sodium alginate ternary nanofluid suspensions driven by stretching surface with magnetic field and arbitrary power-law velocities: an analytical approach

The current research explores the influence of inclined MHD on Casson ternary nanofluid suspension over the accelerated surface with power law velocity. The focal point is a stretching/shrinking sheet featuring mass transpiration. The distinctive aspect of present work lies in examining the ternary nanofluid containing the nanoparticles, namely, TiO₂, Cu, and Ag in the Sodium alginate base fluid. There is a lack of research on ternary nanofluid flows in the presence of magnetic field and power-law velocities, the authors utilized the research gap and worked on the effect of MHD on Casson ternary nanofluid flow across the accelerated surface. Coupled nonlinear PDEs are transformed to ODEs via similarity transformations, and then calculated using the analytical method, the solutions are achieved in terms of closed forms with hyperbolic functions. The investigation outcomes reveals that magnetic field parameter enhances from 0.5 to 5 enhances the shear stress 29%, increasing the magnetic field values 1–4, decreases the both axial and transverse velocities approximately 25% for the injection case and reduces about 20% in suction case, increasing the Casson parameter from 1 to 5 causes a noticeable decline in axial velocity by approximately 26%, and the volume fraction parameter significantly influences the flow structure, lowering the velocity by about 14%. Present investigation has many practical applications in engineering, physical and biological, thrust bearing technologies, and cleaning engine lubricants, also used in magnetic resonance imaging systems which give detailed images of the human body and aid in medical diagnoses.