Stability of dual solutions in aqueous Ti-alloy nanofluid with thermal radiation effect

The current article has identified dual solutions and their stability for the Ti-alloy/water nanofluid over an exponentially shrinking sheet, while taking into consideration the presence of magnetic fields, radiation and thermal buoyancy forces. The Tiwari and Das model has been utilised to formulate mathematical equations, which have subsequently been transformed from partial differential equations to ordinary differential equations using suitable similarity transformations. The transformed equations have been solved using the shooting method incorporated with the Runge–Kutta technique. Through the application of these techniques, it has been ascertained that multiple solutions have emerged for this problem. To assess the stability of these solutions, the eigenvalue approach has been employed. The eigenvalue approach has revealed that only the first solution is physically viable in laboratory settings, while the second solution is not. The effects of radiation on temperature, skin friction, velocity and heat transfer rate have been elaborated upon in detail. Furthermore, flow separation points have been identified and the rationale behind the delay in flow separation has been expounded upon. Streamlined patterns have been drawn and explained to enhance our understanding of the fluid flow behaviour. Finally, it is worth noting that these types of studies have significant applications in the medical and aerospace industries.