Numerical Stability of Magnetized Williamson Nanofluid over a Stretching/shrinking Sheet with Velocity and Thermal Slips Effect

A numerical investigation is carried out on multiple solutions over a stretching/stretching sheet to examine the influence of thermal radiation, Lorentz force, velocity, and thermal slips on Williamson nanofluid. Nanofluids have significant applications owing to their potential properties and versatility. The Navier-Stokes equations are converted in terms of PDEs, which are then altered to ODEs through suitable transformations. The novelty of the current study is to investigate the stability of the Williamson nanofluid with the Prandtl effect over stretching/stretching sheets. The numerical results are obtained by using the Runge-Kutta order 4th-method. The analysis observes two branches (dual solutions) for different parameters due to shrinking phenomena. Due to the non-uniqueness of the solutions, a stability analysis is implemented, and it is observed that the upper branch (first solution) is trustworthy. Dual solutions exist for a shrinking state (lambda(1)c <= lambda(1) <= -0.4578), the single branch exists when lambda(1 )> -0.4578, and no branch exists when lambda(1 )<= lambda(1)c. The findings demonstrate that as the slips and heat parameters are improved, the boundary layer thickness for the multiple solutions declines. Furthermore, the present analysis reveals that when the Williamson parameter is enhanced, the dual solutions for the concentration and temperature profiles are also increased. A validation analysis is carried out with published work and excellent agreement is established.