Existence and nonuniqueness of solutions for flow driven by a revolving hybrid nanofluid above a stationary disk

Abstract

The qualitative and quantitative properties of solutions associated with the nonlinear and coupled boundary value problems (BVPs) that describe the thermo-hydrodynamics of a hybrid nanofluid rotating over a stationary disk with suction are under investigation. First, essential a priori boundedness conditions are derived, and proof guaranteeing the existence of a solution to these BVPs is given. Next, numerically, it is shown that solutions to these equations are non-unique, exhibiting two solution branches to the problem within a particular range of the suction parameter. The influence of relevant flow parameters on radial and tangential shear stresses, Nusselt number, dimensionless velocity, and temperature profiles is presented graphically for both branches of the solution, with a detailed discussion of their physical significance. The results show that the oscillatory behavior of the first solution decreases with increased suction, whereas, in contrast, the second solution branch continues to oscillate as suction increases and extends indefinitely. Furthermore, a linear temporal stability analysis shows that only the first solution branch is stable, while the second branch is unstable. Finally, an asymptotic expression providing insights into the large suction behavior is also derived.