Dual solution of unsteady separated stagnation-point flow in a nanofluid with suction: A finite element analysis

Abstract

Unsteady two-dimensional stagnation-point flow of a viscous and incompressible fluid filled by a nanofluid over a permeable flat plate with suction has been investigated numerically. The mathematical model used for the nanofluid incorporates the effect of Brownian motion and thermophoresis. The velocity of the ambient (inviscisd) fluid has been assumed to vary linearly with the distance from the stagnation-point. The resulting non-linear governing equations with associated boundary conditions have been solved numerically using finite element method (FEM). The effect of the unsteadiness parameter A, mass suction parameter s, Lewis number Le, the Brownian motion parameter Nb and the thermophoresis parameter Nt on the flow, temperature and nanoparticle concentration in the boundary layer region have been analyzed graphically. The impact of the unsteadiness parameter and mass suction/injection parameter on the skin friction, rate of heat transfer and mass transfer have been examined and discussed. Interesting observation is that dual solutions exist for a certain range of the suction/injection parameter, and this range decreases with increasing values of the unsteadiness parameter.