Hybrid nanofluid flow and heat transfer past a permeable stretching/shrinking surface with a convective boundary condition

Abstract

The steady flow and heat transfer past a permeable stretching/shrinking surface in a hybrid nanofluid with a convective boundary condition is studied. The governing equations of the problem are transformed to the similarity equations by using similarity transformation technique. The problem is solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The plots of the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles for selected parameters are presented. Results show that dual solutions exist for a certain range of the stretching/shrinking and suction parameters. The critical values of these parameters decrease with the increasing of the copper (Cu) nanoparticle volume fractions. It is found that the heat transfer rate for hybrid nanofluid is higher than that for nanofluid for the impermeable stretching surface. It is also found that the increasing of the copper (Cu) nanoparticle volume fractions enhances the skin friction coefficient and reduces the local Nusselt number for the shrinking surface. The rise in Biot number leads to the increment of the temperature at the surface and widen the thermal boundary layer for both branches. A temporal stability analysis is performed to determine the stability of the dual solutions in a long run, and it is revealed that only one of them is stable while the other is unstable.