Steady Gyrostatic Nanofluid Flow past a Permeable Stretching/shrinking Sheet with Velocity Slip Condition using the Nanofluid Model Proposed by Buongiorno

A detailed analysis, is presented in this paper, for the steady gyrostatic nanofluid flow past a permeable stretching/shrinking sheet with slip condition using the nanofluid model proposed by Buongiorno. The microorganisms are imposed into the nanofluid to stabilize the nanoparticles to suspend due to a phenomenon called bioconvection. Considering appropriate similarity transformations, the five partial differential equations of mass conservation, momentum, thermal energy and microorganisms are reduced to a set of four ordinary (similar) differential equations with coupled linear boundary conditions. These equations   were both analytical and numerical solved using Runge-Kutta-Fehlberg technique. The influences of important physical parameters, such as, Prandtl number Pr, the Schmidt number Sc, the bioconvection Péclet number Pe, the Brownian motion parameter Nb, the thermophoresis parameter Nt and the stretching/shrinking parameter λ on the skin friction coefficient Cf and the local Nusselt number Nux, as well as on the velocity, temperature and gyration profiles, are interpreted through graphs and tables. Further, multiple (dual, upper and lower branch solutions) are found for the governing similarity equations and the upper branch solution expanded with higher values of the suction parameter. It can be confirmed that the lower branch solution is unstable. It is found that the bioconvection parameters have strong influence towards the reduced skin friction coefficient, reduced heat transfer, velocity and density of motile microorganism’s transport rates.