Heat transfer and axisymmetric stagnation point flow due to a shrinking vertical plate in a nanofluid with slip effects

Abstract

The problem on steady axisymmetric stagnation point flow with velocity slip due to a shrinking vertical plate in a nanofluid was studied. This problem was focussing on the first-order and second-order velocity slip effects on the governing parameters, such as mixed convection parameter σ and nanoparticle volume fraction φ. Three types of nanofluids were considered in this study which known as Copper (Cu), Alumina (Al2O3) and Titania (TiO2) with the Prandtl number, Pr=6.2. In order to solve the problem, solver bvp4c in Matlab has been applied to solve the numerical part. Before the numerical phase, the governing system of partial differential equations was transformed first into ordinary differential equations by similarity transformation. Then, the observation was done to study the effects of first and second order velocity slip parameter, Δ and Λ, mixed convection parameter σ and nanoparticle volume fraction φ on heat transfer and fluid flow. Dual solutions exist for a certain range of mixed convection parameter σ. It is observed that when the nanoparticle volume fraction increase, the shear stress on the shrinking sheet also increase, same goes for heat transfer rate regarding the first-order and the second-order velocity slip parameters, Δ and Λ. The rate of heat transfer can be raised when the magnitude of the first-order and the second-order velocity slip parameter, Δ and Λ, decrease.