Oblique stagnation-point flow of a nanofluid past a shrinking sheet

Abstract

Purpose – The laminar two-dimensional stagnation-point flow and heat transfer of a viscous incompressible nanofluid obliquely impinging on a shrinking surface is formulated as a similarity solution of the Navier-Stokes, energy and concentration equations. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The effect of the dimensionless strain rate, shrinking parameter, Brownian motion parameter and thermophoresis parameter on the flow, temperature and nanoparticle volume fraction is investigated in details. The paper aims to discuss these issues. Design/methodology/approach – The transformed system of ordinary differential equations was solved using the function bvp4c from Matlab. The relative tolerance was set to 10−10. Findings – It is found that dimensionless strain rate and shrinking parameter causes a shift in the position of the point of zero skin friction along the stretching sheet. Obliquity of the flow toward the surface increases as the strain rate intensifies. The results indicate that dual solutions exist for the opposing flow case. Research limitations/implications – The problem is formulated for an incompressible nanofluid with no chemical reactions, dilute mixture, negligible viscous dissipation and negligible radiative heat transfer assuming nanoparticles and base fluid are locally in thermal equilibrium. Beyond the critical point λ c to obtain further solutions, the full basic partial differential equations have to be solved. Originality/value – The present results are original and new for the oblique stagnation-point flow of a nanofluid past a shrinking sheet. Therefore, this study would be important for the researchers working in the relatively new area of nanofluids in order to become familiar with the flow behavior and properties of such nanofluids.