Stability Solution of Unsteady Stagnation-Point Flow and Heat Transfer over a Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect

Abstract

Computational of unsteady flow with slip condition is essential since physically the heat transfer process is time-dependent and there may exist slip between fluid and surface. Therefore, this study aims to investigate the unsteady stagnation-point flow and heat transfer over a stretching/shrinking sheet immersed in nanofluid in the presence of slip velocity. By applying boundary layer theory and Tiwari-Das model, the governing equations are developed and transformed into a system of ordinary differential equations using similarity transformation, which are then solved numerically using bvp4c solver in MATLAB. The influence of slip velocity, stretching/shrinking parameters, nanoparticle volume fraction and unsteadiness parameter on the local skin friction coefficient, local Nusselt number, as well as velocity and temperature profiles are analysed. There are three types of nanoparticles considered, namely Copper (Cu), Alumina (Al203), Titania (TiO2) and water (H20) is the base fluid. It is found that dual solutions occur for certain parameters and the stability analysis is performed. The analysis shows that the first solutions are found to be stable than the second solution. The local skin friction coefficient and local Nusselt number are increasing with slip velocity, nanoparticle volume fraction for shrinking case; however, the opposite trend is observed for stretching case. By raising 20% of nanoparticle volume fraction for the shrinking sheet ( the friction at the surface increases 24% and 15.5% for heat transfer rate for the first solution. Moreover, for 10% of nanoparticle volume fraction for the shrinking sheet (and the first solution, varying slip parameters from 0 to 0.2, give rise to approximately 21% of the friction at the surface and 68% of the heat transfer rate.