Analytical and numerical studies on heat transfer of a nanofluid over a stretching/shrinking sheet with second-order slip flow model

The objective of the present study is to analyse the steady second-order slip flow and heat transfer of an incompressible viscous water-based nanofluid over a stretching/shrinking sheet both analytically and numerically. Using the scaling group transformations, a system of partial differential equations governing the flow and thermal fields is transformed into a system of ordinary differential equations. An exact solution to the momentum equation is obtained, and the solution of the energy equation is obtained in terms of a hypergeometric function for different water-based nanofluids containing Au, Ag, Cu, Al, Al2O3 and TiO2 nanoparticles. Numerical solutions are obtained using a fourth-order Runge–Kutta method coupled with a shooting iteration technique. It is found that there exist a unique solution in the case of a stretching sheet with suction, but there is no solution in both stretching and shrinking sheets with injection. Dual solutions are obtained in a shrinking sheet beyond a suction critical point. The presence of nanoparticles decreases the suction critical point. Excellent agreement is observed between the analytical and numerical results. The effects of important physical parameters are analysed in detail. The corresponding local skin-friction coefficient and the reduced Nusselt number are also calculated and displayed in tables.