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

Background: 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. Methods: 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. Results: 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. Conclusions: 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.

Second-order slip, Heat transfer, Nanofluid, Scaling group transformations, Stretching/shrinking sheet