Dual solutions of a mixed convection flow of nanofluids over a moving vertical plate

This paper deals with the development of a mixed convection flow of nanofluids over a moving vertical plate. The external flow and the stretching velocities are assumed to be constant. It is assumed that the plate moves in the same or opposite direction to the free stream. Using the local similarity method, it has been shown that the dual solutions of velocity and temperature fields exist for certain values of suction/injection, mixed convection, nanoparticle volume fraction and velocity ratio parameters. The non-linear ordinary differential equations along with the boundary conditions form a two point boundary value problem and are solved using Shooting method, by converting into an initial value problem. The initial value problem for a final set of first order system of ordinary differential equations is solved by fourth-order Runge-Kutta method. Three different types of nanoparticles, namely Copper (Cu), Aluminum Oxide (Al2O3), and Titanium Oxide (TiO2) are considered by using water-based fluid with Prandtl number Pr = 6.2. The effect of the solid volume fraction parameter φ of nanofluids on the heat transfer characteristics is also investigated. The results indicate that dual solutions exist when the plate and the free stream moves in the same as well as in the opposite direction. The effects of various parameters on the velocity and temperature profiles are also presented here.