Flow and heat transfer over an unsteady shrinking sheet with suction in nanofluids

The unsteady flow over a continuously shrinking surface with wall mass suction in a water based nanofluid containing different type of nanoparticles: Cu, Al2O3 and TiO2 is numerically studied. Similarity equations are obtained through the application of similarity transformation techniques. The shooting method is used to solve the similarity equations for different values of the wall mass suction, the unsteadiness and the nanoparticle volume fraction parameters. The results of skin friction coefficient image and heat transfer rate −θ′(0) are presented in tables and graphs. It is found that dual solution exists for a certain range of wall mass suction s, volume fraction φ and unsteadiness parameters A. The results of velocity and temperature profiles are also presented. It is seen that two values of boundary layer thickness η∞ are obtained, which gives two different velocity and temperature profiles that satisfy the boundary conditions. It is also found that the nanoparticle volume fraction parameter φ and types of nanofluid play an important role to significantly determine the flow behaviour.