Unsteady flow of Maxwell fluid in the presence of nanoparticles toward a permeable shrinking surface with Navier slip

A detailed study on the problem of unsteady boundary layer flow and heat transfer of an upper-convected Maxwell fluid in the presence of nanoparticles over a permeable shrinking sheet with wall mass transfer is presented. In contrast to the conventional no-slip condition at the surface, Navier's slip condition is applied at the surface. By use of a similarity transformation, the partial differential equations are reduced to a system of ordinary differential equations which is then solved numerically with shooting technique. The numerical results pertaining to the present study indicate that dual solutions exist for negative values of the unsteadiness parameter (A). It results in from the stability analysis that the upper branch solutions are stable and physically realizable, while the lower branch solutions are not stable and, therefore, not physically realizable. It is also found that as the Maxwell parameter (β) and velocity slip parameter (δ) increase, the range of the unsteadiness parameter (A) for which the solution exists gradually increases. The local Nusselt number and the local Sherwood number increase with the increase in the values of Maxwell parameter (β) and velocity slip parameter (δ). Furthermore, the effects of different physical parameters on the flow, temperature and concentration profiles are shown graphically and discussed in details.