Flows of Incompressible Fluids subject to Navier's slip on the boundary

We establish closed form analytical solutions for the flows of a generalized fluid of complexity two which includes the Navier–Stokes fluid, power-law fluid and the second-grade fluid as special subclasses, in special geometries under the assumption that the flows meet the Navier’s slip conditions at the boundary. We also allow for different boundary conditions at different parts of the boundary, that leads to interesting consequences with regard to the solutions. The dependence of the form of the solutions on the boundary conditions is discussed in some detail. We also discuss the nature of the solutions in the two limits, that of no-slipping on the one hand and the no-sticking on the other hand.