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 Navier slip conditions at the boundary. The boundary conditions allow the extremes of no-slipping and no-sticking. We also allow for different boundary conditions at different parts of the boundary, which 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.