Further validation to the variational method to obtain flow relations for generalized Newtonian fluids. Submitted

We continue our investigation to the use of the variational method to derive flow relations for generalized Newtonian fluids in confined geometries. While in the previous investigation we used the straight cylindrical tube geometry with six fluid rheological models to demonstrate and establish the variational method, the focus here is on the plane long thin slit geometry using two rheological models. We demonstrate how the variational principle based on minimizing the total stress in the flow conduit can be used to derive analytical expressions that are previously derived by other methods. Although the examples themselves are of little value, the optimization principle which the variational method is based upon has a significant theoretical value as it reveals the tendency of the flow system to assume a configuration that minimizes the total stress. Our proposal also offers a new methodology to tackle common problems in fluid dynamics and rheology