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We investigate the possibility that the spatial dependency of stress ingeneralized Newtonian flow systems is a function of the applied pressure fieldand the conduit geometry but not of the fluid rheology. This possibility iswell established for the case of a one-dimensional flow through simplyconnected regions, specifically tubes of circular uniform cross sections andplane thin slits. If it can also be established for the more general case ofgeneralized Newtonian flow through non-circular or multiply connectedgeometries, such as the two-dimensional flow through conduits of rectangular orelliptical cross sections or the flow through annular circular pipes, thenanalytical or semi-analytical or highly accurate numerical solutions; regardingstress, rate of strain, velocity profile and volumetric flow rate; for thesegeometries can be obtained from the stress function, which can be easilyobtained from the Newtonian case, in combination with the constitutiverheological relation for the particular non-Newtonian fluid, as done previouslyfor the case of the one-dimensional flow through simply connected regions.

Using the stress function in the flow of generalized Newtonian fluids through conduits with non-circular or multiply connected cross sections