Flow of Power Law Fluids in Tubes of Elliptical Cross Sections

In this paper we continue our previous investigation about the use of stress function in the flow of generalized Newtonian fluids through conduits of circular and non-circular (or/and multiply connected) cross sections where we inspect the flow of power law fluids in tubes of elliptical cross sections. We derive analytical expressions for the flow velocity profile and for the volumetric flow rate. We also develop numerical algorithms for computing the velocity profile and the volumetric flow rate for this flow where these algorithms produce virtually identical results to the results obtained from the aforementioned analytical expressions. The obtained analytical expressions were tested against the available analytical expressions for the special cases of Newtonian flow in circular tubes, Newtonian flow in elliptical tubes and power law flow in circular tubes and the results were identical. The obtained analytical expressions were also tested for sensible trends, tendencies and correlations and they passed all these tests.