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 noncircular (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. [1]

In this paper we continue our previous investigation about energy minimization in the flow of fluids through tubes and networks of interconnected tubes of various geometries. We will show that the principle of energy minimization holds independent of the geometry of the tubes and networks of such interconnected tubes and independent of the type of fluid in such geometries where in this regard we consider generalized Newtonian fluids. We consider in this investigation the flow of Newtonian fluids through tubes and networks of interconnected tubes of elliptical, rectangular, equilateral triangular and concentric circular annular cross sectional geometries. We also consider a combination of geometric factor with a fluid type factor by showing that the principle of energy minimization holds in the flow of some non-Newtonian fluids (namely power law, Ellis and Ree-Eyring fluids) through tubes and networks of interconnected tubes of elliptical cross sections. The relevance of this study extends beyond tubes and networks of fluid flow to include for instance porous media and electrical networks.

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 noncircular (or/and multiply connected) cross sections where we visualize the stages of yield in the process of flow of viscoplastic fluids through tubes of elliptical, rectangular, triangular and annular cross sections. The purpose of this qualitative investigation is to provide an initial idea about the expected yield development in the process of flow of yield-stress fluids through tubes of some of the most common non-circular (and non-simply-connected) cross sectional geometries. [1]