Energy Minimization in Fluid Flow through Tubes and Networks of Various Geometries

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.