Optimality to flow and design of branching ducts

Abstract

Complex flow systems such as the vascular and respiratory trees are made of large and small ducts connected together. While the Hess–Murray law is supported by a number of empirical studies, it will not always hold. To account to this, extensions of this law were put forth by several authors. The numerical study presented in this paper explores the performance of branching systems of ducts in terms of total fluid flow resistance and distribution of shear stresses for both laminar Newtonian and non-Newtonian fluids. Deviations from and extensions to Hess–Murray law are comprehensively identified and discussed. New insights into the dynamics within the assembly of ducts are presented.