Energy minimization for the flow in ducts and networks

TL;DR

This paper explores the energy minimization principle as a fundamental rule governing flow equilibrium in ducts and networks, using both analytical and numerical methods to validate its applicability.

Contribution

It extends previous numerical studies by providing a more general analytical approach to demonstrate the energy minimization principle in flow systems.

Findings

Energy minimization can predict flow fields in ducts and networks

Analytical methods support the validity of the energy minimization principle

Numerical simulations confirm the principle's applicability

Abstract

The present paper is an attempt to demonstrate how the energy minimization principle may be considered as a governing rule for the physical equilibrium that determines the flow fields in tubes and networks. We previously investigated this issue using a numerical stochastic method, specifically simulated annealing, where we demonstrated the problem by some illuminating examples and concluded that energy minimization principle can be a valid hypothesis. The investigation in this paper is more general as it is based to a certain extent on an analytical approach.