A novel lower bound for the friction factor-Reynolds number product in laminar flows of Newtonian fluids through singly connected ducts

Abstract

We revisit the analytical solution for steady, fully developed, pressure-driven flows of Newtonian fluids through n-sided cusped ducts and find that the friction factor–Reynolds number product is a non-monotonic function of n and converges to fRe=64/π2(≅6.486) in the limit as n→∞. To the best of our knowledge, this is the lowest fRe ever reported for laminar flows of Newtonian fluids through singly connected ducts. We discuss the implications of these results in the context of small-scale fluid flow and heat transfer systems and point directions for future studies in the field.