Entropy Generation and Poiseuille Number Link in Developing Isothermal Laminar Micro-Flow

It is well-known that Poiseuille number (Po, hitherto viewed mainly as a fluid mechanics parameter) decreases along a hydrodynamically developing flow, from infinity at inlet to a fixed value downstream. This study reveals that the dimensionless entropy generation rate per unit length due to fluid friction (S gen,fr) varies exactly the same way; hence, Po and S gen,fr are jointly studied for their dependence. Laminar hydrodynamic development of isothermal flow of incompressible fluid (water) in a circular micro-tube (diameter, D) is examined. Results are obtained for a given flow velocity for different D, and then, numerical experiments are conducted for different flow velocities for the same D-values. Striking similarity in trends of Po and S gen,fr shows a unique linear relation between them for the hydrodynamically developing region. It is theoretically shown that Po is a direct measure of entropy generation due to fluid friction, which explains its numerically obtained linear relation with S gen,fr. It is found that in hydrodynamically developing region, both Po and S gen,fr, decrease with decreasing D, which is the identified micro-effect.