Abstract
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 (Sgen,fr) varies exactly the same way; hence, Po and Sgen,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 Sgen,fr show 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 Sgen,fr. It is found that in hydrodynamically developing region, both Po and Sgen,fr decrease with decreasing D, which is the identified micro-effect.