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 (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.

Characterization of the Hydrodynamically Developing Flow in a Microtube Using MTV

Micro-molecular tagging velocimetry (μMTV) has been used to characterize the hydrodynamic developing flow in a microtube inlet with a nominal inner diameter of 180μm. Velocity profile data at 11 axial locations within the hydrodynamic developing region were acquired using the μMTV approach and the results represent the first characterization of hydrodynamically developing pipe flow at the microscale. The uncertainty in measurements of time-averaged velocity profiles ranged from 6% to 7% of the centerline velocity. The uncertainty in instantaneous measurements is in the range 8%–16% of the peak maximum velocity. Data were taken at Reynolds numbers of 60, 100, 140, 290, and 350. The data suggest the formation of a vena contracta with either locally turbulent flow or unsteady laminar flow separation early in the tube for the larger Reynolds (Re) numbers, which is quite different from macroscale experiment or numerical simulation where a vena-contracta is not observed for Re<500. The velocity profiles obtained very near the tube entrance exhibited a uniform velocity core flow surrounded by regions of relatively stagnant fluid in the near wall regions. The size of the inferred recirculation zones, measured velocity rms, and maximum shear rates all exhibit increasing magnitude with increasing Reynolds number. The velocity profiles were observed to evolve in the downstream direction until the classical parabolic distribution existed. The total hydrodynamic entry length agrees well with values published in the literature for laminar flow with a uniform inlet velocity, despite the existence of the observed vena contracta.

Heat Convection in a Horizontal Curved Pipe

Thermally and hydrodynamically developing flow in heated horizontal curved pipes is analyzed. The perturbation solution is quantitatively valid only in a small region near the pipe inlet. The solution, however, provides information about the physical importance of centrifugal force and buoyancy on the developing flow. It also reveals the length and the velocity scales for the downstream regions where the secondary flow can not be treated as a small perturbation. The relative importance of centrifugal force and buoyancy is determined by the ratio of the Dean number and the Grashof number.