Friction numbers and viscous dissipation heating for laminar flows of water in microtubes

The friction numbers for laminar flows of water in microtubes, determined from the temperature rise due to the viscous dissipation heating assuming a velocity slip, show a strong dependence on the diameter and aspect ratio. The calculated values compare well with those determined from experimental data for water flows in glass and diffused silica microtubes (16-101 mu m in diameter D and aspect ratios L/D=499-1479). With a slip, the friction number almost exponentially decreases as D decreases and, to a lesser extent, as L/D increases. For D>400 mu m, the friction number approaches the theoretical Hagen-Poiseuille for macrotubes (64) when L/D>similar to 1500, but higher values at smaller L/D. The developed semiempirical analytical expression for calculating the friction number is in good agreement with the numerical and experimental results. The results suggest the presence of a velocity slip in the experiments and the plausible presence of a thin nanolayer at the walls of the microtubes. For D>200 mu m, this layer, if exists, is estimated to be similar to 18.9 nm, but increases to similar to 21.5 nm for D < 200 mu m, when (R) over bare=800 and L/D=1479.