Viscous dissipation in laminar water flows in micro-tubes

Numerical calculations are performed to investigate the effect of viscous dissipation on the temperature rise and friction numbers for laminar water flows in micro-tubes. The calculated values are compared with those determined from reported experimental data for glass and diffused silica microtubes (D = 16-101 mu m and L/D = 625-1479). The results confirm a definite slip at the wall with slip lengths of similar to 0.7 mu m and 1.0 mu m, which decrease the friction number and the temperature rise in the micro-tubes, but their effect gradually diminishes as either D or L/D increases. The friction number decreases exponentially as D decreases and, to a lesser extent, as L/D increases. The effect of L/D on the friction number is insignificant for micro-tube diameters <= 20 mu m. For D > 400 mu m, the friction number approaches that of Hagen-Posieuille of 64 for macro-tubes when L/D > 1500, but approaches higher values at smaller L/D. The dimensionless analytical expression developed for calculating the friction number and the temperature rise for water flows in micro-tubes is in good agreement with both the numerical and experimental results.