The viscous dissipation as a scaling effect for laminar single-phase flows in micro-channels

Many experimental works on the forced convection through microchannels seem to evidence that, when the hydraulic diameter is less than 1 mm, the conventional theory can no longer be considered as suitable to predict the pressure drop and convective heat transfer coefficients. This conclusion seemed valid for both gas and liquid flows. Sometimes the authors justified this claim by invoking “new” micro-effects. In the last years, this conclusion seems to be controverted by additional, more accurate experimental data. For this reason, in this lecture the explanation of the experimental results obtained for microchannels in terms of friction factors and convective heat transfer in the laminar regime is sought for within the bonds of the conventional theory. In particular, this lecture focuses on the role of viscous heating in liquids flowing through microchannels, considering them as scaling effects. The role of the cross-sectional geometry on the viscous heating is highlighted for adiabatic and diabatic channels. Design-correlations useful in defining the limit of significance of the most important scaling effects for microchannels, like viscous heating and conjugate heat transfer are also presented.