Viscous heating in liquid flows in micro-channels

Many experimental works on forced convection through micro-channels evidenced that when the hydraulic diameter is less than 1 mm, 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. On the contrary, in this paper the explanation of the experimental results obtained for micro-channels in terms of friction factors will be researched inside the conventional theory (Navier-Stokes equations). In particular, this paper will focus on the role of viscous heating in fluids flowing through micro-channels. A criterion will be presented to draw the limit of significance for viscous dissipation effects in micro-channel flows. The role of the cross-sectional geometry on viscous dissipation will be highlighted and the minimum Reynolds number for which viscous dissipation effects can no longer be neglected will be calculated as a function of the hydraulic diameter and of the micro-channel geometry for different fluids. It will be demonstrated how viscous effects can explain some experimental results on the Poiseuille numbers in micro-channels, which recently appeared in the open literature.