Miniature flow passages, defined here as passages with hydraulic diameters smaller than about 1 mm, have numerous applications. Some current applications include monolith chemical reactors, inkjet print-heads, bioengineering and biochemistry (lab-on-the-chip; drug delivery with ultrathin needles, etc.), microflow devices (micropumps, micro heat exchangers, etc.), and cooling systems for microelectronic and high-power magnets, to name a few. Miniature flow passages are an essential part of microfluidic devices, in which can be broadly defined as devices in which minute quantities of fluid are applied. Cooling systems based on microchannels can provide very large volumetric heat disposal rates that are unfeasible with virtually any other cooling technology. Their widespread future applications may in fact revolutionize some branches of medicine and industry.

The serious study of flow in capillaries (tubes with D ≈ 1 mm) goes back to at least the 1960s. The application of microchannels for cooling of high-power systems is relatively new, however (Tuckerman and Pease, 1981). The literature dealing with flow in microtubes is extensive. Useful reviews include those of Papautsky et al. (2001), Morini (2004), Krishnamoorthy et al. (2007), and Fan and Luo (2008). The field of flow in miniature channels, in particular with respect to very small channels (microfluidics and nanofluidics) is a rapidly developing one. In this chapter we review the flow regimes and size-based miniature flow passage categories, and we discuss the limitations of the classical convection heat and mass transfer theory with respect to its application to miniature flow passages.