Experimental uncertainties analysis as a tool for friction factor determination in microchannels

The constant growth of the studies on microchannel flows has brought under question the validity of the relations for heat transfer and fluid flow, which are usually employed at the macroscales. Rarefied flows in the slip-flow region have attracted much attention and solutions have been developed using first- and second-order boundary conditions. These models need to be experimentally validated through careful test in order to be able to use them for more complex problems and engineering applications. In the current work the error propagation analysis is applied to a set of error-free measurements artificially generated in order to assess the influence of the uncertainty on each of the measured quantities on the determination of the Poiseuille number for rarefied flows: it is shown that the most limiting factor is the accuracy on the tube diameter, while flowrate and pressure drop errors can be kept contained provided the measurement ranges for the transducers are suitably chosen. The total uncertainty is also calculated and the limit of the investigable Reynolds numbers defined. The possibility of experimentally evidencing the differences between first- and second-order boundary conditions is investigated and it is concluded that this is the case only for highly rarefied flows (Kn > 0.5).