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In this work the laminar-to-turbulent transition in microchannels of circular cross-section is studied experimentally. In order to single out the effects of relative roughness, compressibility and channel length-to-diameter ratio on the Reynolds number at which transition occurs, experimental runs have been carried out on circular microchannels in fused silica-smooth for all purposes-and in stainless steel (which possess a high surface roughness), with a diameter between 125 and 180 lm and a length of 5-50 cm through which nitrogen flows. For each tube the friction factor has been computed. The values of the critical Reynolds number have been determined plotting the Poiseuille number (i.e., the product of the friction factor, f, times the Reynols number, Re) as a function of the average Mach number between inlet and outlet. The transitional regime was found to start no earlier than at values of the Reynolds number around 1,800-2,000. It has been observed that surface roughness has no effect on the hydraulic resistance in the laminar region for a relative roughness lower than 4.4%, and that friction factor obeys the Poiseuille law, if it is correctly computed taking compressibility into account. It is found that recent correlations for the prediction of the critical Reynolds number in microchannels that link the relative roughness of the microtubes to the critical Reynolds number do not agree with the present results. List of symbolsMass flow rate (kg s -1 ) Ma Mach number P pressure (Pa) R gas constant (J kg -1 K -1 ) Re Reynolds number T temperature (K)Greek symbols D difference d relative uncertainty (%) e roughness (m) c specific heat ratio (c p /c v ) l dynamic viscosity (kg m -1 s -1 ) q density (kg m -3 )

A heat sink consisting of microchannels of rectangular or trapezoidal cross-section through which a polar fluid is circulated by means of an electro-osmotic pump was studied numerically. The equivalent pressure head–volume flow rate curve was determined for both geometries and the influence of the aspect ratio was investigated. The dimensionless temperature profile was determined keeping also the effect of Joule heating into account. The cross-sectional Nusselt number was calculated for the above conditions and was found to be strongly influenced by the ratio of Joule heating to convective heat flux, Mz. The dependence of the Nusselt number on the dimensionless electro-osmotic diameter (kDh) was also investigated for the two geometries and for increasing values of Mz, and a comparison with the values obtained analytically for slug flow under the same conditions was made. The value of the Nusselt number as a function of the aspect ratio was also calculated for increasing values of Mz. The numerical data presented in this paper can be useful to optimize the thermal performance of silicon micro heat-sinks.

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