Shape uncertainty analysis of laminar forced convection in a round microchannel with viscous dissipation

This paper is aimed at analysing the effects of roughness caused by random geometric uncertainties in microchannels and how these can influence heat transfer and pressure drop in fluid flow within such geometries. The shape of a microchannel is typically affected by significant uncertainty due to the small size of the cross-section, which is comparable to the typical wall-roughness length scale. While this uncertainty exists at any scale, it becomes amplified and critically important when the hydraulic diameter is smaller than a few tens of micrometer. The analysis is performed numerically, considering a nominally circular channel with random variations in its cross-section within a prefixed maximum extent, effectively representing roughness at the micro-scale. The adopted mathematical model considers fully developed heat and fluid flow by taking into account the effect of viscous dissipation and an irregular cross-section is generated by random geometric variations. The effects of an increasing wall roughness generally lead to an increase in the Fanning friction factor and a decrease in the wall heat transfer rate, as expressed by the Nusselt number.