Laminar forced convection in circular microchannels with slip-flow: Analysis of randomly distributed roughness

This paper investigates the sensitivity of heat transfer and fluid flow to geometric uncertainties caused by roughness in microchannels. The study considers laminar, fully developed slip flow and temperature jump conditions in the momentum and energy equations, controlled by velocity slip (λ) and temperature jump (λT) parameters, under traditional H1 and H2 heating conditions. Microchannels with nominally circular geometries are analyzed, incorporating random boundary variations defined by a roughness parameter, δrmax∗. These variations generate unique geometries for each δrmax∗, grouped into samples for numerical simulation and statistical analysis. The analysis shows that for every configuration, a normal distribution of Poiseuille and Nusselt numbers values is obtained for each δrmax∗. An examination of the median and standard deviation of each sample reveals that increasing δrmax∗ leads to higher Poiseuille numbers and lower Nusselt numbers, indicating greater pressure drop and reduced heat transfer, respectively. The influence of slip length and temperature jump parameters was also assessed, revealing that while higher λ values reduce the friction factor, these cases are more impacted by roughness. Conversely, although an increase in λT significantly reduces the Nusselt number due to added thermal resistance, cases with lower λT are more sensitive to roughness effects.