Microtube Gas Flows With Second-Order Slip Flow and Temperature Jump Boundary Conditions

Second-order slip flow and temperature jump boundary conditions are applied to solve the momentum and energy equations in a microtube for an isoflux thermal boundary condition. The flow is assumed to be hydrodynamically fully developed, and the thermal field is either fully developed or developing from the tube entrance. In general, first-order boundary conditions are found to over predict the effects of slip and temperature jump, while the effect of the second-order terms is most significant at the upper limit of the slip regime. The second-order terms are found to provide a correction to the first-order approximation. For airflows, the maximum second-order correction to the Nusselt number is on the order of 50%. The second-order effect is also more significant in the entrance region of the tube. Nusselt numbers are found to increase relative to their no-slip values when temperature jump effects are small. In cases where slip and temperature jump effects are of the same order, or where temperature jump effects dominate, the Nusselt number decreases when compared to traditional no-slip conditions.