Notes on factitious shear work of slip flow in a channel

Gas slip flow is observed in a micro scale channel whose characteristic length is less than about 10 μm under atmospheric conditions. To analyze the slip flow, the energy equation with the viscous dissipation term is solved with a boundary condition which includes a factitious sliding shear work term due to the slip at the wall to compensate the energy balance. Recently, an alternate method which uses the boundary condition without inclusion of the factitious sliding shear work term has been proposed. However, it seems that physics of the slip flow has not been properly understood by researchers. In this paper to clarify the issue, a very simple configuration, a steady state laminar slip flow in a hydro-dynamically fully developed region of a circular micro-tube with an adiabatic wall, is considered. Also all thermo-physical properties of the fluid are assumed to be constant. Theoretical justification to the boundary condition of the energy equation is provided using the discontinuity of the velocity of the slip flow on the wall.