Some considerations on thermal boundary condition of slip flow

The slip effect of gaseous flow in a micro-scale channel is dominant when the characteristic length is less than about 10 μm under atmospheric conditions. The slip flow in a channel whose wall temperature is specified can be analyzed by solving the momentum and energy equations with taking into account the slip velocity and temperature jump. However, when there is slip, the shear work due to the slip at the wall should be included to calculate the heat flux from the wall. Unfortunately, the need of inclusion of the shear work in the heat balance equation has not been physically explained. In this paper, the physical reason of the inclusion of the shear work in the heat balance equation is physically explained from the point of view of both conservation law of energy and the kinetic theory of gases.