A generalized heat conduction model in rarefied gas

After showing the failure of the traditional heat conduction law in describing correctly the heat flux phenomenon in a rarefied gas at the slip regime, a generalized heat conduction model is presented. The model predicts a heat conduction boundary layer near the wall with a thickness proportional to the Knudsen number. It reduces to the Fourier law when the Knudsen number is sufficiently small. An analytic solution from the present model shows satisfactory agreement with that from gas molecular-dynamics simulation.