Thermal boundary conditions for convective heat transfer of dilute gases in slip flow regime

For gaseous flows in the slip flow regime, the power of the viscous stress at the wall is not zero. From the fluid domain point of view, it is a sink term, or a lost heat flux, that must be taken into account. It must be added to the diffusive heat flux in the fluid to appropriately model the heat flux transmitted from the fluid to the wall and the temperature field. The present technical note aims at theoretically establishing the appropriate thermal conditions in a general context: both thick and thin walls are considered as well as for imposed temperature (H1), imposed heat flux (H2) and convective heat transfer (H3) at the wall. Recent validations of this model, resulting from experimental and numerical comparisons of the convective heat transfer at the walls, are briefly discussed.