Effect of thermal conductivity on the Knudsen layer at ablative surfaces

In this article we develop an analytical model of the Knudsen layer at the ablative wall taking into account the temperature gradient in the bulk gas. The analysis is based on the premise that the temperature gradient in the bulk gas can be taken into account in the velocity distribution function at the outer boundary of the Knudsen layer. The model uses a bimodal velocity distribution function in the Knudsen layer, which preserves the laws of conservation of mass, momentum, and energy and converges to the Chapman–Enskog velocity distribution function at the outer boundary of the layer. The model is applied to polyethylene ablation, for which two cases are considered: (a) the ablation process is due to pure heat conduction to the surface, with no external heating of the ablated surface, and (b) the ablation is due to both the thermal conduction and an external heating of the surface, e.g., vaporization of a metal exposed to laser radiation. The region of validity of the existing models and effect of the temperature gradient on the Knudsen layer properties are calculated.