Some properties of a gas flow submitted to a temperature gradient

•The gaseous flow through channels generated by a temperature gradient is analyzed.•An expression to estimate the Thermomolecular Pressure Difference is proposed.•A quasi-analytical expression of the relaxation time is proposed.•These estimated TPD and relaxation time are validated by experimental data. The flow of gases through channels generated by a temperature gradient along the channel surfaces is analyzed. This flow is characterized by the Thermomolecular Pressure Difference (TPD) at steady state and by the relaxation time, a characteristic of the transient stage, which indicates the rate at which the flow reaches the steady state. From a simple analytical description an expression to estimate the TPD is proposed. Experimental data obtained in channels with rectangular and circular cross-sections are analyzed, showing good agreement with the estimated TPD. Two normalizations of TPD are suggested that eliminate the gas and cross-section dependences, allowing application of this normalization to a channel with an unknown cross-section. Then, a quasi-analytical expression of the relaxation time is proposed. This expression makes it possible to explicitly calculate the relaxation time for the thermal creep flow in a channel of the rectangular and circular cross-sections using the numerical results obtained from the kinetic theory of gases. The proposed expressions are compared to the experimental data and the good agreement is found. In the case of channels of unknown cross-section, the relaxation time can be related to the channel conductance and the relaxation time can also be calculated using the proposed expression.