Transport Characteristics and Parametric Sensitivity of a Single-Stage Circular-Channel Knudsen Pump

Thermal transpiration enables a Knudsen pump to transport gas without moving components. An axial-integration formulation based on pre-computed transport coefficients from the linearized Shakhov kinetic model is applied to a single-stage unit comprising a circular microchannel and a circular macrochannel in series, with opposite wall-temperature gradients. The pressure-generation and gas-transport capabilities are characterized by the maximum pressure difference or thermomolecular pressure difference (TPD), the maximum mass flow rate, the equivalent TPD, the equivalent flow resistance, and the complete mass-flow-rate-pressure-difference characteristics. The principal quantitative calculations cover temperature differences ranging from 10 to 50 K, while the 75 and 100 K cases are retained only to assess the persistence of the calculated trends. The formulation reproduces benchmark experimental TPD data with a maximum absolute relative deviation of 12.5% and a mean absolute relative deviation of 6.7%, and shows excellent agreement with numerical data from the literature, with deviation below 1%. A decomposition of the microchannel and macrochannel contributions shows that a macrochannel contributing little to the total equivalent flow resistance may nevertheless produce appreciable reverse thermal transpiration. At the baseline condition of the study and for an inlet pressure Pi=10 kPa, the macrochannel contributes only 0.37% of the total equivalent flow resistance but cancels 15.2% of the microchannel equivalent TPD. Over Pi=1-50 kPa, the temperature-difference sensitivity of the TPD ranges from 0.93 to 1.05, whereas the microchannel-radius sensitivity varies from -0.41 to -1.62. For the maximum mass flow rate, the microchannel-radius sensitivity ranges from 2.06 to 2.56 and the microchannel-length sensitivity remains close to -1, while the macrochannel-length effect is negligible. Increasing the macrochannel radius improves both limiting outputs, i.e., TPD and maximum mass flow rate, but with progressively diminishing benefits from further enlargement of the macrochannel. These results provide a quantitative basis for preliminary dimension selection while explicitly identifying the limitations associated with linearization, finite channel length, fully developed flow, and neglected interface losses.