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Thermal transpiration for the linearized Boltzmann equation. (English) Zbl 1107.35004

Summary: The phenomena of thermal transpiration due to the boundary temperature gradient is studied on the level of the linearized Boltzmann equation for the hard-sphere model. We construct such a flow for a highly rarefied gas between two plates and also in a circular pipe. It is shown that the flow velocity parallel to the plates is proportional to the boundary temperature gradient. For a highly rarefied gas, that is, for a sufficiently large Knudsen number \(\kappa\), and the flow velocity between two plates is of the order of log \(\kappa\), and the flow velocity in a pipe is of finite order. Our analysis is based on certain pointwise estimates of the solutions of the linearized Boltzmann equation.

MSC:

35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35Q35 PDEs in connection with fluid mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
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