### Poiseuille and thermal transpiration flows of a highly rarefied gas

Takata, S *(Kyoto)*

Tuesday 14 September 2010, 14:50-15:35

Seminar Room 2, Newton Institute Gatehouse

#### Abstract

Poiseuille and thermal transpiration flows of a highly rarefied gas are investigated on the basis of the linearized Boltzmann equation, with a special interest in the overconcentration of molecules with a velocity parallel to the walls. An iterative approximation procedure with an explicit error estimate is presented, by which the structure of the over-concentration is clarified. A numerical computation on the basis of the procedure is performed for a hard-sphere molecular gas to construct a database that promptly gives the induced net mass flow for an arbitrary value of large Knudsen number. An asymptotic formula of the net mass flow is also presented for molecular models belonging to Grad's hard-potential. Finally, the resemblance of the profiles between the heat flow of the Poiseuille flow and the flow velocity of the thermal transpiration will be pointed out.
This is a joint work with Hitoshi FUNAGANE.

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