## Poiseuille flow of a rarefied gas in a cylindrical tube: Solution of linearized Boltzmann equation.(English)Zbl 0713.76089

Summary: The existence of a minimum in the cylindrical Poiseuille flow of a rarefied gas has been known since the experiments of Knudsen (1909). Previously, the phenomenon has been studied with models of the Boltzmann equation, but results for the Boltzmann equation itself have not been reported. In the present paper, proceeding from recent studies, first the $$S_ N$$ numerical algorithm for solving the linearized Boltzmann equation for the cylindrical geometry is outlined. Then, explicit numerical results for a rigid sphere gas and the boundary condition of diffuse specular reflection are obtained. The results show a minimum of the flow rate, and generally provide a good description of the experimental data.

### MSC:

 76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics 82D05 Statistical mechanics of gases
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### References:

 [1] DOI: 10.1002/andp.19093330106 · JFM 40.0825.02 [2] DOI: 10.1002/andp.19324040804 · Zbl 0004.17702 [3] DOI: 10.1063/1.1761530 [4] DOI: 10.1063/1.1762304 · Zbl 0149.44601 [5] DOI: 10.1007/BF00944451 · Zbl 0496.76070 [6] DOI: 10.1063/1.864817 · Zbl 0547.76087 [7] DOI: 10.1063/1.857433 · Zbl 0659.76085 [8] DOI: 10.1063/1.857433 · Zbl 0659.76085 [9] DOI: 10.1063/1.857433 · Zbl 0659.76085 [10] DOI: 10.1063/1.857433 · Zbl 0659.76085 [11] DOI: 10.1063/1.857433 · Zbl 0659.76085 [12] DOI: 10.1063/1.857457 · Zbl 0661.76082 [13] DOI: 10.1063/1.857457 · Zbl 0661.76082
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