### Mathematical modeling of the heat transfer process in a rectangular channel depending on Knudsen number

#### O. V. Germider^{1}, V. N. Popov^{2}

Annotation | A solution of heat transfer problem in a long rectangular channel has been found using the kinetic approach. In channel the constant temperature gradient along the axis of symmetry is supported. For the basic equation that describes the kinetics of the process Williams kinetic equation is used. For the boundary condition on the channel walls the model of diffuse reflection is used. The deviation from the state of rarefied gas equilibrium is assumed to be small. It allows to consider the solution of the problem in the linearized form. The heat flow vector profile is constructed in the channel and the heat flow through the channel cross-section is calculated, depending on the ratio lengths of rectangular cross-section and values of the Knudsen number. The results obtained upon transition to the free molecular regime and the hydrodynamic regime of the gas flow are analyzed. |
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Keywords | Boltzmann kinetic equation, Williams equation, model of diffuse reflection, analytical solutions, Knudsen number |

^{1}Post graduate student, Northern Arctic federal university named after M. V. Lomonosov, Arkhangelsk; o.germider@narfu.ru.^{2}Head of Mathematics Chair, Northern Arctic federal university named after M. V. Lomonosov, Arkhangelsk; v.popov@narfu.ru.

**Citation**: O. V. Germider , V. N. Popov , "[Mathematical modeling of the heat transfer process in a rectangular channel depending on Knudsen number]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,18:2 (2016) 85–93 (In Russian)