Imperfect accommodation effects on the flow induced by thermal stresses in a rarefied gas

In order to find out the effect of imperfect accommodation of gas molecules at a solid boundary on the flow due to thermal stress, the behavior of gas around an arbitrary but smooth shaped body with a uniform temperature which is placed in an infinite expanse of gas at rest with nonuniform temperature is investigated. The basis of the study is the linearized Boltzmann-Krook-Welander equation with Maxwell type boundary conditions for small Knudsen numbers. A formula for the slip velocity due to thermal stress is derived. The slip coefficient is increased as the accommodation coefficient is decreased. A sphere placed in a gas with a uniform temperature gradient is taken as an example. The physical mechanism of how the flow is induced is also discussed.