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On computing the thermal-slip coefficient from Kramers’ problem

Classical techniques are used to derive a variant of an Onsager relation (used typically for Poiseuille flow and thermal-creep flow) that yields a convenient relationship between the heat flow of Kramers’ problem and the thermal-slip coefficient. The analysis is based on the linearized Boltzmann equation for rigid-sphere interactions, and wall interactions are described by a general law that includes, for example, the Maxwell model (a mixture of specular and diffuse reflection) and the Cercignani–Lampis model.