A flow of a slightly rarefied gas driven by a uniform external force within an infinitely long square duct is considered based on the kinetic theory. The steady behavior of the gas is investigated based on the Bhatnagar–Gross–Krook model of the Boltzmann equation and the diffuse reflection boundary condition. A systematic asymptotic analysis of the system for small Knudsen numbers is carried out, and a set of fluid-dynamic-type equations and their boundary conditions that describe the behavior of the gas are derived. The obtained momentum equation in the cross-sectional directions includes the thermal stress term. This is a rarefaction effect associated with the nonuniform temperature field developed by heating due to viscous dissipation of the main axial flow. Because of the thermal stress, the flow is not strictly unidirectional, and a slow secondary flow of the order of the Knudsen number is induced within the cross section. This secondary flow, through convection, has finite effects on the leading-order axial flow and temperature fields. Numerical examples illustrating these features are presented.

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• Kinetic theory
• Rarefied flows