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Abstract: Flow of a rarefied gas through a cylindrical tube connecting two reservoirs maintained at a small pressure difference is considered using the axisymmetric version of the linearised BGK kinetic model equation subject to Maxwell diffuse–specular boundary conditions. This is a problem of five dimensions in phase space, solved in a fully deterministic manner using a parallelised discrete velocity algorithm. Results include flow rates as well as distributions of density and velocity perturbations, from the free molecular up to the slip regime and for length-over-radius () ratios ranging from zero (orifice flow) up to 20. The dependency of the results on gas rarefaction, wall accommodation and tube length is analysed and discussed. It is found that the Knudsen minimum appears only at . Furthermore, in the case of it is confirmed that the results are practically independent of the accommodation coefficient. Comparing the present linear results with corresponding non-linear ones, it is seen that linearised analysis can capture the correct behaviour of the flow field not only for infinitesimally small but also for small but finite pressure differences and that its range of applicability is wider than expected. Also, the error introduced by the assumption of fully developed flow for channels of moderate length is estimated through a comparison with the present corresponding results. [Copyright &y& Elsevier]

Abstract: The problem of nonlinear heat transfer through a rarefied gas confined between concentric cylinders maintained at different temperatures is investigated. The formulation is based on the nonlinear Shakhov kinetic model subject to Cercignani–Lampis boundary conditions, while molecular interaction is modelled by the inverse power law. The detailed behaviour of the radial heat flow, density, temperature and pressure distributions in terms of the normalized temperature difference between the cylindrical walls, the ratio of the two cylindrical radii and the gas rarefaction is investigated and certain interesting characteristics are revealed. The study includes small, moderate and large temperature differences and various radius ratios and is extended in the whole range of the Knudsen number. It is verified that the type of molecular interaction plays an important role when the heat transfer configuration becomes strongly nonlinear, while the influence of the gas–surface scattering law has similar effects both in linear and nonlinear conditions. By comparing linear and nonlinear results corresponding to the same conditions, it is concluded that linearized analysis can capture the correct behaviour of the heat flow configuration not only for infinitesimally small but also for finite temperature differences and that its range of applicability is wider than expected. [Copyright &y& Elsevier]

Abstract: The fully developed flow of rarefied gases through circular ducts of concentric annular cross sections is solved via kinetic theory. The flow is due to an externally imposed pressure gradient in the longitudinal direction and it is simulated by the BGK kinetic equation, subject to Maxwell diffuse-specular boundary conditions. The approximate principal of the hydraulic diameter is investigated for first time in the field of rarefied gas dynamics. For the specific flow pattern, in addition to the flow rates, results are reported for the Poiseuille number and the exact hydraulic diameter. The corresponding parameters include the whole range of the Knudsen number and various values of the accommodation coefficient and the ratio of the inner over the outer radius. The accuracy of the results is validated in several ways, including the recovery of the analytical solutions at the hydrodynamic and free molecular limits. [Copyright &y& Elsevier]