Heat transfer through rarefied gases between coaxial cylindrical surfaces with arbitrary temperature difference

• Published in: European journal of mechanics, B, Fluids Vol. 29; no. 6; pp. 494 - 509
• Main Authors: Pantazis, Sarantis, Valougeorgis, Dimitris
• Format: Journal Article
• Language: English
• Published: Issy-les-Moulineaux Elsevier Masson SAS 01.11.2010; Elsevier Masson
• Subjects: Applied fluid mechanics; Density; Exact sciences and technology; Fluid dynamics; Fluid flow; Fluidics; Fundamental areas of phenomenology (including applications); Heat transfer; Heat transmission; Instruments, apparatus, components and techniques common to several branches of physics and astronomy; Kinetic theory; Knudsen number; Microheat transfer; Molecular interactions; Nonlinearity; Physics; Rarefaction; Rarefied gas dynamics; Vacuum apparatus and techniques; Vacuum flows; Walls; Knudsen number; Kinetic theory; Microheat transfer; Vacuum flows; Rarefied gas flow; Annular space; Digital simulation; Vacuum techniques; Modelling; Coaxial cylinders; Microstructure; Microfluidics; Heat transfer
• DOI: 10.1016/j.euromechflu.2010.05.004
• ISSN: 0997-7546

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.