13 research outputs found
Kramers' problem and the Knudsen minimum: a theoretical analysis using a linearized 26-moment approach
Determination of Thermal Accommodation Coefficients of Inert Gases on a Surface of Vitreous UO 2
Heat conduction from a spherical nano-particle: status of modeling heat conduction in laser-induced incandescence
15-digit accuracy calculations of Chandrasekhar’s H -function for isotropic scattering by means of the double exponential formula
A Lattice Boltzmann kinetic model for microflow and heat transfer
10.1007/s10955-005-8413-zJournal of Statistical Physics1211-2239-25
Rarefied Pure Gas Transport in Non-Isothermal Porous Media: Effective Transport properties from Homogenization of the Kinetic Equation
Viscous flow, effusion, and thermal transpiration are the main gas transport modalities for a rarefied gas in a macro-porous medium. They have been well quantified only in the case of simple geometries. This paper develops a model based on the homogenization of kinetic equations producing effective transport properties (permeability, Knudsen diffusivity, thermal transpiration ratio) in any porous medium sample, as described e. g. by a digitized 3D image. The homogenization procedure -- neglecting the effect of gas density gradients on heat transfer through the solid -- leads to macroscopic transfer relations, and to closure problems in R^6 for the obtention of effective properties. Coherence of the approach with previous literature on the subject is discussed. The asymptotic limits of the model (rarefied and continuum regimes) are also studied. One of the main results is that the effect of the geometry on thermal transpiration has to be described by a tensor which is distinct from the permeability and Knudsen diffusion tensors