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Abstract
Based on the fast spectral approximation to the Boltzmann collision operator, we present an accurate and efficient deterministic numerical method for solving the Boltzmann equation. First, the linearised Boltzmann equation is solved for Poiseuille and thermal creep flows, where the influence of different molecular models on the mass and heat flow rates is assessed, and the OnsagerCasimir relation at the microscopic level for large Knudsen numbers is demonstrated. Recent experimental measurements of mass flow rates along a rectangular tube with large aspect ratio are compared with numerical results for the linearised Boltzmann equation. Then, a number of twodimensional micro flows in the transition and free molecular flow regimes are simulated using the nonlinear Boltzmann equation. The influence of the molecular model is discussed, as well as the applicability of the linearised Boltzmann equation. For thermally driven flows in the free molecular regime, it is found that the magnitudes of the flow velocity are inversely proportional to the Knudsen number. The streamline patterns of thermal creep flow inside a closed
rectangular channel are analysed in detail: when the Knudsen number is smaller than a critical value, the flow pattern can be predicted based on a linear superposition of the velocity profiles of linearised Poiseuille and thermal creep
flows between parallel plates. For large Knudsen numbers, the flow pattern can be determined using the linearised Poiseuille and thermal creep velocity profiles at the critical Knudsen number. The critical Knudsen number is found to be related to the aspect ratio of the rectangular channel.
rectangular channel are analysed in detail: when the Knudsen number is smaller than a critical value, the flow pattern can be predicted based on a linear superposition of the velocity profiles of linearised Poiseuille and thermal creep
flows between parallel plates. For large Knudsen numbers, the flow pattern can be determined using the linearised Poiseuille and thermal creep velocity profiles at the critical Knudsen number. The critical Knudsen number is found to be related to the aspect ratio of the rectangular channel.
Original language  English 

Pages (fromto)  5384 
Number of pages  32 
Journal  Journal of Fluid Mechanics 
Volume  746 
Early online date  28 Mar 2014 
DOIs  
Publication status  Published  10 May 2014 
Keywords
 computational methods
 micro and nanoscale flows
 fluid dynamics
 rarefied gas flows
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 1 Finished

NonEquilibrium Fluid Dynamics for Micro/Nano Engineering Systems
Reese, J.
EPSRC (Engineering and Physical Sciences Research Council)
1/01/11 → 16/02/16
Project: Research