Extended Thermodynamic Approach for Non-Equilibrium Gas Flow

Gases in microfluidic structures or devices are often in a non-equilibrium state. The conventional thermodynamic models for fluids and heat transfer break down and the Navier-Stokes-Fourier equations are no longer accurate or valid. In this paper, the extended thermodynamic approach is employed to study the rarefied gas flow in microstructures, including the heat transfer between a parallel channel and pressure-driven Poiseuille flows through a parallel microchannel and circular microtube. The gas flow characteristics are studied and it is shown that the heat transfer in the non-equilibrium state no longer obeys the Fourier gradient transport law. In addition, the bimodal distribution of streamwise and spanwise velocity and temperature through a long circular microtube is captured for the first time. AMS subject classifications: 76P05, 82B40

[1]  Ya-Ling He,et al.  Lattice Boltzmann method for gaseous microflows using kinetic theory boundary conditions , 2005 .

[2]  C. Rhie,et al.  Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation , 1983 .

[3]  K. Breuer,et al.  Gaseous slip flow in long microchannels , 1997 .

[4]  H. Struchtrup.  Macroscopic transport equations for rarefied gas flows , 2005 .

[5]  Duncan A. Lockerby,et al.  On the modelling of isothermal gas flows at the microscale , 2008, Journal of Fluid Mechanics.

[6]  M. Gad-el-Hak.  The Fluid Mechanics of Microdevices—The Freeman Scholar Lecture , 1999 .

[7]  David Emerson,et al.  A high-order moment approach for capturing non-equilibrium phenomena in the transition regime , 2009, Journal of Fluid Mechanics.

[8]  Manuel Torrilhon,et al.  Couette and Poiseuille microflows : Analytical solutions for regularized 13-moment equations , 2009 .

[9]  J. Maxwell,et al.  On Stresses in Rarified Gases Arising from Inequalities of Temperature , 2022 .

[10]  Kun Xu,et al.  A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations , 2011, J. Comput. Phys..

[11]  Felix Sharipov,et al.  Non-isothermal gas flow through rectangular microchannels , 1999 .

[12]  COMPARISON OF GAS SLIP MODELS WITH SOLUTIONS OF LINEARIZED BOLTZMANN EQUATION AND DIRECT SIMULATION OF MONTE CARLO METHOD , 2007 .

[13]  W. Steckelmacher.  Molecular gas dynamics and the direct simulation of gas flows , 1996 .

[14]  Manuel Torrilhon,et al.  Higher-order effects in rarefied channel flows. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  D. Emerson,et al.  Kramers’ problem and the Knudsen minimum: a theoretical analysis using a linearized 26-moment approach , 2009 .

[16]  Sudarshan K. Loyalka,et al.  Poiseuille flow of a rarefied gas in a cylindrical tube: Solution of linearized Boltzmann equation , 1990 .

[17]  Qing Li,et al.  Lattice Boltzmann modeling of microchannel flows in the transition flow regime , 2011 .

[18]  Henning Struchtrup,et al.  Temperature jump and velocity slip in the moment method , 2000 .

[19]  Duncan A. Lockerby,et al.  The usefulness of higher-order constitutive relations for describing the Knudsen layer , 2005 .

[20]  J. Torczynski,et al.  Calculations of the near-wall thermophoretic force in rarefied gas flow , 2002 .

[21]  David Emerson,et al.  Lattice Boltzmann modelling Knudsen layer effect in non-equilibrium flows , 2008 .

[22]  P. Taheri,et al.  An extended macroscopic transport model for rarefied gas flows in long capillaries with circular cross section , 2010 .

[23]  V. A. Titarev,et al.  Implicit Unstructured-mesh Method for Calculating Poiseuille Flows of Rarefied Gas , 2010 .

[24]  Ali Beskok,et al.  VALIDATION OF A NEW VELOCITY-SLIP MODEL FOR SEPARATED GAS MICROFLOWS , 2001 .

[25]  H. Grad.  On the kinetic theory of rarefied gases , 1949 .

[26]  H. Struchtrup,et al.  Regularization of Grad’s 13 moment equations: Derivation and linear analysis , 2003 .

[27]  N. Hadjiconstantinou.  Oscillatory shear-driven gas flows in the transition and free-molecular-flow regimes , 2005 .

[28]  Chia-Jung Hsu.  Numerical Heat Transfer and Fluid Flow , 1981 .

[29]  C. Cercignani.  The Boltzmann equation and its applications , 1988 .

[30]  J. B. Young.  Calculation of Knudsen layers and jump conditions using the linearised G13 and R13 moment methods , 2011 .

[31]  N. Hadjiconstantinou,et al.  Constant-Wall-Temperature Nusselt Number in Micro and Nano-Channels 1 , 2002 .

[32]  Ching Shen,et al.  EXAMINATION OF THE LBM IN SIMULATION OF MICROCHANNEL FLOW IN TRANSITIONAL REGIME , 2004 .

[33]  D. Emerson,et al.  Modeling oscillatory flows in the transition regime using a high-order moment method , 2011 .

[34]  L. Mieussens.  Discrete-Velocity Models and Numerical Schemes for the Boltzmann-BGK Equation in Plane and Axisymmetric Geometries , 2000 .

[35]  Kazuo Aoki,et al.  Numerical analysis of the Poiseuille and thermal transpiration flows between two parallel plates on the basis of the Boltzmann equation for hard‐sphere molecules , 1989 .