High Knudsen Number Thermal Flows with the D2Q13 Lattice Boltzmann Model

REFERENCES

• D. A. Lockerby , J. M. Reese , and M. A. Gallis , The Usefulness of Higher-Order Constitutive Relations for Describing the Knudsen Layer , Phys. Fluids , vol. 17 , pp. 100609 , 2005 .
   Web of Science ®Google Scholar
• G. Tunc and Y. Bayazitoglu , Heat Transfer in Microtubes with Viscous Dissipation , Int. J. Heat and Mass Transfer , vol. 44 no. 13 , pp. 2395 – 2403 , 2001 .
   Web of Science ®Google Scholar
• G. Tunc and Y. Bayazitoglu , Heat Transfer in Rectangular Microchannels , Int. J. Heat and Mass Transfer , vol. 45 , pp. 765 – 773 , 2002 .
   Web of Science ®Google Scholar
• Y. Bayazitoglu , G. Tunc , K. Wilson , and I. Tjahjono , Convective Heat Transfer for Single-Phase Gases in Microchannel Slip Flow: Analytical Solutions , in S. Kakac , L. L. Vasiliev , Y. Bayazitoglu , and Y. Yener (eds.), Microscale Heat Transfer: Fundamental and Applications , pp. 125 – 144 , Springer , Norwell , MA , 2005 .
   Google Scholar
• Y. H. Zhang , X. J. Gu , R. W. Barber , and D. R. Emerson , Capturing Knudsen Layer Phenomena Using a Lattice Boltzmann Model , Phys. Rev. E , vol. 74 , pp. 046704 , 2006 .
   Web of Science ®Google Scholar
• Z. L. Guo , B. C. Shi , and C. G. Zheng , An Extended Navier-Stokes Formulation for Gas Flows in the Knudsen Layer near a Wall , EPL J. , vol. 80 , pp. 24001 , 2007 .
   Web of Science ®Google Scholar
• D. W. Stops , The Mean Free Path of Gas Molecules in the Transition Regime , J. Phys. D: Applied Physics , vol. 3 , no. 5 , pp. 685 – 696 , 1970 .
   Web of Science ®Google Scholar
• E. J. Arlemark , S. K. Dadzie , and J. M. Reese , An Extension to the Navier-Stokes Equations to Incorporate Gas Molecular Collisions with Boundaries , J. Heat Transfer , vol. 132 , no. 4 , pp. 041006 , 2010 .
   Web of Science ®Google Scholar
• N. Dongari , Y. H. Zhang , and J. M. Reese , Modeling of Knudsen Layer Effects in Micro/Nanoscale Gas Flows , J. Fluids Eng. , vol. 133 , pp. 071101-1 – 071101-10 , 2011 .
   Web of Science ®Google Scholar
• G. H. Tang , Y. H. Zhang , and D. R. Emerson , Lattice Boltzmann Models for Nonequilibrium Gas Flows , Physical Rev. E , vol. 77 , pp. 046701 , 2008 .
   Web of Science ®Google Scholar
• S. Ansumali and I. V. Karlin , Kinetic Boundary Conditions in the Lattice Boltzmann Method , Phys. Rev. E , vol. 66 , pp. 026311 , 2002 .
   Web of Science ®Google Scholar
• Y. H. Zhang , X. J. Gu , R. W. Barber , and D. R. Emerson , Modelling Thermal Flow in the Transition Regime using a Lattice Boltzmann Approach , EPL J. , vol. 77 , pp. 30003 , 2007 .
   Web of Science ®Google Scholar
• G. H. Tang , Y. H. Zhang , X. J. Gu , and D. R. Emerson , Lattice Boltzmann Modelling Knudsen Layer Effect in Non-Equilibrium Flows , EPL J. , vol. 83 , pp. 40008 , 2008 .
   Web of Science ®Google Scholar
• N. Dongari , Y. H. Zhang , and J. M. Reese , Molecular Free Path Distribution in Rarefied Gases , J. Phys. D , vol. 44 , pp. 125502-1 – 125502-6 , 2011 .
   Google Scholar
• P. Lopez and Y. Bayazitoglu , A Note on Modeling of Nano-Scale Thermal Flow via the Lattice Boltzmann Method, Extended Abstract Submitted for Presentation at the ASME International Mechanical Engineering Congress & Exposition, Houston, TX, USA, 2012.
   Google Scholar
• X. He , S. Chen , and G. D. Doolen , A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit , J. Comput. Phys. , vol. 146 , pp. 282 – 300 , 1998 .
   Web of Science ®Google Scholar
• Y. Shi , T. S. Zhao , and Z. L. Guo , Thermal Lattice Bhatnagar-Gross-Krook Model for Flows with Viscous Heat Dissipation in the Incompressible Limit , Phys. Rev. E , vol. 70 , pp. 066310-1 – 066310-12 , 2004 .
   Web of Science ®Google Scholar
• Q. Zou and X. He , On Pressure and Velocity Flow Boundary Conditions for the Lattice Boltzmann BGK Model , Phys. Fluids , vol. 9, no. 6 , pp. 1591 – 1598 , 1997 .
   Web of Science ®Google Scholar
• C. Y. Lim , C. Shu , X. D. Niu , and Y. T. Chew , Application of Lattice Boltzmann Method to Simulate Microchannel Flows , Physics of Fluids , vol. 14 , no. 7 , pp. 2299 – 2308 , 2002 .
   Web of Science ®Google Scholar
• X. D. Niu , Y. T. Chew , and C. Shu , A Lattice Boltzmann BGK Model for Simulation of Micro Flows , EPL J. , vol. 67 , no. 4 , pp. 600 – 606 , 2004 .
   Web of Science ®Google Scholar
• P. Yuan and L. Schaefer , A Thermal Lattice Boltzmann Two-Phase Flow Model and its Application to Heat Transfer Problems—Part 1. Theoretical Foundation , J. Fluids Eng. , vol. 128 , pp. 142 – 150 , 2006 .
   Web of Science ®Google Scholar
• P. Yuan and L. Schaefer , A Thermal Lattice Boltzmann Two-Phase Flow Model and its Application to Heat Transfer Problems—Part 2. Integration and Validation , J. Fluids Eng. , vol. 128 , pp. 151 – 156 , 2006 .
   Web of Science ®Google Scholar
• G. H. Tang , Y. H. Zhang , X. J. Gu , R. W. Barber , and D. R. Emerson , Lattice Boltzmann Model for Thermal Transpiration , Phys. Rev. E , vol. 79 , pp. 027701-1 – 027701-4 , 2009 .
   Google Scholar
• Y. H. Zhang , R. S. Qin , Y. H. Sun , R. W. Barber , and D. R. Emerson , Gas Flow in Microchannels—A Lattice Boltzmann Method Approach , J. Stat. Phys. , vol. 121 , pp. 257 – 267 , 2005 .
   Web of Science ®Google Scholar
• Y. Sone , Kinetic Theory and Fluid Dynamics , Birkhauser , Boston , 2002 .
   Google Scholar
• Y. Sone , S. Takata , and T. Ohwada , Numerical Analysis of the Plane Couette Flow of a Rarefied Gas on the Basis of the Linearized Boltzmann Equation for Hard-Sphere Molecules , Eur. J. Mech. B/Fluids , vol. 9 , no. 3 , pp. 273 – 288 , 1990 .
   Web of Science ®Google Scholar
• M. A. Gallis , D. J. Rader , and J. R. Torczynski , Calculations of the Near-Wall Thermophoretic Force in Rarefied Gas Flow , Phys. Fluids , vol. 14 , no. 12 , pp. 4290 – 4301 , 2002 .
   Web of Science ®Google Scholar