Theoretical and Numerical Studies of Noncontinuum Gas-Phase Heat Conduction in Micro/Nano Devices

REFERENCES

• C. H. Mastrangelo and R. S. Muller , Microfabricated Thermal Absolute-Pressure Sensor with On-Chip Digital Front-End Processor , IEEE J. Solid-State Circuits , vol. 26 , pp. 1998 – 2007 , 1991 .
   Google Scholar
• J. S. Shie , B. C. S. Chou , and Y. M. Chen , High Performance Pirani Vacuum Gauge , J. Vaccum Sci. Technol., A , vol. 13 , pp. 2972 – 2979 , 1995 .
   Google Scholar
• B. H. Stark , Y. Mei , C. Zhang , and K. Najafi , A Doubly Anchored Surface Micro-machined Pirani Gauge for Vacuum Package Characterization , Proc. IEEE 16th Annual Int. Conf. on Micro Electro Mechanical Systems , pp. 506 – 509 , 2003 .
   Google Scholar
• W. P. King , T. W. Kenny , and K. E. Goodson , Comparison of Thermal and Piezoresistive Sensing Approaches for Atomic Force Microscopy Topography Measurements , Appl. Phys. Lett. , vol. 85 , pp. 2086 – 2088 , 2004 .
   Web of Science ®Google Scholar
• K. J. Kim , K. Park , J. Lee , Z. M. Zhang , and W. P. King , Nanotopographical Imaging Using a Heated Atomic Force Microscope Cantilever Probe , Sensors & Actuators, A , vol. 136 , pp. 95 – 103 , 2007 .
   Google Scholar
• K. Park , J. Lee , Z. M. Zhang , and W. P. King , Topography Imaging with a Heated Atomic Force Microscope Cantilever in Tapping Mode , Rev. Sci. Instrum. , vol. 78 , pp. 043709 – 043709-7 , 2007 .
   Google Scholar
• N. D. Masters , W. Ye , and W. P. King , The Impact of Subcontinuum Gas Conduction on Topography Measurement Sensitivity Using Heated Atomic Force Microscope Cantilevers , Phys. Fluids , vol. 17 , pp. 100615 – 100615-8 , 2005 .
   Google Scholar
• R. P. Manginell , D. A. Rosato , D. A. Benson , and G. C. Frye-Mason , Finite Element Modeling of a Microhotplate for Microfluidic Applications, Proc. Int. Conf. on Modeling and Simulation of Microsystems, Semiconductors, Sensors and Actuators, San Juan, Puerto Rico , pp. 663–666, 1999.
   Google Scholar
• A. Jain , K. Ness , A. McConnell , L. Jiang , and K. Goodson , Design, Fabrication and Thermal Characterization of a MEMS Device for Control of Nerve Cell Growth , Proc. ASME Int. Mechanical Engineering Congress , Washington , DC , 2003 .
   Google Scholar
• J. Peirs , D. Reynaerts , and H. V. Brussel , Scale Effects and Thermal Considerations for Micro-Actuators , IEEE Int. Conf. on Robotics and Automation , Leuven , Belgium , 1998 .
   Google Scholar
• Z. Y. Guo and Z. X. Li , Size Effect on Microscale Single-Phase Flow and Heat Transfer , Int. J. Heat Mass Transfer , vol. 46 , pp. 149 – 159 , 2003 .
   Web of Science ®Google Scholar
• X. J. Hu , A. Jain , and K. E. Goodson , Investigation of the Natural Convection Boundary Condition in Microfabricated Structures , Int. J. Thermal Sci. , vol. 47 , pp. 820 – 824 , 2008 .
   Web of Science ®Google Scholar
• H. Liu , M. Wang , J. Wang , G. Zhang , H. Liao , R. Huang , and X. Zhang , Monte Carlo Simulations of Gas Flow and Heat Transfer in Vacuum Packaged MEMS Devices , Appl. Thermal Eng. , vol. 27 , pp. 323 – 329 , 2007 .
   Web of Science ®Google Scholar
• M. A. Gallis , J. R. Torczynski , and D. J. Rader , A Computational Investigation of Noncontinuum Gas-Phase Heat Transfer between a Heated Microbeam and the Adjacent Ambient Substrate , Sensors & Actuators, A , vol. 134 , pp. 57 – 68 , 2007 .
   Google Scholar
• G. A. Bird , Molecular Gas Dynamics and the Direct Simulation of Gas Flows, , 2nd ed. , Clarendon Press , Oxford , U.K. , 1994 .
   Google Scholar
• M. Wang , X. Lan , and Z. Li , Analyses of Gas Flows in Micro- and Nanochannels , Int. J. Heat Mass Transfer , vol. 51 , pp. 3630 – 3641 , 2008 .
   Web of Science ®Google Scholar
• M. Wang and Z. Li , Non-Ideal Gas Flow , and Heat Transfer in Micro- , and Nanochannels Using the Direct Simulation Monte Carlo Method , Phys. Rev. E , vol. 68 , p. 046704 , 2003 .
   Web of Science ®Google Scholar
• J. Lee , T. L. Wright , M. R. Abel , E. O. Sunden , A. Marchenkov , S. Graham , and W. P. King , Thermal Conduction from Microcantilever Heaters in Partial Vacuum , J. Appl. Phys. , vol. 101 , pp. 014906 – 014906-6 , 2007 .
   Web of Science ®Google Scholar
• Q. W. Wang , C. L. Zhao , M. Zeng , and Y. N. Wu , Numerical Investigation of Rarefied Diatomic Gas Flow and Heat Transfer in a Microchannel Using DSMC with Uniform Heat Flux Boundary Condition—Part I: Numerical Method and Validation , Numer. Heat Transfer B , vol. 53 , pp. 160 – 173 , 2008 .
   Web of Science ®Google Scholar
• Q. W. Wang , C. L. Zhao , M. Zeng , and Y. N. Wu , Numerical Investigation of Rarefied Diatomic Gas Flow and Heat Transfer in a Microchannel Using DSMC with Uniform Heat Flux Boundary Condition—Part II: Applications , Numer. Heat Transfer B , vol. 53 , pp. 174 – 187 , 2008 .
   Web of Science ®Google Scholar
• E. A. Spiegel and J. L. Thiffeault , Higher-Order Continuum Approximation for Rarefied Gases , Phys. Fluids , vol. 15 , pp. 3558 – 3567 , 2003 .
   Google Scholar
• H. Struchtrup , Derivation of 13 Moment Equations for Rarefied Gas Flow to Second Order Accuracy for Arbitrary Interaction Potentials , Multiscale Model. Simul. , vol. 3 , pp. 221 – 243 , 2004 .
   Google Scholar
• M. Torrilhon and H. Struchtrup , Regularized 13-Moment Equations: Shock Structure Calculations and Comparison to Burnett Models , J. Fluid Mech. , vol. 513 , pp. 171 – 198 , 2004 .
   Web of Science ®Google Scholar
• Y. Zheng , J. M. Reese , and H. Struchtrup , Comparing Macroscopic Continuum Models for Rarefied Gas Dynamics: A New Test Method , J. Comput. Phys. , vol. 218 , pp. 748 – 769 , 2006 .
   Google Scholar
• Y. H. Zhang , X. J. Gu , R. W. Barber , and D. R. Emerson , Modeling Thermal Flow in the Transition Regime Using a Lattice Boltzmann Approach , Europhys. Lett. , vol. 77 , pp. 30003.p1 – 30003.p5 , 2007 .
   Google Scholar
• K. Xu , H. Liu , and J. Jiang , Multiple-Temperature Kinetic Model for Continuum , and Near Continuum Flows , Phys. Fluids , vol. 19 , pp. 016101 – 016101-12 , 2007 .
   Google Scholar
• E. H. Kennard , Kinetic Theory of Gases: With an Introduction to Statistical Mechanics , McGraw-Hill , New York , 1938.
   Google Scholar
• C. E. Siewert , The Linearized Boltzmann Equation: A Concise and Accurate Solution of the Temperature-Jump Problem , J. Quant. Spectrosc. Radiat. Transfer , vol. 77 , pp. 417 – 432 , 2003 .
   Google Scholar
• F. Sharipov , Application of the Cercignani-Lampis Scattering Kernel to Calculations of Rarefied Gas Flows. II. Slip and Jump Coefficients , Eur. J. Mech. B. Fluids , vol. 22 , pp. 133 – 143 , 2003 .
   Google Scholar
• A. Q. Zade , M. Renksizbulut , and J. Friedman , Slip/Jump Boundary Conditions for Rarefied Reacting/Non-reacting Multi-component Gaseous Flows , Int. J. Heat Mass Transfer , vol. 51 , pp. 5063 – 5071 , 2008 .
   Web of Science ®Google Scholar
• D. A. Lockerby and J. M. Reese , On the Modeling of Isothermal Gas Flows at the Microscale , J. Fluid Mech. , vol. 604 , pp. 235 – 261 , 2008 .
   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 , Europhys. Lett. , vol. 80 , pp. 24001.p1 – 24001.p6 , 2007 .
   Google Scholar
• Y. Sone , T. Ohwada , and K. Aoki , Temperature Jump and Knudsen Layer in a Rarefied Gas over a Plane Wall: Numerical Analysis of the Linearized Boltzmann Equation for Hard-Sphere Molecules , Phys. Fluids A , vol. 1 , pp. 363 – 370 , 1989 .
   Web of Science ®Google Scholar
• S. K. Loyalka , Temperature Jumps. Rigid-Sphere Gas with Arbitrary Gas/Surface Interaction , Nuclear Sci. Technol , vol. 108 , pp. 69 – 73 , 1991 .
   Google Scholar
• L. S. Pan , T. Y. Ng , D. Xu , G. R. Liu , and K. Y. Lam , Determination of Temperature Jump Coefficient Using the Direct Simulation Monte Carlo Method , J. Micromech. Microeng. , vol. 12 , pp. 41 – 52 , 2002 .
   Google Scholar
• R. G. Deissler , An Analysis of Second-Order Slip Flow and Temperature-Jump Boundary Conditions for Rarefied Gases , Int. J. Heat Mass Transfer , vol. 7 , pp. 681 – 694 , 1964 .
   Google Scholar
• N. G. Hadjiconstantinou , The Limits of Navier-Stokes Theory and Kinetic Extensions for Describing Small-Scale Gaseous Hydrodynamics , Phys. Fluids , vol. 18 , pp. 111301.1 – 111301.19 , 2006 .
   Google Scholar
• G. Karniadakis , A. Beskok , and N. Aluru , Microflows and Nanoflows: Fundamentals and Simulation , Springer-Verlag , New York , 2005 .
   Google Scholar
• R. Narasimha , Orifice Flow of High Knudsen Number , J. Fluid Mech. , vol. 10 , pp. 371 – 384 , 1961 .
   Google Scholar
• C. Cai , Heat Transfer in Vacuum Packaged Microelectromechanical System Devices , Phys. Fluids , vol. 20 , pp. 017103 – 017103-10 , 2008 .
   Google Scholar
• C. Cai and D. D. Liu , Collisionless Gas Flows. I. Inside Arbitrary Enclosures , Phys. Fluids , vol. 20 , pp. 067105 – 067105-8 , 2008 .
   Google Scholar
• C. Shen , Rarefied Gas Dynamics: Fundamentals, Simulations and Micro Flows , Springer-Verlag , Berlin , 2005 .
   Google Scholar
• E. P. Muntz , Rarefied Gas Dynamics , Annu. Rev. Fluid Mech. , vol. 21 , pp. 387 – 422 , 1989 .
   Web of Science ®Google Scholar
• E. S. Oran , C. K. Oh , and B. Z. Cybyk , Direct Simulation Monte Carlo: Recent Advances and Applications , Annu. Rev. Fluid Mech. , vol. 30 , pp. 403 – 441 , 1998 .
   Web of Science ®Google Scholar
• F. J. Alexander , A. L. Garcia , and B. J. Alder , Cell Size Dependence of Transport Coefficients in Stochastic Particle Algorithms , Phys. Fluids , vol. 10 , pp. 1540 – 1542 , 1998 .
   Web of Science ®Google Scholar
• N. G. Hadjiconstantinou , Analysis of Discretization in the Direct Simulation Monte Carlo , Phys. Fluids , vol. 12 , pp. 2634 – 2638 , 2000 .
   Web of Science ®Google Scholar
• M. Wang and Z. Li , Gas Mixing in Microchannels Using the Direct Simulation Monte Carlo Method , Int. J. Heat Mass Transfer , vol. 49 , pp. 1696 – 1702 , 2006 .
   Web of Science ®Google Scholar
• Y. Sone , Flows Induced by Temperature Fields in a Rarefied Gas and Their Ghost Effect on the Behavior of a Gas in the Continuum Limit , Annu. Rev. Fluid Mech. , vol. 32 , pp. 779 – 811 , 2000 .
   Web of Science ®Google Scholar
• H. M. Mott-Smith , The Solution of the Boltzmann Equation for a Shock Wave, Phys. Rev. , vol. 82, pp. 885–892, 1951.
   Google Scholar
• C. Y. Liu and L. Lees , Kinetic Theory Description of Plane Compressible Couette Flow , Rarefied Gas Dynamics: Proc. 2nd Int. Symp. , pp. 391 – 428 , 1961 .
   Google Scholar