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TECHNICAL NOTES

Dissipation in Small Scale Gaseous Flows

[+] Author and Article Information
Nicolas G. Hadjiconstantinou

Mechanical Engineering Department, Massachusetts Institute of Technology, Cambridge, MA 02139

J. Heat Transfer 125(5), 944-947 (Sep 23, 2003) (4 pages) doi:10.1115/1.1571088 History: Received July 12, 2002; Revised February 11, 2003; Online September 23, 2003
Copyright © 2003 by ASME
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References

Cercignani, C., 1988, The Boltzmann Equation and Its Applications, Springer-Verlag, NY.
Beskok,  A., and Karniadakis,  G. E., 1999, “A Model for Flows in Channels and Ducts at Micro and Nano Scales,” Microscale Thermophys. Eng., 3, p. 43.
Ohwada,  T., Sone,  Y., and Aoki,  K., 1989, “Numerical Analysis of the Shear and Thermal Creep Flows of a Rarefied Gas Over a Plane Wall on the Basis of the Linearized Boltzmann Equation for Hard-Sphere Molecules,” Phys. Fluids A, 1, p. 1588.
Sone,  Y., Ohwada,  T., and Aoki,  K., 1989, “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, 1, p. 363.
Vincenti, W. G., and Kruger, C. H., 1965, Introduction to Physical Gas Dynamics, Krieger, FL.
Ou,  J. W., and Cheng,  K. C., 1973, “Viscous Dissipation Effects on Thermal Entrance Region Heat Transfer in Pipes With Uniform Wall Heat Flux,” Appl. Sci. Res., 28, p. 289.
Hadjiconstantinou,  N. G., and Simek,  O., 2002, “Constant-Wall-Temperature Nusselt Number in Micro and Nano Channels,” J. Heat Transfer, 124, p. 356.
Chapman, S., and Cowling, T. G., 1970, The Mathematical Theory of Non-Uniform Gases, Cambridge University Press, Cambridge.
Alexander,  F., Garcia,  A., and Alder,  B., 1998, “Cell Size Dependence of Transport Coefficients in Stochastic Particle Algorithms,” Phys. Fluids, 10, p. 1540, (Erratum: Phys. Fluids, 12, p. 731(2000)).
Hadjiconstantinou,  N. G., 2000, “Analysis of Discretization in the Direct Simulation Monte Carlo,” Phys. Fluids, 12, p. 2634.
Garcia,  A., and Wagner,  W., 2000, “Time Step Truncation Error in Direct Simulation Monte Carlo,” Phys. Fluids, 12, p. 2621.
Ohwada,  T., Sone,  Y., and Aoki,  K., 1989, “Numerical Analysis of the Poiseuille and Thermal Transpiration Flows Between Parallel Plates on the Basis of the Boltzmann Equation for Hard-Sphere Molecules,” Phys. Fluids A, 1, p.2042.
Malek Mansour,  M., Baras,  F., and Garcia,  A. L., 1997, “On the Validity of Hydrodynamics in Plane Poiseuille Flows,” Physica A, 240, p. 255.

Figures

Grahic Jump Location
Variation of the fully developed Nusselt number Nut with Brinkman number for Kn=0.07. The solid line is the prediction of Eq. (13), and the stars denote DSMC simulations.  
Grahic Jump Location
Nondimensional flowrate Q̄ as a function of the Knudsen number. The solid line denotes the numerical solution of the Boltzmann Eq. [12], the stars denote DSMC simulations of gravity-driven flow and the dashed line denotes the slip-flow prediction. Error estimates are given by the star size.
Grahic Jump Location
Nondimensional total heat exchange qt/(ρub22RT) as a function of the Knudsen number. The solid line denotes the theoretical prediction Eq. (21), the stars denote DSMC simulations of gravity-driven flow and the dashed line denotes the slip-flow prediction. Error estimates are given by the star size.

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