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The explicit and reliable analytical solutions for steady plane compressible non-isothermal Couette gas flow are presented. These solutions for velocity and temperature are developed by macroscopic approach from Navier-Stokes-Fourier system of continuum equations and the velocity slip and the temperature jump first order boundary conditions. Variability of the viscosity and thermal conductivity with temperature is involved in the model. The known result for the gas flow with constant and equal temperatures of the walls (isothermal walls) is verified and a new solution for the case of different temperature of the walls is obtained. Evan though the solution for isothermal walls correspond to the gas flow of the Knudsen number Kn≤0.1, i.e. to the slip and continuum flow, it is shown that the gas velocity and related shear stress are also valid for the whole range of the Knudsen number. The deviation from numerical results for the same system is less than 1%. The reliability of the solution is confirmed by comparing with results of other authors which are obtained numerically by microscopic approach. The advantage of the presented solution compared to previous is in a very simple applicability along with high accuracy. [Projekat Ministarstva nauke Republike Srbije, br. 35046 i 174014]
PAPER REVISED: 2016-08-05
PAPER ACCEPTED: 2016-08-05
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THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Issue 6, PAGES [1825 - 1833]
  1. Gad-el-Hak, M., The MEMS Handbook, CRC Press, New York, 2002
  2. Karniadakis, G. E., et al., Microflows and nanoflows. Fundamentals and Simulation, Springer, Berlin, 2005
  3. Gu, X. J., Emerson, D. R., A computational strategy for the regularized 13 moment equations with enhanced wall-boundary conditions, J. Comput. Phys., 225 (2007), pp. 263-283
  4. Gu, X. J., Emerson, D. R., A high-order moment approach for capturing non-equilibrium phenomena in the transition regime, J. Fluid Mech., 636 (2009), pp. 177-216
  5. Taheri, P., et al., Couette and Poiseuille microflows: Analytical solutions for regularized 13-moment equations, Phys. Fluids, 21 (2009), 017102
  6. Misdanitis, S., Valougeorgis, D., Couette flow with heat transfer in the whole range of the Knudsen number, Proceedings (ASME), 6th ICNMM, Darmstadt, Germany, 2008
  7. Xue, H., et al., Prediction of flow and heat transfer characteristics in micro-Couette flow, Microscale Thermophysical Engineering, 7 (2003), 1, pp. 51-68
  8. Lockerby, D.A., Reese, J.M., High-resolution Burnett simulations of micro Couette flow and heat transfer, J. Comput. Physics, 18 (2003), pp. 333-347
  9. Marques, W. Jr, et al., Couette flow with slip and jump boundary conditions, Continuum Mech. Thermodyn., 12 (2000), pp. 379-386
  10. Torczynski, J. R., Gallis, M. A., DSMC-Based Shear-Stress/Velocity-Slip Boundary Condition for Navier-Stokes Couette-Flow Simulations, AIP Conf. Proc. 1333, 27th International Symposium on Rarefied Gas Dynamics, Pacific Grove, USA, 2010, pp. 802-807
  11. Gallis, M. A., et al., Normal solutions of the Boltzmann equation for highly nonequilibrium Fourier flow and Couette flow, Phys. Fluids, 18 (2006), 017104
  12. Zhou, W. D., et al., Rarefied-gas heat transfer in micro- and nanoscale Couette flows, Phys. Rev. E, 81 (2010), 011204
  13. Ansumali, S., et al., Hydrodynamics beyond Navier-Stokes: Exact Solution to the Lattice Boltzmann Hierarchy, Phys. Rev. Lett., 98 (2007), 124502
  14. Milicev, S. S., Stevanovic, D. N., A Non-Isothermal Couette Slip Gas Flow, Sci. China-Phys. Mech. Astron., 56 (2013), pp. 1782-1797
  15. Stevanovic, D. N., A new analytical solution of microchannel gas flow, J. Micromech. Microeng., 17 (2007), pp. 1695-1702
  16. Stevanovic, D., N., Analytical solution of gas lubricated slider microbearing, Microfluid. Nanofluid., 7 (2009), pp. 97-105
  17. Milicev, S. S., Stevanovic, D. N., A Microbearing Gas Flow with Different Walls' Temperatures, Thermal Science, 16 (2012), 1, pp.119-132
  18. Hamdan, M. A., et al., Effect of Second Order Velocity-Slip/Temperature-Jump on Basic Gaseous Fluctuating Micro-Flows, ASME J. Fluids Eng., 132 (2010), 7, pp. 0745031-0745036
  19. Vincenti, W. G., Kruger, C. H., Introduction to physical gas dynamics, Wiley & Sons, New York, 1965
  20. Wang, C. Y., Brief Review of Exact Solutions for Slip-Flow in Ducts and Channels, ASME J. Fluids Eng., 134 (2012), 9, 094501

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