EVALUATION OF NUSSELT NUMBER FOR A FLOW IN A MICROTUBE USING SECOND-ORDER SLIP MODEL

Abstract

In this paper, the fully-developed temperature profile and corresponding Nusselt value is determined analytically for a gaseous flow in a microtube with a thermal boundary condition of constant wall heat flux. The flow assumed to be laminar, and hydrodynamically and thermally fully developed. The fluid is assumed to be constant property and incompressible. The effect of rarefaction, viscous dissipation and axial conduction, which are important at the microscale, are included in the analysis. Second-order slip model is used for the slip-flow and temperature jump boundary conditions for the implementation of the rarefaction effect. Closed form solutions for the temperature field and the fully-developed Nusselt number is derived as a function of Knudsen number, Brinkman number and Peclet number.

Dates

  • Submission Date2010-07-01
  • Revision Date2010-09-14
  • Acceptance Date2010-11-11

DOI Reference

10.2298/TSCI11S1103C

References

  1. Karniadakis, G. E., Beskok, A., Micro Flows: Fundamentals and Simulation, Springer-Verlag, New York, 2002
  2. Deissler, R. G., An Analysis of Second-Order Slip Fow and Temperature-Jump Boundary Conditions for Rarefied Gases, Int. J. Heat Mass Transfer 7 (1964), 6, pp. 681-694
  3. Karniadakis, G. E., Beskok, A., Aluru, N., Microflows and Nanoflows: Fundamentals and Simulation, Springer-Verlag, New York, 2005
  4. Çetin, B., Yazicioglu, A., Kakac, S., Fluid Fow in Microtubes with Axial Conduction Including Rarefaction and Viscous Dissipation, Int. Comm. Heat Mass Transfer, 35 (2008), 5, pp. 535-544
  5. Colin, S., Lalonde, P., Caen, R., Validation of a Second-Order Slip-Flow Model in Rectangular Microchannels, Heat Transfer Eng., 25 (2004), 3, pp. 23-30
  6. Aubert, C., Colin, S., High-Order Boundary Conditions for Gaseous Flows in Rectangular Microducts, MicroscaleThermophys. Eng., 5 (2001), 1, pp. 41-54
  7. Ameel, T. A., et al., Laminar Forced Convection in a Circular Tube with Constant Heat Flux and Slip Flow, MicroscaleThermophys. Eng., 1 (1997), 4, pp. 303-320
  8. Xue, H., Ji, H., Shu, C., Prediction of Flow and Heat Transfer Characteristics in Micro-Couette Flow, Microscale Thermophysical Eng., 7 (2003), 1, pp. 51-68
  9. Chen, C. S., Kuo, W. J., Heat Transfer Characteristics of Gaseous Flow in Long Mini- and Microtubes, Numerical Heat Transfer-Part A, 46 (2004), 5, pp. 497-514
  10. Jeong, H. E., Jeong, J. T., Extended Graetz Problem Including Streamwise Conduction and Viscous Dissipation in Microchannels, Int. J. Heat Mass Transfer, 49 (2006), 13-14, pp. 2151-2157
  11. Aydin, O., Avci, M., Analysis of Micro-Graetz Problem in a Microtube, Nanoscale and Microscale Thermophysical Engineering, 10 (2006), 4, pp. 345-358
  12. Roy, S., Chakraborty, S., Near-Wall Effects in Micro Scale Couette Flow and Heat Transfer in the Maxwell-Slip Regime, Microfluid Nanofluid, 3 (2007), 4, pp. 437-449
  13. Duan, Z., Muzychka, Y. S., Slip Flow Heat Transfer in Annular Microchannels with Constant Heat Flux, J. Heat Transfer, 130 (2008), 092401
  14. Cetin, B., Yazicioglu, A., Kakac, S., Slip-Flow Heat Transfer in Microtubes with Axial Conduction and Viscous Dissipation-An Extended Graetz Problem, Int. J. Thermal Sciences, 48 (2009), 9, pp. 1673-1678
  15. Cetin, B., Yuncu, H., Kakac, S., Gaseous Flow in Microchannels with Viscous Dissipation, Int. J. Transport Phenom., 8 (2006), 4, pp. 297-315
  16. Xiao, N., Elsnab, J., Ameel, T., Microtube Gas Flows with Second-Order Slip Flow and Temperature Jump Boundary Conditions, Int. J. Thermal Sciences, 48 (2009), 2, pp. 243-251
  17. van Rij, J., Ameel, T., Harman, T., An Evaluation of Secondary Effects on Microchannel Frictional and Convective Heat Transfer Characteristics, Int. J. Heat and Mass Transfer, 52 (2009), 11-12, pp. 2792-2801
  18. Deen, W. M., Analysis of Transport Phenomena, Oxford University Press, Oxford, UK, 1998
  19. Vick, B., Ozisik, M. N., An Exact Analysis of Low Peclet Number Heat Transfer in Laminar Fow with Axial Conduction, Lett. in Heat Mass Transfer, 8 (1981), 1, pp. 1-10
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