Analysis of laminar heat transfer in micro-Poiseuille flow (original) (raw)

Abstract

The present study examines laminar forced convective heat transfer of a Newtonian fluid in a microchannel between two parallel plates analytically. The viscous dissipation effect, the velocity slip and the temperature jump at the wall are included in the analysis. Both hydrodynamically and thermally fully developed flow case is examined. Either the hot wall or the cold wall case is considered for the two different thermal boundary conditions, namely the constant heat flux (CHF) and the constant wall temperature (CWT). The interactive effects of the Brinkman number and the Knudsen number on the Nusselt numbers are analytically determined. Different definitions of the Brinkman number based on the definition of the dimensionless temperature are discussed. It is disclosed that for the cases studied here, singularities for the Brinkman number-dependence of the Nusselt number are observed and they are discussed in view of the energy balance.

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References (34)

  1. M. Gad-el-Hak (Ed.), The MEMS Handbook, CRC Press, New York, 2001.
  2. A. Beskok, G.E. Karniadakis, Simulation of heat and momentum transfer in complex micro-geometries, Journal of Thermophysics Heat Transfer 8 (1994) 355-370.
  3. C.M. Ho, C.Y. Tai, Micro-electro-mechanical systems (MEMS) and fluid flows, Annu. Rev. Fluid Mech. 30 (1998) 579-612.
  4. B. Palm, Heat transfer in microchannels, Microscale Thermophysical En- gineering 5 (2001) 155-175.
  5. C.B. Sobhan, S.V. Garimella, A comparative analysis of studies on heat transfer and fluid flow in microchannels, Microscale Thermophysical En- gineering 5 (2001) 293-311.
  6. N.T. Obot, Toward a better understanding of friction and heat/mass trans- fer in microchannels-A literature review, Microscale Thermophysical Engineering 6 (2002) 155-173.
  7. A.A. Rostami, N. Saniei, A.S. Mujumdar, Liquid flow and heat transfer in microchannels: A review, Heat Technol. 18 (2000) 59-68.
  8. A.A. Rostami, A.S. Mujumdar, N. Saniei, Flow and heat transfer for gas flowing in microchannels: A review, Heat and Mass Transfer 38 (2002) 359-367.
  9. M. Gad-el-Hak, Flow physics in MEMS, Mec. Ind. 2 (2001) 313-341.
  10. Z. Y Guo, Z.X. Li, Size effect on microscale single-phase flow and heat transfer, International Journal of Heat and Mass Transfer 46 (2003) 59- 149.
  11. Z. Y Guo, Z.X. Li, Size effect on single-phase channel flow and heat trans- fer at microscale, International Journal of Heat and Fluid Flow 24 (3) (2003) 284-298.
  12. G.L. Morini, Single-phase convective heat transfer in microchannels: a re- view of experimental results, International Journal of Thermal Sciences 43 (2004) 631-651.
  13. E.B. Arkilic, M.A. Schmidt, K.S. Breuer, Gaseous slip flow in long mi- crochannels, Journal of Microelectromechanical Systems 6 (2) (1997) 167-178.
  14. P. Gravesen, J. Branebjerg, O.S. Jensen, Microfluidics-A review, Journal of Micromechanics and Microengineering 3 (1993) 168-182.
  15. J.C. Harley, Y. Huang, H.H. Bau, J.N. Zemel, Gas flow in micro-channels, Journal of Fluid Mechanics 285 (1995) 257-274.
  16. R.F. Barron , X.M. Wang, R.O. Warrington, T. Ameel, Evaluation of the eigenvalues for the Graetz problem in slip-flow, Int. Comm. Heat Mass Transfer 23 (4) (1996) 563-574.
  17. R.F. Barron, X. Wang, T.A. Ameel, R.O. Warrington, The Graetz prob- lem extended to slip-flow, International Journal of Heat and Mass Trans- fer 40 (8) (1997) 1817-1823.
  18. T.A. Ameel, X.M. Wang, R.F. Barron, R.O. Warrington, Laminar forced convection in a circular tube with constant heat flux and slip flow, Mi- croscale Thermal Engineering 1 (4) (1997) 303-320.
  19. S. Yu, T.A. Ameel, Slip-flow heat transfer in rectangular microchannels, International Journal of Heat and Mass Transfer 44 (2001) 4225-4234.
  20. S. Yu, T.A. Ameel, A universal entrance Nusselt number for internal slip flow, Int. Comm. Heat Mass Transfer 28 (7) (2001) 905-910.
  21. C.P. Tso, S.P. Mahulikar, Use of the Brinkman number for single phase forced convective heat transfer in microchannels, International Journal of Heat and Mass Transfer 41 (1998) 1759-1769.
  22. C.P. Tso, S.P. Mahulikar, The role of the Brinkman number in analyzing flow transitions in microchannels, International Journal of Heat and Mass Transfer 42 (1999) 1813-1833.
  23. C.P. Tso, S.P. Mahulikar, Experimental verification of the role of Brinkman number in microchannels using local parameters, International Journal of Heat and Mass Transfer 43 (2000) 1837-1849.
  24. J.M. Li, B.X. Wang, X.F. Peng, Wall-adjacent layer analysis for developed-flow laminar heat transfer of gases in microchannels, Interna- tional Journal of Heat and Mass Transfer 43 (2000) 839-847.
  25. G. Tunc, Y. Bayazitoglu, Heat transfer in microtubes with viscous dissi- pation, International Journal of Heat and Mass Transfer 44 (2001) 2395- 2403.
  26. K.C. Toh, X.Y. Chen, J.C. Chai, Numerical computation of fluid flow and heat transfer in microchannels, International Journal of Heat and Mass Transfer 45 (2002) 5133-5141.
  27. B. Xu, K.T. Ooi, C. Mavriplis, M.E. Zaghloul, Evaluation of viscous dis- sipation in liquid flow in microchannels, Journal of Micromechanics and Microengineering 13 (2003) 53-57.
  28. X. Zhu, M.D. Xin, Q. Liano, Analysis of heat transfer between two un- symmetrically heated parallel plates with microspacing in the slip flow regime, Microscale Thermophysical Engineering 6 (2002) 287-301.
  29. N.G. Hadjiconstantinou, Dissipation in small scale gaseous flows, Journal of Heat Transfer 125 (2003) 944-947.
  30. J. Koo, C. Kleinstreuer, Viscous dissipation effects in microtubes and mi- crochannels, International Journal of Heat and Mass Transfer 47 (2004) 3159-3169.
  31. J. Koo, C. Kleinstreuer, Liquid flow in microchannels: Experimental ob- servations and computational analyses of microfludics effects, Journal of Micromechanics and Microengineering 13 (2003) 568-579.
  32. S.S. Hsieh, H.H. Tsai, C.Y. Lin, C.F. Huang, C.M. Chien, Gas flow in a long microchannel, International Journal of Heat and Mass Trans- fer 47 (17-18) (2004) 3877-3887.
  33. O. Aydın, M. Avcı, Viscous dissipation effects on the heat transfer in a Poiseuille flow, Applied Energy 83 (2006) 495-512.
  34. P.H. Oosthuizen, D. Naylor, Introduction to Convective Heat Transfer Analysis, McGraw-Hill, New York, 1999, pp. 158-167.