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Convective Heat Transfer in Microscale Slip Flow

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Abstract

In this lecture, steady-state convective heat transfer in different microchannels (microtube and parallel plates) will be presented in the slip flow regime. Laminar, thermally and/or hydrodynamically developing flows will be considered. In the analyses, in addition to rarefaction, axial conduction, and viscous dissipation effects, which are generally neglected in macroscale problems, surface roughness effects, and temperature-variable thermophysical properties of the fluid will also be taken into consideration. Navier-Stokes and energy equations will be solved and the variation of Nusselt number, the dimensionless parameter for convection heat transfer, along the channels will be presented in tabular and graphical forms as a function of Knudsen, Peclet, and Brinkman numbers, which represent the effects of rarefaction, axial conduction, and viscous dissipation, respectively. The results will be compared and verified with available experimental, analytical, and numerical solutions in literature.

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References

  1. D.B. Tuckerman and R.F. Pease, Optimized convective cooling using micromachined structure, Journal of the Electrochemical Society 129, P. C 98 (1982).

    Google Scholar 

  2. P.Y. Wu and W.A. Little, Measurement of heat transfer characteristics of gas flow in fine channels heat exchangers used for microminiature refrigerators, Cryogenics 24, 415–420 (1984).

    Article  Google Scholar 

  3. S.B. Choi, R.F. Barron, and R.O. Warrington, Fluid flow and heat transfer in microtubes, Micromechanical Sensors, Actuators, and Systems, ASME DSC 32, 123–134 (1991).

    Google Scholar 

  4. C.P. Tso and S.P. Mahulikar, Experimental verification of the role of Brinkman number in microchannels using local parameters, International Journal of Heat and Mass Transfer 43, 1837–1849 (2000).

    Article  Google Scholar 

  5. J.Y. Jung and H.Y. Kwak, Fluid flow and heat transfer in microchannels with rectangular cross section, Heat Mass Transfer 44, 1041–1049 (2008).

    Article  ADS  Google Scholar 

  6. H.S. Park and J. Punch, Friction factor and heat transfer in multiple microchannels with uniform flow distribution, International Journal of Heat and Mass Transfer 51, 4535–4543 (2008).

    Article  Google Scholar 

  7. R.F. Barron, X.M. Wang, R.O. Warrington, and T.A. Ameel, The Graetz problem extended to slip flow, International Journal of Heat and Mass Transfer 40, 1817–1823 (1997).

    Article  MATH  Google Scholar 

  8. T.A. Ameel, R.F. Barron, X.M. Wang, and R.O. Warrington, Laminar forced convection in a circular tube with constant heat flux and slip flow, Microscale Thermophysical Engineering 1, 303–320 (1997).

    Article  Google Scholar 

  9. B. Cetin, H. Yuncu, and S. Kakac, Gaseous flow in microconduits with viscous dissipation, International Journal of Transport Phenomena 8, 297–315 (2006).

    Google Scholar 

  10. B. Cetin, A. Guvenc Yazicioglu, and S. Kakac, Fluid flow in microtubes with axial conduction including rarefaction and viscous dissipation, International Communications in Heat and Mass Transfer 35, 535–544 (2008).

    Article  Google Scholar 

  11. G. Tunc and Y. Bayazitoglu, Heat transfer in microtubes with viscous dissipation, International Journal of Heat and Mass Transfer 44, 2395–2403 (2001).

    Article  MATH  Google Scholar 

  12. G. Tunc and Y. Bayazitoglu, Convection at the entrance of micropipes with sudden wall temperature change, Proceedings of IMECE, November 17–22, 2002, New Orleans, Louisiana.

    Google Scholar 

  13. S.P. Yu and T.A. Ameel, Slip-flow heat transfer in rectangular microchannels, International Journal of Heat and Mass Transfer 44, 4225–4235 (2001).

    Article  MATH  Google Scholar 

  14. H.-E. Jeong and J.-T. Jeong, Extended Graetz problem including streamwise conduction and viscous dissipation in microchannel, International Journal of Heat and Mass Transfer 49, 2151–2157 (2006).

    Article  MATH  Google Scholar 

  15. Gh.M. Mala and D. Li, Flow characteristics of water in microtubes, International Journal of Heat and Fluid Flow 20, 142–148 (1999).

    Article  Google Scholar 

  16. C. Kleinstreuer and J. Koo, Computational analysis of wall roughness effect for liquid flow in micro-conduits, Journal of Fluids Engineering 126, 1–9 (2004).

    Article  Google Scholar 

  17. G. Croce and P. D’Agaro, Numerical analysis of roughness effect on microtube heat transfer, Superlattices and Microstructures 35, 601–616 (2004).

    Article  ADS  Google Scholar 

  18. G. Croce and P. D’Agaro, Numerical simulation of roughness effect on microchannel heat transfer and pressure drop in laminar flow, Journal of Physics D: Applied Physics 38, 1518–1530 (2005).

    Article  ADS  Google Scholar 

  19. G. Croce, P. D’Agaro, and C. Nonini, Three-dimensional roughness effect on microchannel heat transfer and pressure drop, International Journal of Heat and Mass Transfer 50, 5249–5259 (2007).

    Article  MATH  Google Scholar 

  20. G. Croce, P. D’Agaro, and A. Filippo, Compressibility and rarefaction effects on pressure drop in rough microchannels, Heat Transfer Engineering 28, 688–695 (2007).

    Article  ADS  Google Scholar 

  21. Y. Ji, K. Yuan, and J.N. Chung, Numerical simulation of wall roughness on gaseous flow and heat transfer in a microchannel, International Journal of Heat and Mass Transfer 49, 1329–1339 (2006).

    Article  MATH  Google Scholar 

  22. Z. Li, X. Huai, Y. Tao, and H. Chen, Effects of thermal property variations on the liquid flow and heat transfer in microchannel heat sinks, Applied Thermal Engineering 27, 2803–2814 (2007).

    Article  Google Scholar 

  23. S.P. Guidice, C. Nonino, and S. Savino, Effects of viscous dissipation and temperature dependent viscosity in thermally and simultaneously developing laminar flows in microchannels, International Journal of Heat and Fluid Flow 28, 15–27 (2007).

    Article  Google Scholar 

  24. J.T. Liu, X.F. Peng, and B.X. Wang, Variable-property effect on liquid flow and heat transfer in microchannels, Chemical Engineering Journal 141, 346–353 (2008).

    Article  Google Scholar 

  25. M.S. El-Genk and I. Yang, Numerical analysis of laminar flow in micro-tubes with a slip boundary, Energy Conversion and Management 50, 1481–1490 (2009).

    Article  Google Scholar 

  26. N.P. Gulhane and S.P. Mahulikar, Variations in gas properties in laminar micro-convection with entrance effect, International Journal of Heat and Mass Transfer 52, 1980–1990 (2009).

    Article  MATH  Google Scholar 

  27. M. Gad-El-Hak, The fluid mechanics of microdevices, Journal of Fluids Engineering 121, 5–33 (1999).

    Article  Google Scholar 

  28. G.L. Morini, Single-phase convective heat transfer in microchannels: A review of experimental results, International Journal of Thermal Sciences 43, 631–651 (2004).

    Article  Google Scholar 

  29. Y. Bayazitoglu and S. Kakac, Flow regimes in microchannel single-phase gaseous flow, Microscale Heat Transfer - Fundamentals and Applications in Biological Systems and MEMS, edited by S. Kakac, L. Vasiliev, Y. Bayazitoglu, and Y. Yener (Kluwer Academic Publishers, The Netherlands 2005).

    Google Scholar 

  30. G. Hetsroni, A. Mosyak, E. Pogrebnyak, and L.P. Yarin, Heat transfer in micro-channels: Comparison of experiments with theory and numerical results, International Journal of Heat and Mass Transfer 25–26, 5580–5601 (2005).

    Article  Google Scholar 

  31. Y. Yener, S. Kakac, M. Avelino, and T. Okutucu, Single phase forced convection in microchannels - State-of art-review, Microscale Heat Transfer- Fundamentals and Applications in Biological Systems and MEMS, edited by S. Kakac, L. Vasiliev, Y. Bayazitoglu, and Y. Yener (Kluwer Academic Publishers, The Netherlands 2005).

    Google Scholar 

  32. R.M. Cotta, S. Kakaç, M.D. Mikhailov, F.V. Castellos, Transient flow and thermal analysis in microfluidics, Microscale Heat Transfer- Fundamentals and Applications in Biological Systems and MEMS, edited by S. Kakac, L. Vasiliev, Y. Bayazitoglu, and Y. Yener (Kluwer Academic Publishers, The Netherlands 2005).

    Google Scholar 

  33. P. Rosa, T.G. Karayiannis, and M.W. Collins, Single-phase heat transfer in microchannels: The importance of scaling, Applied Thermal Engineering 29, 3447–3468 (2009).

    Article  Google Scholar 

  34. G. Karniadakis, A. Beskok, and N. Aluru, Microflows and Nanoflows: Fundamentals and Simulation (Springer, New York, 2005).

    MATH  Google Scholar 

  35. C.B. Sobhan and G.P. Peterson, Microscale and Nanoscale Heat Transfer: Fundamentals and Engineering Applications (CRC Press, Florida, 2008).

    Google Scholar 

  36. L.P. Yarin, A. Mosyak, and G. Hetsroni, Fluid Flow, Heat Transfer and Boiling in Micro-Channels (Springer, New York, 2008).

    Google Scholar 

  37. Y. Bayazitoglu, G. Tunc, K. Wilson, and I. Tjahjono, Convective heat transfer for single phase gases in microchannel slip flow: Analytical solutions, Microscale Heat Transfer - Fundamentals and Applications in Biological Systems and MEMS, edited by S. Kakac, L. Vasiliev, Y. Bayazitoglu, and Y. Yener (Kluwer Academic Publishers, The Netherlands 2005).

    Google Scholar 

  38. N.T. Obot, Toward a better understanding of friction and heat/mass transfer in microchannels - A literature review, Microscale Thermophysical Engineering 6, 155–173 (2002).

    Article  Google Scholar 

  39. Beskok, G.E. Karniadakis, and W. Trimmer, Rarefaction, compressibility effects in gas microflows, Journal of Fluids Engineering 118, 448–456 (1996).

    Article  Google Scholar 

  40. W. Sun, S. Kakac, and A. Guvenc Yazicioglu, A numerical study of single-phase convective heat transfer in microtubes for slip flow, International Journal of Thermal Sciences 46, 1084–94 (2007).

    Article  Google Scholar 

  41. B. Cetin, Analysis of single phase convective heat transfer in microtubes and microchannels, M.Sc. Thesis, Middle East Technical University, Ankara, Turkey (2005).

    Google Scholar 

  42. M. Barisik, Analytical solution for single phase microtube heat transfer including axial conduction and viscous dissipation, M.Sc. Thesis, Middle East Technical University, Ankara, Turkey (2008).

    Google Scholar 

  43. G. Tunc and Y. Bayazitoglu, Heat transfer in microtubes with viscous dissipation, International Journal of Heat and Mass Transfer 44, 2395–2403 (2001).

    Article  MATH  Google Scholar 

  44. S. Kakac and Y. Yener, Convective Heat Transfer (CRC Press, Florida, 1994).

    Google Scholar 

  45. R.K. Shah and A.L. London, Laminar flow forced convection in ducts, Advances in Heat Transfer, edited by T.F.Jr. Irvine, and J.P. Hartnett (Academic Press, New York 1978), pp. 78–152.

    Google Scholar 

  46. J. Lahjomri and A. Oubarra, Analytical solution of the Graetz problem with axial conduction, Journal of Heat Transfer 121, 1078–1083 (1999).

    Article  Google Scholar 

  47. W. Qu, Gh.M. Mala, and D. Li, Heat transfer for water flow in trapezoidal silicon microchannels, International Journal of Heat and Mass Transfer 43, 3925–3936 (2000).

    Article  MATH  Google Scholar 

  48. J. Koo and C. Kleinstreuer, Analysis of surface roughness effects on heat transfer in micro-conduits, International Journal of Heat and Mass Transfer 48, 2625–2634 (2005).

    Article  MATH  Google Scholar 

  49. M.B. Turgay and A. Guvenc Yazicioglu, Effect of surface roughness in parallel-plate microchannels on heat transfer, Numerical Heat Transfer 56, 497–514 (2009).

    Article  Google Scholar 

  50. M.B. Turgay, Effect of surface roughness in microchannels on heat transfer, M.Sc. Thesis, Middle East Technical University, Ankara, Turkey (2008).

    Google Scholar 

  51. R.G. Deisler, Analytical investigation of turbulent flow in smooth pipes with heat transfer, with variable fluid properties for Prandtl number of 1, NACA Technical Note 2242 (1950).

    Google Scholar 

  52. R. Oskay and S. Kakac, Effect of viscosity variations on forced convection heat transfer in pipe flow, METU Journal of Pure and Applied Sciences 6, 211–230 (1973).

    Google Scholar 

  53. H. Herwig and S.P. Mahulikar, Variable property effects in single-phase incompressible flows through microchannels, International Journal of Thermal Sciences 45, 977–981 (2006).

    Article  Google Scholar 

  54. C. Gozukara, Heat transfer analysis of single phase forced convection in microchannels and microtubes with variable property effect, M.Sc. Thesis, Middle East Technical University, Ankara, Turkey (2010).

    Google Scholar 

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Acknowledgement

The authors would like to thank the Turkish Scientific and Technical Research Council, TUBITAK, Grant No. 106M076, for financial support.

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Correspondence to A. Guvenc Yazicioglu .

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Yazicioglu, A.G., Kakaç, S. (2010). Convective Heat Transfer in Microscale Slip Flow. In: Kakaç, S., Kosoy, B., Li, D., Pramuanjaroenkij, A. (eds) Microfluidics Based Microsystems. NATO Science for Peace and Security Series A: Chemistry and Biology. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9029-4_2

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