0
Research Papers

Effect of Thermal Creep on Heat Transfer for a Two-Dimensional Microchannel Flow: An Analytical Approach

[+] Author and Article Information
Barbaros Çetin

Mechanical Engineering Department,
Microfluidics & Lab-on-a-Chip Research Group,
Ihsan Dogramaci Bilkent University,
Ankara 06800, Turkey
e-mails: barbaros.cetin@bilkent.edu.tr,
barbaroscetin@gmail.com

The incompressible flow assumption requires Mach number is less than 0.3.

The coefficients of the ξ term and 1/Pe2 slightly differ from that of Ref. [31] due to the nondimensionlization of the velocity with uo instead of umean.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received July 13, 2012; final manuscript received November 15, 2012; published online September 11, 2013. Assoc. Editor: Sushanta K. Mitra.

J. Heat Transfer 135(10), 101007 (Sep 11, 2013) (8 pages) Paper No: HT-12-1366; doi: 10.1115/1.4024504 History: Received July 13, 2012; Revised November 15, 2012

In this paper, velocity profile, temperature profile, and the corresponding Poiseuille and Nusselt numbers for a flow in a microtube and in a slit-channel are derived analytically with an isoflux thermal boundary condition. The flow is assumed to be hydrodynamically and thermally fully developed. The effects of rarefaction, viscous dissipation, axial conduction are included in the analysis. For the implementation of the rarefaction effect, two different second-order slip models (Karniadakis and Deissler model) are used for the slip-flow and temperature-jump boundary conditions together with the thermal creep at the wall. The effect of the thermal creep on the Poiseuille and Nusselt numbers are discussed. The results of the present study are important (i) to gain the fundamental understanding of the effect of thermal creep on convective heat transfer characteristics of a microchannel fluid flow and (ii) for the optimum design of thermal systems which includes convective heat transfer in a microchannel especially operating at low Reynolds numbers.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Yaman, M., Khudiyev, T., Ozgur, E., Kanik, M., Aktas, O., Ozgur, E. O., Deniz, H., Korkut, E., and Bayindir, M., 2011, “Arrays of Indefinitely Long Uniform Nanowires and Nanotubes,” Nature Mater., 10(7), pp. 494–501. [CrossRef]
Colin, S., 2004, “Validation of a Second-Order Slip Flow Model in Rectangular Microchannels,” Heat Transfer Eng., 25(3), pp. 23–30. [CrossRef]
Colin, S., 2005, “Rarefaction and Compressibility Effects on Steady and Transient Gas Flows in Microchannels,” Microfluid. Nanofluid., 1, pp. 268–279. [CrossRef]
Weng, H. C., 2010. “Laminar, Transitional and Turbulent Friction Factors for Gas Flows in Smooth and Rough Microtubes,” Int. J. Therm. Sci., 49, pp. 248–255. [CrossRef]
Yang, Y., Morini, G. L., Lorenzini, M., Hong, C., Asako, Y., and Brandner, J. J., 2012, “Transitional and Turbulent Convective Heat Transfer compressible Gas Flows Through Microtubes,” Proceedings of the ASME 2012 10th International Conference on Nanochannles, Microchannels and Minichannels, ICNMM2012, Puerto Rico, USA, Paper No. 73261, July 8–12.
Karniadakis, G. E., Beskok, A., and Aluru, N., 2005, Microflows and Nanoflows: Fundamentals and Simulations, Springer, New York, pp. 51–74, 167–172.
Deissler, R. G., 1964, “An Analysis of Second-Order Slip Flow and Temperature-Jump Boundary Conditions for Rarefied Gases,” Int. J. Heat Mass Transfer, 7, pp. 681–694. [CrossRef]
Duan, Z., 2012, “Second-Order Gaseous Slip Flow Models in Long Circular and Noncircular Microchannels and Nanochannels,” Microfluid. Nanofluid., 12, pp. 805–820. [CrossRef]
Weng, H. C., and Chen, C.-K., 2008, “A Challenge in Navier–Stokes Based Continuum Modeling: Maxwell–Burnett Slip Law,” Phys. Fluids, 20, p. 106101. [CrossRef]
Cetin, B., Yazicioglu, A., and Kakac, S., 2008, “Fluid Flow in Microtubes With Axial Conduction Including Rarefaction and Viscous Dissipation,” Int. Commun. Heat Mass Transfer, 35, pp. 535–544. [CrossRef]
Aubert, C., and Colin, S., 2001, “High-Order Boundary Conditions for Gaseous Flows in Rectangular Microducts,” Microscale Thermophys. Eng., 5, pp. 41–54. [CrossRef]
Niazmand, H., Amiri-Jaghargh, A., and Renksizbulut, M., 2010, “Slip-Flow and Heat Transfer in Isoflux Rectangular Microchannels With Thermal Creep Effects,” J. Appl. Fluid Mech., 3(2), pp. 33–41, Available at www.jafmonline.net
Amiri-Jaghargh, A., Niazmand, H., and Renksizbulut, M., 2010, “Cooling in a Constant Wall Temperature Microchannels With Thermal Creep Effects,” Proceedings of the ASME 8th International Conference on Nanochannles, Microchannels and Minichannels, ICNMM2010, Montreal, Canada, Paper No. 30770, August 1–5.
Ameel, T. A., Barron, R. F., Wang, X. M., and Warrington, R. O., 1997, “Laminar Forced Convection in a Circular Tube With Constant Heat Flux and Slip Flow,” Microscale Thermophys. Eng., 1, pp. 303–320. [CrossRef]
Chen, C. S., and Kuo, W. J., 2004, “Heat Transfer Characteristics of Gaseous Flow in Long Mini- and Microtubes,” Numer. Heat Transfer, Part A, 46(5), pp. 497–514. [CrossRef]
Aydin, O., and Avci, M., 2006, “Analysis of Micro-Graetz Problem in a Microtube,” Nanoscale Microscale Thermophys. Eng., 10(4), pp. 345–358. [CrossRef]
Cetin, B., Yazicioglu, A., and Kakac, S., 2009, “Slip-Flow Heat Transfer in Microtubes With Axial Conduction and Viscous Dissipation—An Extended Graetz Problem,” Int. J. Therm. Sci., 48, pp. 1673–1678. [CrossRef]
Çetin, B., Yuncu, H., and Kakac, S., 2006, “Gaseous Flow in Microchannels With Viscous Dissipation,” Int. J. Transp. Phenom., 8, pp. 297–315.
Xiao, N., Elsnab, J., and Ameel, T., 2009, “Microtube Gas Flows With Second-Order Slip Flow and Temperature Jump Boundary Conditions,” Int. J. Therm. Sci., 48(2), pp. 243–251. [CrossRef]
Cetin, B., and Bayer, O., 2011, “Evaluation of Nusselt Number for a Flow in a Microtube Using Second-Order Slip Model,” Therm. Sci., 15(Suppl. 1), pp. 103–109. [CrossRef]
Cetin, B., 2012, “Evaluation of Nusselt Number for a Flow in a Microtube With Second-Order Model Including Thermal Creep,” Proceedings of the ASME 10th International Conference on Nanochannles, Microchannels and Minichannels, ICNMM2012, Puerto Rico, USA, Paper No. 73321, July 8–12.
Xue, H., Ji, H., and Shu, C., 2003, “Prediction of Flow and Heat Transfer Characteristics in Micro-Couette Flow,” Microscale Thermophys. Eng., 7(1), pp. 51–68. [CrossRef]
Jeong, H. E., and Jeong, J. T., 2006, “Extended Graetz Problem Including Streamwise Conduction and Viscous Dissipation in Microchannels,” Int. J. Heat Mass Transfer, 49, pp. 2151–2157. [CrossRef]
Roy, S., and Chakraborty, S., 2007, “Near-Wall Effects in Micro Scale Couette Flow and Heat Transfer in the Maxwell-Slip Regime,” Microfluid. Nanofluid., 3(4), pp. 437–449. [CrossRef]
Niazmand, H., and Rahimi, B., 2010, “High Order Slip and Thermal Creep Effects in Micro Channel Natural Convection,” Proceedings of the ASME 8th International Conference on Nanochannles, Microchannels and Minichannels, ICNMM2010, Montreal, Canada, Paper No. 30688, August 1–5.
Weng, H. C., and Chen, C.-K., 2008, “On the Importance of Thermal Creep in Natural Convection Gas Microflow With Wall Heat Fluxes,” J. Phys. D: Appl. Phys., 41, p. 115501. [CrossRef]
van Rij, J., Ameel, T., and Harman, T., 2009, “An Evaluation of Secondary Effects on Microchannel Frictional and Convective Heat Transfer Characteristics,” Int. J. Heat Mass Transfer, 52, pp. 2792–2801. [CrossRef]
Duan, Z., and Muzychka, Y. S., 2008, “Slip Flow Heat Transfer in Annular Microchannels With Constant Heat Flux,” ASME J. Heat Transfer, 130, p. 092401. [CrossRef]
Aziz, A., and Niedbalski, N., 2011, “Thermally Developing Microtube Gas Flow With Axial Conduction and Viscous Dissipation,” Int. J. Therm. Sci., 50, pp. 332–340. [CrossRef]
van Rij, J., Harman, T., and Ameel, T., 2007, “The Effect of Creep Flow on Two-Dimensional Isoflux Microchannels,” Int. J. Therm. Sci., 46, pp. 1095–1103. [CrossRef]
Vick, B., and Ozisik, M. N., 1981, “An Exact Analysis of Low Peclet Number Heat Transfer in Laminar Flow With Axial Conduction,” Lett. Heat Mass Transfer, 8, pp. 1–10. [CrossRef]
Incropera, F. P., and DeWitt, D. P., 1996, Fundamentals of Heat and Mass Transfer, 4th ed., John Wiley & Sons, New York, p. 426.
Weng, H. C., 2010, “Second-Order Slip Flow and Heat Transfer in a Microchannel,” Comput. Commun. Control Autom. (3CA), 2, pp. 13–16.

Figures

Grahic Jump Location
Fig. 1

Creep velocity over mean velocity for different Kn

Grahic Jump Location
Fig. 2

Critical Br for different Kn

Grahic Jump Location
Fig. 3

Variation of the Po as a function of Kn (a) Br = 0, (b) Br = 0.1, and (c) Br = −0.1

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In