Advertisement

Journal of Mechanical Science and Technology

, Volume 20, Issue 1, pp 158–166 | Cite as

Extended Graetz Problem Including Axial Conduction and Viscous Dissipation in Microtube

  • Ho-Eyoul Jeong
  • Jae-Tack JeongEmail author
Article

Abstract

Extended Graetz problem in microtube is analyzed by using eigenfunction expansion to solve the energy equation. For the eigenvalue problem we applied the shooting method and Galerkin method. The hydrodynamically isothermal developed flow is assumed to enter the microtube with uniform temperature or uniform heat flux boundary condition. The effects of velocity and temperature jump boundary condition on the microtube wall, axial conduction and viscous dissipation are included. From the temperature field obtained, the local Nusselt number distributions on the tube wall are obtained as the dimensionless parameters (Peclet number, Knudsen number, Brinkman number) vary. The fully developed Nusselt number for each boundary condition is obtained also in terms of these parameters.

Key Words

Graetz Problem Microtube Slip Boundary Condition Viscous Dissipation Axial Conduction Eigenvalue Problem Knudsen Number Peclet Number Brinkman Number 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ameel, T. A., Barron, R. F., Wang, X. and Warrington, R. O., 1997, “Laminar Forced Convection in a Circular tube with Constant Heat Flux and Slip Flow,”Microscale Thermophys. Eng., Vol. 1(4), pp. 303–320.CrossRefGoogle Scholar
  2. Barron, R. F., Wang, X., Ameel, T. A. and Warrington, R. O., 1997, “The Graetz Problem Extended to Slip-Flow,”Int. J. Heat Mass Transfer, Vol. 40(8), pp. 1817–1823.zbMATHCrossRefGoogle Scholar
  3. Choi, S. B., Barren, R. F. and Warrington, R. O., 1991, “Fluid Flow and Heat Transfer in Microtubes, In Micromechanical Sensors, Actuators, and System,”ASME DSC 32, pp. 123–134.Google Scholar
  4. Graetz, L. and Uber die Warmeleitungsfa- higheit von Flussingkeiten, 1883, 1885, Annalen der Physik und Chemie part 1, Vol. 18, pp. 79–94, part 2, Vol. 25, pp. 337–357.Google Scholar
  5. Karniadakis, G. E. and Beskok, A., 2002,Micro flows Fundamentals and Simulation, Springer-Verlag, New York, pp. 45–53.zbMATHGoogle Scholar
  6. Lahjomri, J. and Oubarra, A., 1999, “Analytical Solution of the Graetz Problem with Axial Conduction,”ASME J. Heat Transfer, Vol. 121, pp. 1078–1083.CrossRefGoogle Scholar
  7. Nield, D. A., Kuznetsov, A. V. and Xiong, M., 2003, “Thermally Developing Forced Convection in a Porous Medium: Parallel Plate Channel with Walls at Uniform Temperature, with Axial Conduction and Viscous Dissipation Effects,”Int. J. Heat Mass Transfer, Vol. 46, pp. 643 - 651.zbMATHCrossRefGoogle Scholar
  8. Ou, J.W. and Cheng, K. C., 1974, “Viscous Dissipation Effects on Thermal Entrance Heat Transfer in Laminar and Turbulent Pipe Flows with Uniform wall Temperature,”Am. Inst. Aeronaut. Astron., Pap. 74–743 orAm. Soc. Mech. Eng., Pap. 74-HT-50.Google Scholar
  9. Sellars, J. R., Tribus, M. and Klein, J. S., 1956, “Heat Transfer to Laminar Flow in a Round Tube or Flat Conduit-the Graetz Problem Extended,”Trans. ASME, Vol. 78, pp. 441–448.Google Scholar
  10. Shah, R. K. and London, A. L., 1978,Laminar Flow Forced Convection in Ducts, Academic Press, New York, pp. 109–111.Google Scholar
  11. Tuckerman, D. B. and Pease, R. F. W., 1981, “High Performance Heat Sinking for VLSI, IEEE Electron Device Letters,” Vol. EDL-2 No. 5, pp. 126–129.Google Scholar
  12. Tune, G. and Bayazitoglu, Y., 2001, “Heat Transfer in Microtubes with Viscous Dissipation,”Int. J. Heat Mass Transfer, Vol. 44, pp. 2395–2403.CrossRefGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2006

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringChonnam National UniversityGwangjuKorea

Personalised recommendations