Extended Graetz Problem Including Axial Conduction and Viscous Dissipation in Microtube
- 191 Downloads
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 WordsGraetz Problem Microtube Slip Boundary Condition Viscous Dissipation Axial Conduction Eigenvalue Problem Knudsen Number Peclet Number Brinkman Number
Unable to display preview. Download preview PDF.
- 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
- 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
- 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
- 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
- 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
- Shah, R. K. and London, A. L., 1978,Laminar Flow Forced Convection in Ducts, Academic Press, New York, pp. 109–111.Google Scholar
- 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