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


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 


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Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2006

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringChonnam National UniversityGwangjuKorea

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