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Technical Briefs

Analytical Solution of the Graetz Problem Extended to Slip-Flow in Microtube

[+] Author and Article Information
Fayao Xu

College of Power Engineering,  University of Shanghai for Science and Technology, Shanghai 200093, China

Hugen Ma

College of Power Engineering,  University of Shanghai for Science and Technology, Shanghai 200093, Chinamahugen406@hotmail.com

J. Heat Transfer 134(10), 104501 (Aug 07, 2012) (2 pages) doi:10.1115/1.4006717 History: Received February 24, 2011; Revised March 20, 2012; Published August 06, 2012; Online August 07, 2012

The original Graetz problem is extended to slip-flow in microtube. The extended Graetz problem in slip-flow with the isothermal boundary condition on the wall was solved using conventional energy equation with both the velocity slip and the temperature jump condition of slip-flow. The analytical solution was obtained by solving the energy equation with the method of separation of variables. The accurate eigenvalues were obtained by solving the eigenfunction with the method of power series expansion. In the end, temperature distributions, local Nusselt number Nux , and dimensionless temperature jump θs were obtained. In addition, the influences of Knudsen number Kn on Nux , Nu∞ , and θs were discussed.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 2

Local Nusselt number as a function of axial location

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