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.
Issue Section:
Technical Briefs
References
1.
Sun
, Z.
, and Jaluria
, Y.
, 2011, “Conjugate Thermal Transport in Gas Flow in Long Rectangular Microchannel
,” ASME J. Electron. Packag.
, 133
(6
), p. 021008
.2.
Sadeghi
, A.
, Baghani
, M.
, and Saidi
, M. H.
, 2010, “Second Law Analysis for Extended Graetz Problem Including Viscous Dissipation
,” Proceedings of the ASME 2010 3rd Joint US-European Fluid Engineering Summer Meeting and 8th International Conference on Nanochannels, Microchannels and Minichannels
, Montreal, QC, Canada
, pp. 503
–514
.3.
Colin
, S.
, 2012, “Gas Microflows in the Slip Flow Regime: A Critical Review on Convective Heat Transfer
,” ASME J. Heat Transfer
, 134
(2
), p. 020908
.4.
Barron
, R. F.
, Wang
, X.
, Warrington
, R. O.
, and Ameel
, T.
, 1996, “Evaluation of the Eigenvalues for the Graetz Problem in Slip-Flow
,” Int. Commun. Heat Mass Transfer
, 23
(4
), pp. 563
–574
.5.
Barron
, R. F.
, Wang
, X.
, Ameel
, T.
, and Warrington
, R. O.
, 1997, “The Graetz Problem Extended to Slip Flow
,” Int. J. Heat Mass Transfer
, 40
(8
), pp. 1817
–1823
.6.
Wang
, X. M.
, 1995, “Evaluation of the Eigenvaluations for the Graetz Problem in Slip Flow
,” M.S. thesis, Louisiana Tech University, Ruston, LA.7.
Arkilic
, E. B.
, Bruer
, K. S.
, and Schmidt
, M. A.
, 1994, “Gaseous Flow in Microchannels
, ” Application of Microfabrication to Fluid Mechanics
, ASME FED
, Chicago, IL
, Vol. 197
, pp. 57
–66
.8.
Larrode
, F. E.
, Housiadas
, C.
, and Drossinos
, Y.
, 2000, “Slip-Flow Heat Transfer in Circular Tubes
,” Int. J. Heat Mass Transfer
, 43
, pp. 2669
–2680
.9.
Tunc
, G.
, and Bayazitoglu
, Y.
, 2001, “Heat Transfer in Microtubes With Viscous Dissipation
,” Int. J. Heat Mass Transfer
, 44
, pp. 2395
–2403
.10.
Aydin
, O.
, and Avci
, M.
, 2006, “Analysis of Micro-Graetz Problem in a Microtube
,” Nanoscale Microscale Thermophys. Eng.
, 10
, pp. 345
–358
.11.
Jeong
, H. E.
, and Jeong
, J. T.
, 2006, “Extended Graetz Problem Including Streamwise Conduction and Viscous Dissipation in Microchannel
,” Int. J. Heat Mass Transfer
, 49
, pp. 2151
–2157
.Copyright © 2012
by American Society of Mechanical Engineers
You do not currently have access to this content.
