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Research Papers: Natural and Mixed Convection

Second-Order Mixed Convective Flow in a Long Vertical Microchannel

[+] Author and Article Information
Huei Chu Weng

Department of Mechanical Engineering,
Chung Yuan Christian University,
Chungli, 32023, Taiwan, ROC

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received April 2, 2012; final manuscript received July 18, 2012; published online January 4, 2013. Assoc. Editor: Bruce L. Drolen.

J. Heat Transfer 135(2), 022506 (Jan 04, 2013) (5 pages) Paper No: HT-12-1148; doi: 10.1115/1.4007423 History: Received April 02, 2012; Revised July 18, 2012

The present investigation is concerned with the role of second-order slip in the mixed convection through a long heated vertical planar microchannel with asymmetric wall temperatures. The fully developed solutions of fields and the corresponding characteristics are analytically derived on the basis of second-order Maxwell–Smoluchowski–Burnett (MSB) slip/jump boundary conditions. Results reveal that second-order slip has an appreciable effect on the flow but a negligible effect on the heat transfer. The effect is to raise the gas motion speeds near the heated walls and to enlarge the pressure gradient required to drive the flow. It then leads to the reduction of local flow drag, except for the case where a reversed flow region exists. The second-order effect could be magnified by increasing the mixed convection number, the ratio of the Grashof number to the Reynolds number.

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Figures

Grahic Jump Location
Fig. 2

Velocity distribution for different values of Gr/Re with Kn=0.1

Grahic Jump Location
Fig. 3

Pressure gradient versus Gr/Re with Kn=0.1

Grahic Jump Location
Fig. 4

Local flow drag versus Gr/Re for different values of ξ with Kn=0.1

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