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Research Papers

Effect of Thermal Creep on Heat Transfer for a Two-Dimensional Microchannel Flow: An Analytical Approach

[+] Author and Article Information
Barbaros Çetin

Mechanical Engineering Department,
Microfluidics & Lab-on-a-Chip Research Group,
Ihsan Dogramaci Bilkent University,
Ankara 06800, Turkey
e-mails: barbaros.cetin@bilkent.edu.tr,
barbaroscetin@gmail.com

The incompressible flow assumption requires Mach number is less than 0.3.

The coefficients of the ξ term and 1/Pe2 slightly differ from that of Ref. [31] due to the nondimensionlization of the velocity with uo instead of umean.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received July 13, 2012; final manuscript received November 15, 2012; published online September 11, 2013. Assoc. Editor: Sushanta K. Mitra.

J. Heat Transfer 135(10), 101007 (Sep 11, 2013) (8 pages) Paper No: HT-12-1366; doi: 10.1115/1.4024504 History: Received July 13, 2012; Revised November 15, 2012

In this paper, velocity profile, temperature profile, and the corresponding Poiseuille and Nusselt numbers for a flow in a microtube and in a slit-channel are derived analytically with an isoflux thermal boundary condition. The flow is assumed to be hydrodynamically and thermally fully developed. The effects of rarefaction, viscous dissipation, axial conduction are included in the analysis. For the implementation of the rarefaction effect, two different second-order slip models (Karniadakis and Deissler model) are used for the slip-flow and temperature-jump boundary conditions together with the thermal creep at the wall. The effect of the thermal creep on the Poiseuille and Nusselt numbers are discussed. The results of the present study are important (i) to gain the fundamental understanding of the effect of thermal creep on convective heat transfer characteristics of a microchannel fluid flow and (ii) for the optimum design of thermal systems which includes convective heat transfer in a microchannel especially operating at low Reynolds numbers.

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References

Figures

Grahic Jump Location
Fig. 1

Creep velocity over mean velocity for different Kn

Grahic Jump Location
Fig. 2

Critical Br for different Kn

Grahic Jump Location
Fig. 3

Variation of the Po as a function of Kn (a) Br = 0, (b) Br = 0.1, and (c) Br = −0.1

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