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RESEARCH PAPERS: Natural and Mixed Convection

The Role of the Viscous Dissipation in Heated Microchannels

[+] Author and Article Information
Gian Luca Morini

 DIENCA-Università degli Studi di Bologna, Viale Risorgimento 2, 40136 Bologna, Italygianluca.morini@mail.ing.unibo.it

Marco Spiga

Dipartimento di Ingegneria Industriale,  Parco Area delle Scienze 181A, 43100 Parma, Italy

J. Heat Transfer 129(3), 308-318 (May 12, 2006) (11 pages) doi:10.1115/1.2430725 History: Received November 30, 2005; Revised May 12, 2006

Many experimental works appeared in the last decade in the open literature dealing with forced convection through microchannels. The earliest experimental results on single-phase flows in microchannels evidenced that for channels having a hydraulic diameter less than 1mm the conventional continuum models can no longer be considered as able to accurately predict pressure drop and convective heat transfer coefficients. This conclusion seemed to be valid for both gas and liquid flows. Sometimes the authors justified this conclusion by invoking new micro-effects, e.g., electrostatic interaction between the fluid and the walls or scaling effects (axial heat conduction, viscous forces, conjugate heat transfer, wall roughness, and so on). In this paper the role of the viscous dissipation in liquids flowing through heated microchannels will be analyzed by using the conventional theory. We will present a correlation between the Brinkman number and the Nusselt number for silicon ⟨100⟩ and ⟨110⟩ microchannels. It will be demonstrated that the fluid is of importance in establishing the exact limit of significance of the viscous dissipation in microchannels; a criterion to analyze the significance of the viscous effects will be presented. The role of the cross-section aspect ratio on the viscous dissipation will be highlighted. The main goal of this work is to demonstrate that the problem of heat transfer enhancement in microdevices cannot be solved by indefinitely reducing the microchannel dimensions because the viscous dissipation effects shall offset the gains of high heat transfer coefficients associated with a reduction in the channel size.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Typical microchannel cross-sections obtained by chemical etching on ⟨100⟩ and ⟨110⟩ silicon wafers

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Figure 2

Sketch of a silicon heat sink

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Figure 3

Maximum value of the Brinkman number for which the viscous dissipation effects can be neglected for trapezoidal (ϕ=54.74deg) and rectangular (ϕ=90deg) microchannels as a function of the aspect ratio β

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Figure 4

Maximum Reynolds numbers for which the effects of the viscous dissipation can be neglected

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Figure 5

Comparison between the numerical and the analytical values of the average fully developed Nusselt number for rectangular channels with β=1 and β=0.5 (four sides heated)

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Figure 6

Local Nusselt number along the perimeter of two trapezoidal microchannels with four heated sides for β=1 (a) and β=0.2 (b) as a function of the Brinkman number

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Figure 7

The average fully developed Nusselt number as a function of the Brinkman number for trapezoidal silicon microchannels with three (a) and four (b) sides heated

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Figure 8

The average fully developed Nusselt number for microchannels with an uniform wall temperature with three (a) and four (b) sides heated as a function of the cross-section aspect ratio (β)

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Figure 9

The area goodness factor (jH1∕f) for rectangular and trapezoidal microchannels with four sides heated as a function of the aspect ratio

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Figure 10

The area goodness factor (jH1∕f) for rectangular and trapezoidal microchannels with three sides heated as a function of the aspect ratio

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