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Research Papers: Micro/Nanoscale Heat Transfer

Thermal Analysis of Power-Law Fluid Flow in a Circular Microchannel

[+] Author and Article Information
Amir-Hossein Sarabandi

Mechanical Engineering,
Shahrood University of Technology,
Shahrood 3619995161, Iran

Ali Jabari Moghadam

Associate Professor
Department of Mechanical Engineering,
Shahrood University of Technology,
P.O. Box 316,
Shahrood 3619995161, Iran
e-mail: jm.ali.project@gmail.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 25, 2016; final manuscript received October 5, 2016; published online December 7, 2016. Assoc. Editor: Jim A. Liburdy.

J. Heat Transfer 139(3), 032401 (Dec 07, 2016) (14 pages) Paper No: HT-16-1028; doi: 10.1115/1.4035040 History: Received January 25, 2016; Revised October 05, 2016

The steady-state fully developed laminar flow of non-Newtonian power-law fluids is analytically studied in a circular microchannel under an imposed uniform and constant wall heat flux. Increasing the flow behavior index results in broadening the dimensionless temperature distribution, i.e., in enlarging the wall and bulk fluid temperature difference. Similar behavior may also be observed when heating or cooling flux is reduced. For any particular value of the flow behavior index, a critical Brinkman number exists in which the bulk mean fluid temperature equals the wall temperature; in this special case of surface cooling, the Nusselt number tends to infinity. Dilatants (shear-thickening fluids) demonstrate more tangible reactions than pseudoplastics (shear-thinning fluids) to changes in the Brinkman number. Entropy generation increases with the flow behavior index as well as the Brinkman number. For shear-thickening fluids, the entropy generation rate from heat transfer is more than the entropy generation rate from fluid friction, while an opposite trend is observed for shear-thinning fluids.

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Figures

Grahic Jump Location
Fig. 1

Schematic of physical model

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Fig. 2

Dimensionless velocity profiles for different n

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Fig. 3

Poiseuille number versus power-law index

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Fig. 9

Dimensionless temperature gradient distributions versus radial coordinate for (a) n = 0.5 and (b) n = 1.5

Grahic Jump Location
Fig. 10

Dimensionless entropy generation from heat transfer for (a) Br = 0, (b) Br = 0.5, (c) n = 0.5, and (d) n = 1.5

Grahic Jump Location
Fig. 11

Dimensionless entropy generation from fluid friction for (a) Br = 0.5, (b) n = 0.5, and (c) n = 1.5

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Fig. 12

Dimensionless total entropy generation for (a) Br = 0.5, (b) Br = 1, (c) n = 0.5, and (d) n = 1.5

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Fig. 4

Dimensionless temperature distributions versus radial coordinate for (a) Br = 0, (b) Br = 0.5, and (c) Br=−0.5

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Fig. 5

Dimensionless temperature distributions versus radial coordinate for (a) n = 0.5 and (b) n = 1.5

Grahic Jump Location
Fig. 6

Nusselt number versus Brinkman number for different power-law index, for (a) 0 < Br < 1, (b) −1 < Br < 1, n = 0.5, (c) −1 < Br < 1, n = 1.5, and (d) Nusselt number versus power-law index for different Brinkman number

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Fig. 7

Critical Brinkman number versus power-law index

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Fig. 8

Variations of dimensionless temperature gradient distributions with R for (a) Br = 0, (b) Br = 0.5, and (c) Br=−0.5

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Fig. 13

Dimensionless average total entropy generation as a function of power-law index and Brinkman number

Grahic Jump Location
Fig. 14

Bejan number as a function of radial coordinate and Brinkman number for (a) n = 0.5 and (b) n = 1.5

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