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Research Papers

Thermodynamics Analyses of Porous Microchannels With Asymmetric Thick Walls and Exothermicity: An Entropic Model of Microreactors

[+] Author and Article Information
Alexander Elliott

School of Engineering,
University of Glasgow,
Glasgow G12 8QQ, UK

Mohsen Torabi

The George W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mails: Torabi_mech@yahoo.com;
Mohsen.Torabi@my.cityu.edu.hk

Nader Karimi

School of Engineering,
University of Glasgow,
Glasgow G12 8QQ, UK
e-mail: Nader.Karimi@glasgow.ac.uk

1Corresponding authors.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received September 13, 2016; final manuscript received April 11, 2017; published online July 25, 2017. Assoc. Editor: Samuel Sami.

J. Thermal Sci. Eng. Appl 9(4), 041013 (Jul 25, 2017) (11 pages) Paper No: TSEA-16-1264; doi: 10.1115/1.4036802 History: Received September 13, 2016; Revised April 11, 2017

This paper presents a study of the thermal characteristics and entropy generation of a porous microchannel with thick walls featuring uneven thicknesses. Two sets of asymmetric boundary conditions are considered. The first includes constant temperatures at the surface of the outer walls, with the lower wall experiencing a higher temperature than the upper wall. The second case imposes a constant heat flux on the lower wall and a convection boundary condition on the upper wall. These set thermal models for microreactors featuring highly exothermic or endothermic reactions such as those encountered in fuel reforming processes. The porous system is considered to be under local thermal nonequilibrium (LTNE) condition. Analytical solutions are, primarily, developed for the temperature and local entropy fields and then are extended to the total entropy generation within the system. It is shown that the ratio of the solid to fluid effective thermal conductivity and the internal heat sources are the most influential parameters in the thermal and entropic behaviors of the system. In particular, the results demonstrate that the internal heat sources can affect the entropy generation in a nonmonotonic way and that the variation of the total entropy with internal heat sources may include extremum points.

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Figures

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Fig. 1

Schematic configuration of the model microreactors: (a) case one and (b) case two

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Fig. 2

Temperature distribution with various values of Biot number: (a) case one and (b) case two. Black: Bi=0.1, blue: Bi=1, red: Bi=10 (see color figure online).

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Fig. 3

Temperature distribution with various values for internal heat generation through the fluid medium: (a) case one and (b)case two. Black: wf=−1, blue: wf=0, red: wf=1 (see color figure online).

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Fig. 4

Temperature distribution with various values for the hottemperature boundary condition (case one). Black: θH=1.5, blue: θH=3, red: θH=5 (see color figure online).

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Fig. 5

Temperature distribution with various values for the heat flux boundary condition (case two). Black: QH=0, blue: QH=1, red: QH=5 (see color figure online).

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Fig. 6

Total entropy generation distribution versus Biot number: (a) case one and (b) case two. Black: Da=0.001, blue: Da=0.0001, red: Da=0.00001 (see color figure online).

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Fig. 7

Total entropy generation distribution versus thermal conductivity ratio: (a) case one and (b) case two. Black: Da=0.001, blue: Da=0.0001, red: Da=0.00001 (see color figure online).

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Fig. 8

Total entropy generation distribution versus Darcy number: (a) case one and (b) case two. Black: ε=0.9, blue: ε=0.7, red: ε=0.5 (see color figure online).

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Fig. 9

Total entropy generation distribution versus Brinkman number: (a) case one and (b) case two. Black: Da=0.001, blue: Da=0.0001, red: Da=0.00001 (see color figure online).

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Fig. 10

Total entropy generation distribution versus internalheat generation through the fluid medium: (a) case one and (b) case two. Black: Da=0.001, blue: Da=0.0001, red: Da=0.00001 (see color figure online).

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Fig. 11

Total entropy generation distribution versus internal heat generation through the solid medium: (a) case one and (b)case two. Black: Da=0.001, blue: Da=0.0001, red: Da=0.00001 (see color figure online).

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Fig. 12

Total entropy generation distribution versus the hot temperature boundary condition (case one). Black: Da=0.001, blue: Da=0.0001, red: Da=0.00001 (see color figure online).

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Fig. 13

Total entropy generation distribution versus the heat flux boundary condition (case two). Black: Da=0.001, blue: Da=0.0001, red: Da=0.00001 (see color figure online).

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Fig. 14

Total entropy generation distribution versus the convection boundary condition (case two). Black: Da=0.001, blue: Da=0.0001, red: Da=0.00001 (see color figure online).

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