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Research Papers: Porous Media

Predicting the Nusselt Number of Heterogeneous (Porous) Enclosures Using a Generic Form of the Berkovsky–Polevikov Correlations

[+] Author and Article Information
José L. Lage

e-mail: jll@smu.edu
Mechanical Engineering Department,
Southern Methodist University,
Dallas, TX 75275

Admilson T. Franco

Mechanical Engineering Department,
Federal University of Technology Paraná,
Curitiba, PR, Brazil 80230-901

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 14, 2012; final manuscript received April 11, 2013; published online July 10, 2013. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 135(8), 082601 (Jul 10, 2013) (8 pages) Paper No: HT-12-1503; doi: 10.1115/1.4024281 History: Received September 14, 2012; Revised April 11, 2013

A well-known set of Berkovsky–Polevikov (BP) correlations have been extremely useful in predicting the wall-averaged Nusselt number of “wide” enclosures heated from the side and filled with a fluid undergoing natural convection. A generic form of these correlations, dependent on only two coefficients, is now proposed for predicting the Nusselt number of a heterogeneous (fluid–solid), porous enclosure, i.e., an enclosure filled not only with a fluid but also with uniformly distributed, disconnected and conducting, homogeneous solid particles. The final correlations, and their overall accuracies, are determined by curve fitting the numerical simulation results of the natural convection process inside the heterogeneous enclosure. Results for several Ra and Pr, and for 1, 4, 9, 16, and 36 solid particles, with the fluid volume-fraction (porosity) maintained constant, indicate the accuracy of these correlations to be detrimentally affected by the interference phenomenon caused by the solid particles onto the vertical boundary layers that develop along the hot and cold walls of the enclosure; the resulting correlations, in this case, present standard deviation varying between 6.5% and 19.7%. An analytical tool is then developed for predicting the interference phenomenon, using geometric parameters and scale analysis results. When used to identify and isolate the interference phenomenon, this tool is shown to yield correlations with much improved accuracies between 2.8% and 9.2%.

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Figures

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Fig. 1

Sketch of a heterogeneous porous enclosure filled with a fluid and with 36 uniformly distributed solid square particles. Also shown are the coordinates and velocity components, the acceleration of gravity, as well as some geometrical parameters.

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Fig. 2

Streamlines for Pr = 1, Ra = 106, and N = 4 (left) and N = 36 (right)

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Fig. 3

Isotherms for Pr = 1, Ra = 106, and N = 4 (left) and N = 36 (right)

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Fig. 4

Streamlines for Pr = 1, Ra = 107, and N = 4 (left) and N = 36 (right)

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Fig. 5

Isotherms for Pr = 1, Ra = 107, and N = 4 (left) and N = 36 (right)

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Fig. 7

Nuav versus log(γ) for several N values. The symbols are the numerical results and the lines represent the best curve fit using the generic Berkovsky–Polevikov correlation, without using the interference data points, namely, Nuav = AγB″.

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Fig. 6

Nuav versus log(γ) for several N values. The symbols are the numerical results and the lines represent the best curve fit using the extended Berkovsky–Polevikov correlation, namely, Nuav = A γB.

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