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RESEARCH PAPERS: Porous Media

# Flow, Thermal, Energy Transfer, and Entropy Generation Characteristics Inside Wavy Enclosures Filled With Microstructures

[+] Author and Article Information
Shohel Mahmud, Roydon Andrew Fraser

Department of Mechanical Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

Ioan Pop

Faculty of Mathematics, University of Cluj, R-3400 Cluj, CP 253, Romania

J. Heat Transfer 129(11), 1564-1575 (Feb 24, 2007) (12 pages) doi:10.1115/1.2759976 History: Received July 28, 2006; Revised February 24, 2007

## Abstract

Flow, thermal, energy, and irreversibility characteristics inside wavy enclosures packed with microstructures are reported in this paper. It is assumed that the entire enclosure has sufficient and interconnected void spaces; those allow fluid movement inside the cavity. The Darcy momentum equation is selected for momentum transfer modeling by considering a relatively small pore Reynolds number $(Rep)$. Modeled equations are solved numerically using the finite volume method. Streamlines, isothermal lines, energy streamlines, average Nusselt number, and average entropy generation number are calculated and displayed in order to show their dependency on and variation with Rayleigh number (Ra), surface waviness $(λ)$, and aspect ratio $(AR)$ of the enclosure. Depending on the wall waviness pattern, the enclosure is divided into three modes (phase-plus, phase-zero, and phase-minus modes). However, for the current calculation, wall waviness is kept symmetric with respect to the vertical and horizontal centerlines of the enclosure.

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## Figures

Figure 1

Cross sections of wavy cavities packed with micropinfins at (a) phase-plus mode and (b) phase-minus mode

Figure 3

Streamlines at (a)Ra=10, λ=0.25(Ψmax=0.783); (b)Ra=100, λ=0.25(Ψmax=5.42); (c)Ra=1000, λ=0.25(Ψmax=21.81); (d)Ra=10, λ=0.0(Ψmax=0.7178); (e) Ra=100, λ=0.0(Ψmax=4.707); (f)Ra=1000, λ=0.0(Ψmax=20.48); (g)Ra=10, λ=−0.25(Ψmax=0.59); (h)Ra=100, −0.25(Ψmax=4.259); and (i)Ra=1000, −0.25(Ψmax=18.84). Aspect ratio AR=1.

Figure 4

Isothermal lines at (a)Ra=10, λ=0.25; (b)Ra=100, λ=0.25; (c)Ra=1000, λ=0.25; (d)Ra=10, λ=0.0; (e)Ra=100, λ=0.0; (f)Ra=1000, λ=0.0; (g)Ra=10, λ=−0.25; (h)Ra=100, λ=−0.25; (i)Ra=1000, λ=−0.25. Aspect ratio AR=1.

Figure 5

Energy streamlines at (a)Ra=0, λ=0.25; (b)Ra=10, λ=0.25; (c)Ra=100, λ=0.25; (d)Ra=0, λ=0; (e)Ra=10, λ=0; (f)Ra=0, λ=0; (g)Ra=0, λ=−0.25; (h)Ra=10, λ=−0.25, and (i)Ra=100, λ=−0.25. Aspect ratio AR=1.

Figure 2

Schematic of the problem under consideration with boundary conditions (PPM: phase plus mode, PZM: phase zero mode, PMM: phase minus mode, HCL: horizontal centerline, VCL: vertical centerline)

Figure 7

Average Nusselt number as a function of Ra at different λ

Figure 6

Local Nusselt number distribution at Ra=1 (dashed-dotted lines) and Ra=100 (solid lines). The NuL labels at the right ordinate are for Ra=1 and at the left ordinate are for Ra=100.

Figure 8

Average Nusselt number as a function of λ at different Ra

Figure 9

Streamlines at Ra=250 for different values of λ: (a)λ=−0.25(Ψmax=7.943), (b)λ=−0.2(Ψmax=8.057), (c)λ=−0.075(Ψmax=8.428), (d)λ=0.075(Ψmax=9.0637), (e)λ=0.2(Ψmax=9.599), and (f)λ=0.25(Ψmax=9.81)

Figure 10

Isothermal lines at Ra=250 for different values of λ: (a)λ=−0.25, (b)λ=−0.2, (c)λ=−0.075, (d)λ=0.075, (e)λ=0.2, and (f)λ=0.25

Figure 11

Magnified view of the upper right portion of the cavity (at Ra=250 and λ=−0.25) is showing velocity vectors, isothermal lines, and paths of ten particles released from a line

Figure 12

Mesh-contour plot of Nuav as a function of λ and AR at (a)Ra=50 and (b)Ra=500

Figure 13

Average entropy generation number as a function of Ra at different λ

Figure 14

Average Bejan number as a function of Ra at different λ

Figure 15

Contours of Nsav (dotted lines) and Beav (solid lines) at (a)Ra=50 and (b)Ra=500

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