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Research Papers: Porous Media

Forced Convection Heat Transfer From a Bank of Circular Cylinders Embedded in a Porous Medium

[+] Author and Article Information
Gazy F. Al-Sumaily

Fluids Laboratory for Aeronautical and Industrial Research (FLAIR),
Department of Mechanical
and Aerospace Engineering,
Monash University,
Victoria 3800, Australia
Department of Mechanics
and Equipments Engineering,
University of Technology,
Baghdad, Iraq
e-mail: gazy.alsumaily@monash.edu, gazy.alsumaily@uotechnology.edu.iq

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 15, 2013; final manuscript received September 16, 2013; published online February 12, 2014. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 136(4), 042602 (Feb 12, 2014) (11 pages) Paper No: HT-13-1202; doi: 10.1115/1.4025661 History: Received April 15, 2013; Revised September 16, 2013

The characteristics of fluid flow and forced convection heat transfer around a bank of four circular cylinders embedded in a metallic or non-metallic porous materials have been investigated numerically. Both a staggered and an in-line arrangement have been studied. The governing continuity, Darcy–Brinkman–Forchheimer momentum, and local thermal non-equilibrium energy equations are solved by the spectral-element method. Attention is focused on how the spacing parameter SP ∈ [1.5, 3.0] (the space between cylinder centers) affects the local and average heat transfer from the cylinders at three different solid-to-fluid thermal conductivity ratios kr = 1.725, 57.5, 248, and at different Reynolds numbers ReD ∈ [1, 250] in both arrangements. Perhaps not surprisingly, the results show that both the average Nusselt number, Nuf, and the local Nusselt number, Nu, are dependent strongly on ReD, SP, and the cylinder arrangement. However, it is found that the trend of the variations of Nuf with SP is not considerably altered by kr in both cylinders’ configurations. The results also show that the thermal performance of the staggered arrangement is higher than that for the in-line one, with less occupied space; therefore, it is practically and economically recommended that this arrangement to be used in manufacturing tubular heat exchangers for applications involving porous media.

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Figures

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Fig. 1

Schematic diagram for the models analyzed

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Fig. 2

Typical computational macro-mesh: (left) staggered cylinders at SP = 2.75; and (right) in-line cylinders at SP = 1.75

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Fig. 3

Comparison between two numerical models: the present model and the model used by Ref. [10]

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Fig. 4

Fluid (top) and solid (bottom) isotherms, around four heated staggered cylinders, at (a) ReD = 1.0 and (b) 250, for the range of spacing SP = 1.5–3.0, from left to right in step of 0.5. Red (blue) contours represent hot (cold) temperatures, with contour level between 0 and 1.

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Fig. 5

Fluid (top) and solid (bottom) isotherms, around four heated in-line cylinders, at (a) ReD = 1.0 and (b) 250, for the range of spacing SP = 1.5–3.0, from left to right in step of 0.5. Red (blue) contours represent hot (cold) temperatures, with contour level between 0 and 1.

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Fig. 6

The profiles of Nufφ over the perimeters of four staggered cylinders, for different spacing parameter, i.e., SP = 1.5 (black), SP = 2.0 (blue), SP = 2.5 (red), and SP = 3.0 (green), at (a) ReD = 1.0 and (b) 250

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Fig. 7

The profiles of Nufφ over the perimeters of four in-line cylinders, for different spacing parameter, i.e., SP = 1.5 (black), SP = 2.0 (blue), SP = 2.5 (red), and SP = 3.0 (green), at (a) ReD = 1.0 and (b) 250

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Fig. 8

The variation of Nuf from four staggered cylinders, () cylinder A, (○) cylinder B, (▽) cylinder C, and (×) cylinder D, against SP, at different ReD. Ellipses and arrows refer to the relevant scale used for each group of plots

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Fig. 9

The variation of Nuf from four in-line cylinders, () cylinder A, (○) cylinder B, (▽) cylinder C, and (×) cylinder D, against SP, at different ReD. Ellipses and arrows refer to the relevant scale used for each group of plots

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Fig. 10

The variation of Nuf with SP, for four staggered cylinders, (a) front cylinder A, (b) side cylinder B, (c) back cylinder C, and (d) side cylinder D, in different porous channels, at ReD = 250

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Fig. 11

The variation of Nuf with SP, for four in-line cylinders, (a) front cylinders A and B, and (b) back cylinders C and D, in different porous channels, at ReD = 250

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Fig. 12

The variation of the total (fluid and solid) Nusselt number Nut from all four staggered cylinders (solid lines with ), and all four in-line cylinders (dashed lines, ○), per their occupied area Ao, against the spacing parameter SP, at different ReD

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