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Research Papers: Natural and Mixed Convection

Mixed Convective Heat Transfer Past a Heated Square Porous Cylinder in a Horizontal Channel With Varying Channel Height

[+] Author and Article Information
Horng-Wen Wu1

Department of Systems and Naval Mechatronic Engineering, National Cheng Kung University, Tainan, 701 Taiwan, R.O.C.z7708033@email.ncku.edu.tw

Ren-Hung Wang

Department of Systems and Naval Mechatronic Engineering, National Cheng Kung University, Tainan, 701 Taiwan, R.O.C.

1

Corresponding author.

J. Heat Transfer 133(2), 022503 (Nov 03, 2010) (10 pages) doi:10.1115/1.4002632 History: Received November 13, 2009; Revised September 23, 2010; Published November 03, 2010; Online November 03, 2010

The laminar mixed convection flow across the porous square cylinder with the heated cylinder bottom at the axis in the channel has been carried out numerically in this paper using a semi-implicit projection finite element method. The governing equations with the Brinkman–Forcheimer-extended Darcy model for the region of square porous cylinder were solved. The parameter studies including Grashof number, Darcy number, and channel-to-cylinder height ratio on heat transfer performance have been explored in detail. The results indicate that the heat transfer is augmented as the Darcy number and channel-to-cylinder height ratio increase. The buoyancy effect on the local Nusselt number is clearer for B/H=0.1 than for B/H=0.3 and B/H=0.5.

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Figures

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Figure 1

Schematic of the physical domain

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Figure 2

(a) Grid sensitivity and (b) time-step size sensitivity at Gr=62,500, Re=250, Da=10−4, and ε=0.8 with three different B/H on the local Nusselt number for the lower bottom surface

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Figure 3

Comparisons of Nu¯ on each heat source with those of Rachedi and Chikh (12)

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Figure 4

Temperature distributions for the surface of the square porous cylinder, the external fluid, and the internal fluid at Re=250, Da=10−2, B/H=0.5, Gr=0, and ε=0.8

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Figure 5

Time-mean Nusselt number profiles along bottom surfaces of the square porous cylinder for four Gr values at Da=10−2: (a) B/H=0.1, (b) B/H=0.3, and (c) B/H=0.5

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Figure 6

Streamline contours at CL=max and Da=10−2: (a) B/H=0.1 and Gr=0, (a-1) B/H=0.1 and Gr=625,000, (b) B/H=0.3 and Gr=0, (b-1) B/H=0.3 and Gr=625,000, (c) B/H=0.5 and Gr=0, and (c-1) B/H=0.5 and Gr=625,000

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Figure 7

Effects of B/H at the bottom of the square porous cylinder on heat transfer Gr=1,250,000, Da=10−4, and ε=0.8: (a) local Nusselt number and (b) temperature distribution

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Figure 8

Streamline contours at CL=max, Re=250, Gr=1,250,000, Da=10−4, and ε=0.8: (a) B/H=0.1, (b) B/H=0.3, and (c) B/H=0.5

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Figure 9

Sequence of streamlines for the square porous cylinder under Da=10−2 at Gr=1,250,000 and B/H=0.1 during 1 cycle: (a) t=241.205, (b) t=242.767, (c) t=244.329, (d) t=245.859, and (e) t=247.389 for Re=250

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Figure 10

Sequence of streamlines for the square porous cylinder under Da=10−5 at Gr=1,250,000 and B/H=0.1 during 1 cycle: (a) t=239.541, (b) t=241.21, (c) t=242.879, (d) t=244.421, and (e) t=245.962 for Re=250

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Figure 11

Time histories of lift coefficient CL for the square porous cylinder for Re=250 with different values of Gr at Da=10−4: (a) B/H=0.1, (b) B/H=0.3, and (c) B/H=0.5

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