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Secondary Flow and Entropy Generation of Laminar Mixed Convection in the Entrance Region of a Horizontal Square Duct

[+] Author and Article Information
Y. Y. Huang

Institute of Refrigeration and Cryogenics,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: morceau@sjtu.edu.cn

L. J. Zhang

Institute of Refrigeration and Cryogenics,
Shanghai Jiao Tong University,
Shanghai 200240, China;
Shanghai Key Laboratory of Spacecraft Mechanism,
Aerospace System Engineering,
Shanghai 201108, China
e-mail: liangjunzh@126.com

G. Yang

Institute of Refrigeration and Cryogenics,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: y_g@sjtu.edu.cn

J. Y. Wu

Institute of Refrigeration and Cryogenics,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: jywu@sjtu.edu.cn

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 25, 2017; final manuscript received August 9, 2017; published online November 7, 2017. Assoc. Editor: Sara Rainieri.

J. Heat Transfer 140(3), 034503 (Nov 07, 2017) (7 pages) Paper No: HT-17-1300; doi: 10.1115/1.4038134 History: Received May 25, 2017; Revised August 09, 2017

The flow structure, heat transfer, and entropy generation characteristics in the entrance region of mixed convection under the effect of transverse buoyancy force are investigated numerically. Results are obtained for laminar flow of uniform inlet velocity and temperature through a square duct with uniform wall temperature. The buoyancy induced-secondary flow is observed in the entrance region where flow structure and heat transfer are significantly affected. The flow entrance region is extended by buoyancy, while the thermal entrance region is shortened. The developments of Nusselt number and local entropy generation are discussed in detail for Richardson numbers of 0 ≤ Ri ≤ 10, Reynolds number Re = 100 and Prandtl number Pr = 0.7. The total heat transfer rate and global entropy generation by friction increase with buoyancy, while global entropy generation by heat convection changes a little. The effect of Reynolds number on entropy generation is also discussed.

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Figures

Grahic Jump Location
Fig. 1

Schematic of the flow, horizontal duct and coordinate system

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Fig. 2

Secondary flow pattern at X = 0.1 of Ri = 10, Re = 100

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Fig. 3

Development of absolute value of streamwise vorticity for 0 ≤ Ri ≤ 10, Re = 100

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Fig. 4

Dimensionless axial velocity at middle plane of the duct (Y = 0.5) for 0 ≤ Ri ≤ 10, Re = 100

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Fig. 5

Isotherms at middle plane of the duct (Y = 0.5, 0 ≤ X ≤ 10) for 0 ≤ Ri ≤ 10, Re = 100

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Fig. 6

Development of dimensionless average bulk temperature for 0 ≤ Ri ≤ 10, Re = 100

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Fig. 7

Development of average bulk Nusselt number for 0 ≤ Ri ≤ 10, Re = 100

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Fig. 8

Comparison of average ambient Nusselt number on top, bottom, and side walls for forced convection and mixed convection (Ri = 10) with Re = 100

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Fig. 9

Development of dimensionless entropy generation distribution due to fluid friction at the cross section of X = 1, 2, 5 (from top to bottom) for Ri = 1, 5, 10 (from left to right), Re = 100

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Fig. 10

Development of cross-sectional entropy generation due to fluid friction for Richardson number of 0 ≤ Ri ≤ 10, Re = 100

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Fig. 11

Development of dimensionless entropy generation distribution due to heat transfer at the cross section of X = 0.5, 1, 2 (from top to bottom) for Ri = 1, 5, 10 (from left to right), Re = 100

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Fig. 12

Development of cross-sectional entropy generation due to heat transfer for 0 ≤ Ri ≤ 10, Re = 100

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Fig. 13

Bejan number and Global entropy generation due to fluid friction and heat transfer for 0 ≤ Ri ≤ 10, Re = 100

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Fig. 14

Global entropy generation due to fluid friction and heat transfer for 50 ≤ Re ≤ 1000, Ri = 10

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