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Research Papers: Natural and Mixed Convection

Numerical Investigation of Laminar Natural Convection in a Square Cavity With Wavy Wall and Horizontal Fin Attached to the Hot Wall

[+] Author and Article Information
Ahmed Kadari

Laboratory of Industrial Technologies,
Department of Mechanical Engineering,
University Ibn Khaldoun,
Tiaret 14000, Algeria
e-mail: Kaduniv14@hotmail.fr

Nord-Eddine Sad Chemloul

Laboratory of Industrial Technologies,
Department of Mechanical Engineering,
University Ibn Khaldoun,
Tiaret 14000, Algeria
e-mail: sad_2412@yahoo.fr

Said Mekroussi

Laboratory of Industrial Technologies,
Department of Mechanical Engineering,
University Ibn Khaldoun,
Tiaret 14000, Algeria
e-mail: Mekroussi_said@yahoo.fr

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 4, 2017; final manuscript received December 9, 2017; published online March 30, 2018. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 140(7), 072503 (Mar 30, 2018) (15 pages) Paper No: HT-17-1391; doi: 10.1115/1.4039081 History: Received July 04, 2017; Revised December 09, 2017

Laminar natural convection in differentially heated square cavity with right cold wavy wall and horizontal conducting fin attached to its left hot wall has been investigated numerically. The vertical walls are maintained at different isothermal temperatures, while the horizontal walls are insulated. The fluid that filled the cavity is air with Prandtl number of 0.71. The investigation has been performed for Rayleigh number in the range of 103–106, the thermal conductivity ratio was varied from 10 to 105, three fin lengths and positions have been examined (0.25, 0.5, and 0.75), and three numbers of undulation were tested (one, two, and three undulations). The wave amplitude and the fin thickness were kept constant at 0.05 and 0.04, respectively. The results obtained show that increasing the fin thermal conductivity or the Rayleigh number increases the average Nusselt number especially when the fin length increases. It was also found that the fin position enhances the heat transfer when the fin is placed opposite to the crest of the wavy wall. The trend of the local Nusselt number is wavy. The effect of undulations number appears when the fin length is greater than 0.5. The average Nusselt number enhanced when a conducting fin is added to the cavity with wavy wall and without fin by 51.23% and 56.85% for one and three undulations, respectively, when the Rayleigh number is 105 and the fin length is 0.75.

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Figures

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Fig. 1

Geometrical characteristics of the used cavity with boundary conditions: (a) one undulation, (b) two undulations, (c) three undulations, and (d) mesh for one undulation and fin with H = 0.5 and L = 0.5

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Fig. 2

Comparison of (a) streamlines and (b) isothermal lines with those given by Tasnim and Collins [22]

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Fig. 3

Streamlines at Ra=105 and Rk = 103 for one undulation

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Fig. 4

Isothermal lines at Ra=105 and Rk = 103 for one undulation

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Fig. 5

Streamlines at Ra=105 and Rk = 103 for two undulations

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Fig. 6

Isothermal lines at Ra=105 and Rk = 103 for two undulations

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Fig. 7

Streamlines at Ra=105 and Rk = 103 for three undulations

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Fig. 8

Isothermal lines at Ra=105 and Rk = 103 for three undulations

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Fig. 9

Temperature distribution along the fin for Ra=105 and H = 0.5

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Fig. 10

Local Nusselt number distribution for different fin length at Ra=105 and Rk = 103 for (a) one undulation, (b) two undulations, and (c) three undulations

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Fig. 11

Local Nusselt number distribution at Ra=105 and Rk = 103 for different numbers of undulations

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Fig. 12

Local Nusselt number distribution at Rk = 103 for (a) one undulation, (b) two undulations, and (c) three undulations

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Fig. 13

Local Nusselt number distribution at Ra=105 for (a) one undulation, (b) two undulations, and (c) three undulations

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Fig. 14

Average Nusselt number as a function of fin length at Ra=105 and Rk = 103 for (a) H = 0.25, (b) H = 0.5, and (c) H = 0.75

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Fig. 15

Variation of average Nusselt number as a function of (a1-3) thermal conductivity ratio and (b1-3) Rayleigh number

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