Research Papers: Heat Transfer Enhancement

Efficiencies for Partially Wetted Spine Fins: Uniform Cross Section, Conical, Concave Parabolic, and Convex Parabolic Spines

[+] Author and Article Information
Worachest Pirompugd

Department of Mechanical Engineering,
Faculty of Engineering,
Burapha University, Saensook,
Muang, Chonburi 20131, Thailand

Somchai Wongwises

Fluid Mechanics, Thermal Engineering and
Multiphase Flow Research Lab. (FUTURE),
Department of Mechanical Engineering,
Faculty of Engineering,
King Mongkut's University of
Technology Thonburi,
Bangmod, Bangkok 10140, Thailand
e-mail: somchai.won@kmutt.ac.th

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received September 21, 2012; final manuscript received March 11, 2013; published online July 18, 2013. Assoc. Editor: Giulio Lorenzini.

J. Heat Transfer 135(8), 081903 (Jul 18, 2013) (11 pages) Paper No: HT-12-1514; doi: 10.1115/1.4024017 History: Received September 21, 2012; Revised March 11, 2013

In this study, efficiencies for partially wetted fins for the uniform cross section spine, conical spine, concave parabolic spine, and convex parabolic spine are presented using an analytical method. Depending on the set of boundary conditions, there are two methods for deriving the efficiencies of partially wet fins for each spine. The eight equations for fin efficiencies were investigated. Fin efficiency is a function of the length of the dry portion. Thus, the equations for calculating the length of the dry portion are also presented. The findings indicate that a larger cross-sectional fin results in a higher conduction heat transfer rate. Contrarily, the fin efficiency is lower. This is different from the longitudinal fin, for which the trend lines of heat transfer rate and fin efficiency are the same. This converse relationship is due to the effect of the ratio of the cross-sectional area to the surface area. Moreover, partially wet fin efficiencies decrease with increased relative humidity. For convenience, the approximate equation for efficiencies for partially wet fins, which is derived from the equations for fully wet and fully dry fin efficiencies, is also presented.

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Fig. 1

Four spines in partially wet surface conditions

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Fig. 3

Temperature distribution for four spines

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Fig. 4

Heat transfer through four spines

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Fig. 5

Constant section spine efficiency plotted against relative humidity

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Fig. 6

Conical spine efficiency plotted against relative humidity

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Fig. 7

Concave parabolic spine efficiency plotted against relative humidity

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Fig. 8

Convex parabolic spine efficiency plotted against relative humidity

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Fig. 9

Comparison of approximate η and η at many MTb

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Fig. 2

Fin efficiency plotted against mTb

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Fig. 10

Heat transfer along the conical spine



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