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Research Papers

Natural Convective Heat Transfer From the Horizontal Isothermal Surface of Polygons of Octagonal and Hexagonal Shapes

[+] Author and Article Information
Ahmad Kalendar, Sayed Karar

Department of Mechanical Power and Refrigeration Technology,
College of Technological Studies-PAAET,
Shuwaikh 24758, Kuwait

Abdulrahim Kalendar

Department of Mechanical Power and Refrigeration Technology,
College of Technological Studies-PAAET,
Shuwaikh 24758, Kuwait
e-mail: ay.kalendar1@paaet.edu.kw

Yousuf Alhendal

Department of Mechanical Power and Refrigeration Technology,
College of Technological Studies-PAAET,
Shuwaikh 24758, Kuwait
e-mail: ya.alhendal@paaet.edu.kw

Adel Alenzi

Department of Chemical Engineering Technology,
College of Technological Studies-PAAET,
Shuwaikh 24758, Kuwait
e-mail: af.alenzi@paaet.edu.kw

Patrick Oosthuizen

Department of Mechanical and Materials Engineering,
Queen’s University,
Kingston, ON, K7L 3N6, Canada
e-mail: patrick.oosthuizen@queensu.ca

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Thermal Science and Engineering Applications. Manuscript received November 22, 2018; final manuscript received February 21, 2019; published online March 27, 2019. Assoc. Editor: Gerard F. Jones.

J. Thermal Sci. Eng. Appl 11(5), 051009 (Mar 27, 2019) (13 pages) Paper No: TSEA-18-1599; doi: 10.1115/1.4043006 History: Received November 22, 2018; Accepted February 22, 2019

Heat transfer often occurs effectively from horizontal elements of relatively complex shapes in natural convective cooling of electronic and electrical devices used in industrial applications. The effect of complex surface shapes on laminar natural convective heat transfer from horizontal isothermal polygons of hexagonal and octagonal flat surfaces facing upward and downward of different aspect ratios has been numerically investigated. The polygons’ surface is embedded in a large surrounding plane adiabatic surface, where the adiabatic surface is in the same plane as the surface of the heated element. For the Boussinesq approach used in this work, the density of the fluid varies with temperature, which causes the buoyancy force, while other fluid properties are assumed constants. The numerical solution of the full three-dimensional form of governing equations is obtained by using the finite volume method-based computational fluid dynamics (CFD) code, FLUENT14.5. The solution parameters include surface shape, dimensionless surface width, different characteristic lengths, the Rayleigh number, and the Prandtl number. These parameters are considered as follows: the Prandtl number is 0.7, the Rayleigh numbers are between 103 and 108, and for various surface shapes the width-to-height ratios are between 0 and 1. The effect of different characteristic lengths has been investigated in defining the Nusselt and Rayleigh numbers for such complex shapes. The effect of these parameters on the mean Nusselt number has been studied, and correlation equations for the mean heat transfer rate have been derived.

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Figures

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Fig. 1

Flow conditions modeled in the present study

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Fig. 2

Surface shapes and geometries modeled: (a) equilateral hexagon (L = w), (b) unequal hexagon (L > w > 0), (c) rhombus (w = 0), (d) equilateral octagon (L = w, h = d), (e) unequal octagon (L > w > 0, h = d), (f) rhombus (w = 0, h = d), (g) unequal octagon (L > w > 0, hd), (h) unequal octagon (w = 0, hd), and (i) square (h = L) [38]. (Reprinted with permission of John Wiley and Sons copyright 2016.)

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Fig. 3

Upward and downward facing element orientations

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Fig. 4

Numerical solution domain for the upward facing heated element

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Fig. 5

Numerical versus empirical mean Nusselt numbers with different Ra based on w = 1 for (a) the square upward facing surface and (b) the square downward facing surface

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Fig. 6

Numerical versus empirical mean Nusselt numbers with different Ra based on A for the upward facing octagon surface (h = d, different W)

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Fig. 7

Numerical versus empirical mean Nusselt numbers with different Ra based on m for the upward facing octagon surface (h = d, different W)

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Fig. 8

Numerical versus empirical mean Nusselt numbers with different Ra based on m for the upward facing hexagonal surface of h = d for different W

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Fig. 9

Numerical versus empirical mean Nusselt numbers with different Ra based on m for the upward facing octagon surface (hd, different W)

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Fig. 10

Numerical versus empirical mean Nusselt numbers with different Ra based on m for the downward facing octagon surface (h = d, different W)

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Fig. 11

Numerical versus empirical mean Nusselt numbers with different Ra based on m for the downward facing hexagonal surface of h = d for different W

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Fig. 12

Numerical versus empirical mean Nusselt numbers with different Ra based on m for the downward facing octagon surface (hd, different W)

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Fig. 13

Comparison between numerical mean Nusselt numbers and Rayleigh numbers based on h for different aspect ratios of (a) octagonal facing up surface, (b) hexagonal facing up surface, (c) octagonal facing down surface, and (d) hexagonal facing down surface

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Fig. 14

The distributions of the local Nusselt number over the upward facing surfaces of a hexagon (left), octagon (h = d) (middle), and octagon (hd) (right) at various W for Ra = 105

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Fig. 15

The distributions of the local Nusselt number over the downward facing surfaces of a hexagon (left), octagon (h = d) (middle), and octagon (hd) (right) at various W for Ra = 105

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Fig. 16

Comparison of the numerical Nuuemp with Ram based on the characteristic length m for isothermal upward facing with various W of all considered surface shapes

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Fig. 17

Comparison of the numerical Nudemp with Ram based on the characteristic length m for isothermal downward facing with various W of all considered surface shapes

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