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Research Papers: Natural and Mixed Convection

# Natural Convection Heat Transfer in a Partially Open Square Cavity With a Thin Fin Attached to the Hot Wall

[+] Author and Article Information
Abdullatif Ben-Nakhi1

Mechanical Power & Refrigeration Department, College of Technological Studies, PAAET, P.O. Box 3665, Salmiya 22037, State of Kuwaitabdnakhi@yahoo.com

M. M. Eftekhari, D. I. Loveday

Department of Civil and Building Engineering, Loughborough University, Loughborough, Leicestershire LE11 3TU, UK

1

Corresponding author.

J. Heat Transfer 130(5), 052502 (Apr 10, 2008) (9 pages) doi:10.1115/1.2885166 History: Received November 19, 2006; Revised August 25, 2007; Published April 10, 2008

## Abstract

A computational study of steady, laminar, natural convective fluid flow in a partially open square enclosure with a highly conductive thin fin of arbitrary length attached to the hot wall at various levels is considered. The horizontal walls and the partially open vertical wall are adiabatic while the vertical wall facing the partial opening is isothermally hot. The current work investigates the flow modification due to the (a) attachment of a highly conductive thin fin of length equal to 20%, 35%, or 50% of the enclosure width, attached to the hot wall at different heights, and (b) variation of the size and height of the aperture located on the vertical wall facing the hot wall. Furthermore, the study examines the impact of Rayleigh number $(104⩽Ra⩽107)$ and inclination of the enclosure. The problem is put into dimensionless formulation and solved numerically by means of the finite-volume method. The results show that the presence of the fin has counteracting effects on flow and temperature fields. These effects are dependent, in a complex way, on the fin level and length, aperture altitude and size, cavity inclination angle, and Rayleigh number. In general, Nusselt number is directly related to aperture altitude and size. However, after reaching a peak Nusselt number, Nusselt number may decrease slightly if the aperture’s size increases further. The impact of aperture altitude diminishes for large aperture sizes because the geometrical differences decrease. Furthermore, a longer fin causes higher rate of heat transfer to the fluid, although the equivalent finless cavity may have higher heat transfer rate. In general, the volumetric flow rate and the rate of heat loss from the hot surfaces are interrelated and are increasing functions of Rayleigh number. The relationship between Nusselt number and the inclination angle is nonlinear.

###### FIGURES IN THIS ARTICLE
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Copyright © 2008 by American Society of Mechanical Engineers
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## Figures

Figure 1

Schematic diagram and coordinate system for a partially open square enclosure with thin fin

Figure 2

Comparison of stream functions and isotherms with those of Bilgen and Oztop (11)

Figure 6

Effects of C on the contour maps of the streamlines and isotherms for B=0.5, D=0.125, H=0.25, ε=90deg, and Ra=105

Figure 7

Effects of C and D on the local Nusselt number at the hot wall and fin for B=0.5, H=0.25, ε=90deg, and Ra=105

Figure 8

Effects of H on the contour maps of the streamlines and isotherms for high aperture, B=0.5, C=0.35, ε=90deg, and Ra=105

Figure 9

Nu¯ as a function of C, D, and H for B=0.5, ε=90deg, and Ra=105

Figure 3

Comparison of results from extended and limited domains for B=0.5, C=0.5, H=1.0, ε=90deg, Pr=0.7, and Ra=105

Figure 10

Nut as a function of C, D, and H for B=0.5, ε=90deg, and Ra=105

Figure 11

Nut as a function of B, C, and H for D=0.5, ε=90deg, and Ra=105

Figure 4

Effects of C on the contour maps of the streamlines and isotherms for B=0.5, D=0.875, H=0.25, ε=90deg, and Ra=105

Figure 12

Effects of Ra on Nu¯ and V̇ for B=0.5, C=0.35, D=0.5, H=0.5, and ε=90deg

Figure 13

Effects of ε on Nu¯ and V̇ for B=0.5, C=0.35, D=0.5, H=0.5, and Ra=105

Figure 5

Effects of C on the contour maps of the streamlines and isotherms for B=0.5, D=0.5, H=0.25, ε=90deg, and Ra=105

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