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Research Papers: Natural and Mixed Convection

# The Effect of the Top Wall Temperature on the Laminar Natural Convection in Rectangular Cavities With Different Aspect Ratios

[+] Author and Article Information
Wenjiang Wu

Department of Mechanical Engineering, McMaster University, 1280 Main Street West, Hamilton, ON, L8S 4L7, Canadawuw6@mcmaster.ca

Chan Y. Ching

Department of Mechanical Engineering, McMaster University, 1280 Main Street West, Hamilton, ON, L8S 4L7, Canadachingcy@mcmaster.ca

J. Heat Transfer 131(5), 052501 (Mar 16, 2009) (11 pages) doi:10.1115/1.2993138 History: Received June 27, 2007; Revised July 29, 2008; Published March 16, 2009

## Abstract

The effect of the top wall temperature on the laminar natural convection in air-filled rectangular cavities driven by a temperature difference across the vertical walls was investigated for three different aspect ratios of 0.5, 1.0, and 2.0. The temperature distributions along the heated vertical wall were measured, and the flow patterns in the cavities were visualized. The experiments were performed for a global Grashof number of approximately $1.8×108$ and nondimensional top wall temperatures from 0.52 (insulated) to 1.42. As the top wall was heated, the flow separated from the top wall with an undulating flow region in the corner of the cavity, which resulted in a nonuniformity in the temperature profiles in this region. The location and extent of the undulation in the flow are primarily determined by the top wall temperature and nearly independent of the aspect ratio of the cavity. The local Nusselt number was correlated with the local Rayleigh number for all three cavities in the form of $Nu=C⋅Ran$, but the values of the constants $C$ and $n$ changed with the aspect ratio.

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## Figures

Figure 2

Nondimensional temperature distributions on the insulated top wall with aspect ratio of (△) 0.5, (◯) 1.0, and (◻) 2.0

Figure 5

Nondimensional temperature profiles in cavities with aspect ratios of (a) 0.5, (b) 1.0, and (c) 2.0 for nondimensional top wall temperatures of approximately 1.42. Here, the open and filled symbols were used to distinguish the temperature distributions at the different heights.

Figure 6

Nondimensional temperature profiles in cavities (left) and flow patterns in the upper corner region (right) for cases with aspect ratios of (a) 0.5, (b) 1.0, and (c) 2.0 for nondimensional top wall temperatures of approximately 1.14. Here, open and filled symbols were used to distinguish the temperature distributions at the different heights.

Figure 7

Nondimensional temperature profiles in cavities (left) and flow patterns in the upper corner region (right) for cases with aspect ratios of (a) 0.5, (b) 1.0, and (c) 2.0 for nondimensional top wall temperatures of approximately 1. Here, open and filled symbols were used to distinguish the temperature distributions at the different heights.

Figure 8

Nondimensional temperature profiles in cavities (left) and flow patterns in the upper corner region (right) for cases with aspect ratios of (a) 0.5, (b) 1.0, and (c) 2.0 for nondimensional top wall temperatures of approximately 0.83. Here, open and filled symbols were used to distinguish the temperature distributions at the different heights.

Figure 1

Schematic of the enclosure with an adjustable aspect ratio

Figure 3

Best linear fit used to determine the slope of the temperature profile at the nondimensional height y/H=0.6 of the square cavity with the top wall temperature of 109°C

Figure 4

Flow patterns in the upper left region of the rectangular cavities with the aspect ratios of (a) 0.5, (b) 1.0, and (c) 2.0 for nondimensional top wall temperatures of approximately 1.42

Figure 9

Nondimensional temperature profiles in cavities (left) and flow patterns in the upper corner region (right) for cases with aspect ratios of (a) 0.5, (b) 1.0, and (c) 2.0 for nondimensional top wall temperatures of approximately 0.52 (insulated). Here, open and filled symbols were used to distinguish the temperature distributions at the different heights.

Figure 10

Comparison of the nondimensional temperature outside of the boundary layer for cases with aspect ratios of (a) 0.5, (b) 1.0, and (c) 2.0. Here the nondimensional bop wall temperatures were (△) 0.52 (insulated), (◯) 0.83, (◇) 1, (◻) 1.14, and (×) 1.42.

Figure 11

Change in the vertical gradient of the temperature outside the boundary layer on the heated vertical wall with the change in the top wall temperature for cases with aspect ratios of (△) 0.5, (◯) 1.0, and (◻) 2.0

Figure 12

Comparison of the local heat flux along the heated vertical wall of cavities with aspect ratios of (a) 0.5, (b) 1.0, and (c) 2.0. The symbols are the same as in Fig. 1.

Figure 13

Change in the local Nusselt number with the local Rayleigh number for cases with aspect ratios of (a) 0.5, (b) 1.0, and (c) 2.0. The symbols are the same as in Fig. 1. Here error bars with ±8% were added to the data in the cases with nondimensional top wall temperature of approximately 1.

Figure 14

Change in the local Nusselt number with the local Rayleigh number along the heated vertical wall from y/H=0.2 to 0.7 for cases with aspect ratios of 0.5 (small size symbols), 1.0 (midsize symbols), and 2.0 (large size symbols) under the nondimensional top wall temperatures of (+) 0.52 (insulated), (×) 0.83, (◯) 1, (∗) 1.14, and (△) 1.42

## Errata

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