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# Oscillation and Chaos in Combined Heat Transfer by Natural Convection, Conduction, and Surface Radiation in an Open Cavity

[+] Author and Article Information
Zhiyun Wang

Mo Yang1

Ling Li

School of Energy and Power Engineering,  University of Shanghai for Science and Technology, Shanghai 200093, China

Yuwen Zhang

Department of Mechanical and Aerospace Engineering,  University of Missouri, Columbia, MO 65211

1

Corresponding author.

J. Heat Transfer 134(9), 094501 (Jun 25, 2012) (6 pages) doi:10.1115/1.4006269 History: Received December 06, 2010; Revised February 20, 2012; Published June 25, 2012; Online June 25, 2012

## Abstract

Combined heat transfer by natural convection, conduction, and surface radiation in an open cavity is solved numerically by employing SIMPLE algorithm with QUICK scheme. The unsteady-state flow and heat transfer exhibited periodic oscillating or chaotic behaviors due to formation of the thermal plumes at the bottom wall. If the formation of thermal plumes is periodic, the oscillations of flow and heat transfer are also periodic. On the other hand, chaotic oscillations of flow and heat transfer can be observed when the formation of thermal plumes at the bottom surface is chaotic.

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## Figures

Figure 1

Physical model

Figure 2

Streamlines for Ra = 107 , ɛ = 0.2, kr  = 10 (1 ≤ τ≤ 80)

Figure 3

Streamlines for Ra = 107 , ɛ = 0.7, kr  = 100 (180 ≤ τ≤ 202)

Figure 4

Isotherms for Ra = 107 , ɛ = 0.7, kr  = 100 (180 ≤ τ ≤ 202)

Figure 5

History of the average convective Nusselt numbers for kr  = 102 , Ra = 5 × 106 : (a) ɛ = 0.2, (b) ɛ = 0.4, and (c) ɛ = 0.6

Figure 6

The time-averaged total Nusselt number (400 ≤ τ≤ 600) as a function of kr for ɛ = 0.4

Figure 7

Isotherms when Ra = 4 × 106 , ɛ = 0.4 at τ = 600

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