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TECHNICAL PAPERS: Natural and Mixed Convection

# Aspect Ratio Effect on Natural Convection Flow in a Cavity Submitted to a Periodical Temperature Boundary

[+] Author and Article Information

Faculté des Sciences de Tunis, Département de Physique, University of El-Manar II, Tunis 2092, Tunisianadeṟbc@yahoo.fr

Brahim Ben Beya, Taieb Lili

Faculté des Sciences de Tunis, Département de Physique, University of El-Manar II, Tunis 2092, Tunisia

J. Heat Transfer 129(8), 1060-1068 (Sep 30, 2006) (9 pages) doi:10.1115/1.2728908 History: Received May 09, 2006; Revised September 30, 2006

## Abstract

The effect of aspect ratio on natural convection flow in a cavity submitted to periodic temperature boundary, is investigated numerically. The temperature of the heated wall is either maintained constant or varied sinusoidally with time while the temperature of the opposite vertical wall is maintained constant. The results are given for a range of varied parameters as Rayleigh number $(5×103⩽Ra⩽106)$, cavity aspect ratio $(1∕6⩽A⩽8)$, and period of the sinusoidally heated wall $(1⩽τ⩽1600)$. The amplitude of oscillation $(a=0.8)$ and the Prandtl number $(Pr=0.71)$ were kept constant. The results obtained in the steady state regime show that the heat transfer averaged over the cold wall is maximum when the aspect ratio is in the range $1⩽A⩽2$. In the case of a periodic temperature boundary, it is shown that the deviation between the mean heat transfer and the heat transfer of the constant heated case is larger for shallow cavities.

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## Figures

Figure 1

Schematic diagram of the physical model and coordinate system

Figure 2

Streamlines (left) and isotherms (right) for Ra=104, for aspect ratios A=8, A=6, A=4, and A=2

Figure 3

Streamlines and isotherms for Ra=104, for aspect ratios 1∕6⩽A⩽1

Figure 4

Evolution and amplitude of Nuc, ψmin, and ψmax related to aspect ratio A=8

Figure 5

Streamlines for Ra=104, A=1∕2, and τ=20 at ten equal increments

Figure 6

Isotherms for Ra=104, A=1∕2, and τ=20 at ten equal increments

Figure 7

Time-averaged values: Nuc¯, ψ¯max, and ∣ψ¯min∣ according to aspect ratio A for 20⩽τ⩽160 and Ra=104

Figure 8

Time-averaged Nusselt number according to period, τ, for aspect ratios A=1∕2 and A=2 related to Ra=104 and Ra=105

Figure 9

Maximum secondary positive cell sizes (solid lines) at τ=τr: (a) Ra=105 and A=1∕6; (b) Ra=106 and A=1∕6; and (c) Ra=105 and A=4

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