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RESEARCH PAPERS: Natural and Mixed Convection

# Turbulent Heat Transfer in an Enclosure With a Horizontal Permeable Plate in the Middle

[+] Author and Article Information
Edimilson J. Braga

Departamento de Energia—IEME, Instituto Tecnológico de Aeronáutica—ITA, 12228-900, São José dos Campos, SP, Brazil

Marcelo J. de Lemos1

Departamento de Energia—IEME, Instituto Tecnológico de Aeronáutica—ITA, 12228-900, São José dos Campos, SP, Brazildelemos@ita.br

1

Corresponding author.

J. Heat Transfer 128(11), 1122-1129 (Apr 05, 2006) (8 pages) doi:10.1115/1.2352779 History: Received April 15, 2005; Revised April 05, 2006

## Abstract

Turbulent natural convection in a vertical two-dimensional square cavity, isothermally heated from below and cooled at the upper surface, is numerically analyzed using the finite volume method. The enclosure has a thin horizontal porous obstruction, made of a highly porous material and extremely permeable, located at the cavity midheight. Governing equations are written in terms of primitive variables and are recast into a general form. For empty cavities, no discrepancies result for the Nusselt number when laminar and turbulent model solutions are compared for Rayleigh numbers up to $107$. Also, in general the porous obstruction decreases the heat transfer across the heated walls showing overall lower Nusselt numbers when compared with those without the porous obstruction. However, the presence of a porous plate in the cavity seems to force an earlier separation from laminar to turbulence model solutions due to higher generation rates of turbulent kinetic energy into the porous matrix.

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## Figures

Figure 1

Geometry under consideration

Figure 2

Isotherms for laminar solution for a square cavity heated from below and cooled from the ceiling for Ra=4×104

Figure 3

Streamlines of turbulent solution of a vertical square cavity with a porous obstruction for Ra=4×104, 106, and 107 with ϕ=0.95 and Dp=1mm

Figure 4

Isotherms of turbulent solution of a vertical square cavity with a porous obstruction for (a) Ra=4×104, (b) 106, and (c) 107 with ϕ=0.95 and Dp=1mm

Figure 5

Isolines of k for turbulent solution for a vertical square cavity with a porous obstruction for Ra=4×104, 106, and 107 with ϕ=0.95 and Dp=1mm

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