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Journal of Porous Media
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ISSN Imprimir: 1091-028X
ISSN En Línea: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v7.i4.10
12 pages

Development of Boundary Layers in Transient Buoyant Convection about a Vertical Plate in a Porous Medium

K. H. Kim
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 373-1, Kusong-dong, Yusong-gu, Taejon 305-701, (South) Korea
Sung Jin Kim
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Daejeon 34141, Republic of Korea
Jae Min Hyun
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Taejon, South Korea

SINOPSIS

Transient natural convection over a vertical plate in a porous medium is considered. The Brinkman-extended Darcy flow model is adopted. The Rayleigh number is large to render a boundary layer-type flow pattern. An order-of-magnitude analysis is performed. Numerical solutions are secured over broad ranges of nondimensional parameters. The results indicate that, for high Darcy and Rayleigh numbers, the porous system shows a double boundary layer structure (δm > δT), similar to the pure fluid system. In the opposite limit of low Darcy and Rayleigh numbers, the Darcy term effect is notable in the thermal and momentum boundary layers, and the present results are in accord with the Darcy model. In the intermediate parameter region, ε3/2J1/2Pr < Ra1/2Da < εJ1/2σ1/2Pr and (ε/J)1/2 < Ra1/2Da < ε3/2J1/2Pr, the Darcy term effect is seen only in the outer momentum boundary layer for transient periods. At very small times (t < JKσ/εκe, Kvf), the Darcy term effect is very small in both the thermal and momentum boundary layers even for low Darcy numbers. The early-time boundary layer structure of the porous system is akin to that based on the pure-fluid model. In all of the parameter regions, with high heat capacity ratio σ, the ratio of δm to δT for small times is larger than that of the steady state.


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