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Journal of Porous Media
IF: 1.49 5-Year IF: 1.159 SJR: 0.43 SNIP: 0.671 CiteScore™: 1.58

ISSN Print: 1091-028X
ISSN Online: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v18.i12.80
pages 1251-1264

ANALYSIS OF THE INFLUENCE OF THERMAL EXPANSION ON A STAGNATION-POINT FLOW ESTABLISHED IN AN INERT POROUS MEDIUM

M. A. Endo Kokubun
lnstituto Nacional de Matematica Pura e Aplicada, Estrada Dona Castorina, 110, Rio de Janeiro, Rio de Janeiro 22460-320, Brazil
Fernando F. Fachini
Grupo de Mecanica de Fluidos Reativos, Laboratorio de Combustao e Propulsao, Instituto Nacional de Pesquisas Espaciais, Cachoeira Paulista, Sao Paulo 12630-000, Brazil

ABSTRACT

In the present work we analyze the influence of gas thermal expansion in the properties of a stagnation-point flow established in an inert porous medium. With the use of a semi-heuristic, non-Darcean formulation for the flow, we compare the obtained results with the results of the incompressible (constant-density) model. When thermal expansion is considered, the Darcy resistance term is proportional to the inverse of the Darcy number (dimensionless permeability), to the square of the local gas temperature and to the local mass flux. It is shown that if the Darcy number is low enough, an increase on the wall temperatures can lead to a decrease on the wall shear, a result opposed to what is observed for non-confined problems and that is not captured by incompressible models. The pressure recovery from the wall to the outside of the boundary layer is greatly affected by the Darcy number and by the thermal expansion imposed by the hot wall. For instance, if the Darcy number (wall temperature) is low (high) enough, the maximum pressure is achieved above the stagnation point. The effects of porosity, wall temperature, solid-to-gas thermal conductivities ratio, and interphase heat exchange coefficient on the wall properties are also analyzed. The results presented here are of relevance for the design of electronic devices porous coolers that have a maximum operating temperature, above which its component may be damaged.


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