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Validity of the local thermal equilibrium assumption in a natural convection from a vertical plate embedded in a porous medium. (English) Zbl 1159.76380
Summary: The validity of the local thermal equilibrium assumption in natural convection over a vertical flat plate embedded in a porous medium is investigated analytically. The study is based on the two-phase (Schumann) model, using the Darcy model (slip condition) to govern the flow. It is found that there are three dimensionless parameters controlling the local thermal equilibrium assumption: the Biot number (Bi), the modified Rayleigh number (Ra\(_m\)), and the Darcy number (Da). The effects of these parameters are investigated and a correlation equation is developed in order to determine the region where the local thermal equilibrium assumption is valid.

MSC:
76R10 Free convection
76S05 Flows in porous media; filtration; seepage
80A20 Heat and mass transfer, heat flow (MSC2010)
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