Convection in Porous Media by Donald A. Nield, Adrian Bejan

By Donald A. Nield, Adrian Bejan

This ebook offers a straight forward creation to convection in porous media, similar to fibrous insulation, geological strata, and catalytic reactors. The presentation is self-contained, requiring merely regimen classical arithmetic and the elemental parts of fluid mechanics and warmth move. it is going to therefore be of use not just to researchers and training engineers as a evaluation and reference, but additionally to graduate scholars and others simply getting into the sector.

Convection in Porous Media contains approximately one thousand new references and covers: convection in deforming porous media, "designed" porous media, the idea of deformable media, modeling viscous dissipation in hyperporous media, and more.

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Energy Equation: Extensions to More Complex Situations 29 due to porosity variation near the walls. 7. Some of the discrepancy may be due to the difficulty of measuring a truly stagnant thermal conductivity in this case (Nield, 1991b). In the case when the fluid is a rarefied gas and the Knudsen number has a large value, temperature slip occurs in the fluid at the pore boundaries. In these circumstances one could expect that the fluid conductivity would tend to zero as the Knudsen number increases. Then in the case of external heating the heat would be conducted almost entirely through the solid matrix.

Heat Transfer through a Porous Medium volume of fluid, due to the convection. Note further that in writing Eq. 2) use has been made of the Dupuit-Forchheimer relationship v = ␸V. Setting Ts = T f = T and adding Eqs. 6) are, respectively, the overall heat capacity per unit volume, overall thermal conductivity, and overall heat production per unit volume of the medium. 2. 1. Overall Thermal Conductivity of a Porous Medium In general, the overall thermal conductivity of a porous medium depends in a complex fashion on the geometry of the medium.

The other two terms in Eq. 1) also contain the factor (1 – ␸) because this is the ratio of volume occupied by solid to the total volume of the element. In Eq. 2) there also appears a convective term, due to the seepage velocity. We recognize that V · ∇T f is the rate of change of temperature in the elemental volume due to the convection of fluid into it, so this, multiplied by (␳ c P ) f , must be the rate of change of thermal energy, per unit ␸(␳ c P ) f 28 2. Heat Transfer through a Porous Medium volume of fluid, due to the convection.

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