By Donald A. Nield, Adrian Bejan
This booklet offers a simple advent to convection in porous media, comparable to fibrous insulation, geological strata, and catalytic reactors. The presentation is self-contained, requiring purely regimen classical arithmetic and the elemental components of fluid mechanics and warmth move. it's going to therefore be of use not just to researchers and training engineers as a evaluation and reference, but in addition to graduate scholars and others simply getting into the sector.
Convection in Porous Media comprises approximately one thousand new references and covers: convection in deforming porous media, "designed" porous media, the speculation of deformable media, modeling viscous dissipation in hyperporous media, and more.
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12) are based on the implicit assumption that the thermal resistances of the ﬂuid and solid phases are in series. 12a) where k f = ks = k H with k H given by Eq. 8). 12) have to be solved subject to certain applied thermal boundary conditions. If a boundary is at uniform temperature, then one has T f = Ts on the boundary. If uniform heat ﬂux is imposed on the boundary, then there is some ambiguity about the distribution of ﬂux between the two phases. v. scale has to be distributed between the ﬂuid and solid phases in the ratio of the surface fractions; for a homogeneous medium that means in the ratio of the volume fractions, that is in the ratio : (1 − ).
5. Extensions of Darcy’s Law 13 Either Eqs. , 1979). A correlation slightly different from that of Ergun was presented by Lee and Ogawa (1994). Papathanasiou et al. (2001) showed that for ﬁbrous material the Ergun equation overpredicts the observed friction factor when the usual Reynolds number (based on the particle diameter) is greater than unity, and they proposed an alternative correlation, based directly on the Forchheimer equation and a Reynolds number based on the square root of the permeability.
Nield (1983) applied this procedure to the porous-medium analog of the Rayleigh-B´enard problem. Alternatively, the Brinkman equation, together with a formula such as Eq. 26), can be employed to model the situation. 25) where v is the velocity inside the porous medium and vt is its tangential component, and where ∇t is the tangential component of the operator ∇. Haber and Mauri argue that Eq. 25) should be preferred to v · n = 0, since the former accords better with solutions obtained by solving some model problems using Brinkman’s equation.