By Donald A. Nield, Adrian Bejan
This e-book offers a easy creation to convection in porous media, resembling fibrous insulation, geological strata, and catalytic reactors. The presentation is self-contained, requiring in simple terms 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 practising engineers as a overview and reference, but additionally to graduate scholars and others simply getting into the sphere.
Convection in Porous Media comprises approximately a 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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This publication offers a undemanding creation to convection in porous media, corresponding to fibrous insulation, geological strata, and catalytic reactors. The presentation is self-contained, requiring in basic terms 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 assessment and reference, but in addition to graduate scholars and others simply getting into the sphere.
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In other words, the internal regularity can have an important 30 2. Heat Transfer through a Porous Medium effect. The authors considered situations where the obstacles were separated from the boundary walls, and thus some of the difference is due to a channeling effect. 2. , the condition 1 is not met], then a term –␤T (∂ P/∂t + v·∇ P) needs to be ␤T (g␤/c P f )L added to the left-hand side of Eq. 3). Here ␤ is the coefﬁcient of volumetric thermal expansion, deﬁned by ␤=− 1 ∂ ∂T . 10) P Viscous dissipation is negligible in natural convection if (g␤/c P f )L 1, which is usually the case.
Nield (2004b) suggested that the Brinkman equation may break down in this limit. Nield (2000) noted that scale analysis, involving the comparison of the magnitude of the viscous dissipation term to the thermal diffusion term, shows that viscous dissipation is negligible if N 1, where N = U 2 L 2 /K c P km T = Br/Da, where the Brinkman number is deﬁned by Br = U 2 /c P km T = EcPr, where the Eckert number Ec is deﬁned by Ec = U 2 /c P T . For most situations the Darcy number K /L 2 is small, so viscous dissipation is important at even modest values of the Brinkman number.
1996) using volume averaging. Some wider aspects have been discussed by Shah and Yortsos (1995). Using homogenization theory, they show that the macroscopic power law has the same form as the power law for a single capillary, at low Reynolds numbers (a regime that is reached at low velocities only if n < 2). However, the power-law permeability may depend also on the orientation of the pressure gradient. The homogenization method, together with the theory of isotropic tensor function of tensor arguments, was used by Auriault et al.