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Fluid Mechanics

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Principles of Heat Transfer in Porous Media

Part of the book series: Mechanical Engineering Series ((MES))

Abstract

In this chapter we examine the isothermal, single-phase flow through porous media by starting from the Darcy law. We then examine the permeability tensor and its relation with the matrix structure. The deviation from the Darcy law observed at high velocities and the pore-level fluid dynamics are then examined. Attempts at arriving at the Darcy law (the macroscopic momentum equation) from the point description of the flow field (Navier-Stokes equation) by the local volume-averaging and homogenization techniques are reviewed. Then, a semiempirical momentum equation, which includes the bulk and boundary viscous effects, the flow development in porous media, and the high-velocity effects, is given. The significance of these terms is assessed by the order-of-magnitude analyses and some estimations. When the porous media arc bounded by the fluid occupying them, the hydrodynamic boundary conditions on these interfaces must be specified. The available slip velocity model and the Brinkman no-slip (uniform and variable effective viscosity) model for this interface are examined. The dependence of the slip coefficient (and the interfacial effective viscosity) on the bulk and surface structures of the matrix are studied. The velocity nonuniformities observed near the bounding impermeable surfaces and the various theoretical treatments of them are investigated. The chapter ends with an examination of the analogy between porous media- and magneto- hydrodynamics.

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  1. Department of Mechanical Engineering and Applied Mechanics, University of Michigan, 48109-2125, Ann Arbor, MI, USA

    M. Kaviany

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Kaviany, M. (1995). Fluid Mechanics. In: Principles of Heat Transfer in Porous Media. Mechanical Engineering Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4254-3_2

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  • DOI: https://doi.org/10.1007/978-1-4612-4254-3_2

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