Convective Flows in Porous Media

Fluid flow in porous media deserves great attention because of its paramount importance both for engineering and for geophysical applications such as filtration of water, hydrocarbons and gases in the soil. Indeed, the practical interest in convective heat transfer in porous media has greatly increased in the last decades, due to the wide range of applications, such as thermal energy storage, geothermal energy utilisation, petroleum reservoirs, chemical catalytic convectors, storage of grain, pollutant dispersion in aquifers, buried electrical cables, food processing, ceramic radiant porous burners used in industrial plants as efficient heat transfer devices, etc. The fundamental nature and the growing volume of work in this area are widely documented in the books by Nield and Bejan (2006), Ingham and Pop (1998, 2002, 2005), Vafai (2005), Pop and Ingham (2001), Bejan et al. (2004), de Lemos (2006), Vadasz (2008) and Kaviany (1995). In this chapter, a review on the flow in porous media is presented. First, a description of the porous medium is provided, by introducing the most important features and quantities needed when dealing with this matter. Then, the governing equations, i.e. the local mass, momentum and energy balances, are presented, and their main features are discussed. With reference to free convection flows, the local balance equations are written either according to the streamfunction formulation or according to the pressure formulation. Moreover, the governing equations have been solved in the case of two-dimensional convection in a plane porous layer saturated by a fluid, by employing Darcy’s law, Forcheimer’s extension and Brinkman’s model. The vertical thermal boundary layer is discussed, with particular reference to the similarity solutions available in the literature. Finally, with reference to the local energy balance, the local thermal nonequilibrium (LTNE) is discussed, and the two-temperature models are presented. Moreover, an example of the study of the thermal entrance region, in forced convection, by employing an LTNE model is discussed.