Natural convection in porous media

NATURAL CONVECTION IN POROUS MEDIA-FILLED ENCLOSURES... 

Hong, J.-T., Tien, C.-L. and Kaviany. M., Non-Darcean Effects on Vertical Plate Natural Convection in Porous Media with High Porosity . Int. J. Heat Mass Transfer, Vol. 28, pp. 2149-2157. 1985. 

Natural Convection in Porous Media-Filled Enclosures 531... 

The first section presents some fundamental ideas that are frequently referred to in the remainder of the chapter. The next three sections deal with the major topics in natural convection. The first of these addresses problems of heat exchange between a body and an extensive quiescent ambient fluid, such as that depicted in Fig. 4.1a. Open cavity problems, such as natural convection in fin arrays or through cooling slots (Fig. 4.1fe), are considered next. The last major section deals with natural convection in enclosures, such as in the annulus between cylinders (Fig. 4.1c). The remaining sections present results for special topics including transient convection, natural convection with internal heat generation, mixed convection, and natural convection in porous media. 

Prasad, V, Kulacki, FA., 1985. Natural convection in porous media bounded by short concentric vertical... 

Heat transfer by natural convection across porous media-filled enclosures occurs in a number of oractical situations and will be considered in this sectif T 6] to f511... 

In the formulation of thermal convection in porous media at steady state, it was demonstrated that the horizontal gradient of temperature drives the thermal convection. In fact, the driving force for both thermal convection (that is, the convection due to thermal gradient) and natural convection (that is, the convection due to both thermal gradient and composition gradient) is governed by (dp/dx) at steady state. The expression for (dp/9x) is given by... 

Natural convective flows in porous media occur in a number of important practical situations, e.g., in air-saturated fibrous insulation material surrounding a heated body and about pipes buried in water-saturated soils. To illustrate how such flows can be analyzed, e.g., see [20] to [22], attention will be given in this section to flow over the outer surface of a body in a porous medium, the flow being caused purely by the buoyancy forces resulting from the temperature differences in the flow. The simplest such situation is two-dimensional flow over an isothermal vertical flat surface imbedded in a porous medium, this situation being shown schematically in Fig. 10.25. 

Natural convective boundary layer-type solutions have beer obtained for a number of other geometrical configurations. A number of studies of mixed convective flows in porous media are also available, e.g., [23] to [35]. 

Flow through a solid matrix which is saturated with a fluid and through which the fluid is flowing occurs in many practical situations. In many such cases, temperature differences exist and heat transfer, therefore, occurs. The extension of the methods of analyzing convective heat transfer rates that were discussed in the earlier chapters of this book to deal with heat transfer in porous media flows have been discussed in this chapter. Both forced and natural convective flows have been discussed. 

Chan, B.K.C., Ivey, C.M., and Barry, J.M., Natural Convection in Enclosed Porous Media with Rectangular Boundaries . J. Heat Transfer. Vol. 92. pp. 21-27. 1970. 

Oosthuizen, P.H., Natural Convection in an Inclined Suuure F.nclosure Partly Filled with a Porous Medium and with a Partially Heated Will". Heat Transfer in Porous Media and Two-Phase Flow. ASME HTD-Vol. 302. Energy- Sources Technology Conference and Exhibition. Houston. TX. 1995, pp. 29-42. 

The book provides a comprehensive coverage of the subject giving a full discussion of forced, natural, and mixed convection including some discussion of turbulent natural and mixed convection. A comprehensive discussion of convective heat transfer in porous media flows and of condensation heat transfer is also provided. The book contains a large number of worked examples that illustrate the use of the derived results. All chapters in the book also contain an extensive set of problems. 

The final topic of this chapter is natural convection and diffusion in porous media with the objective of studying composition variation in hydrocarbon reservoirs. The understanding of irreversible phenomena facilitates such a study the use of the Gibbs sedimentation equation, —Migdz, which has been used by some authors in the literature, is not justified because of entropy production. 

Microfiltration and ultrafiltration are the two main filtration techniques for which ceramic membranes have been widely used to date. As described in Section 6.2.1.2, MF and UF ceramic membranes exhibit macro- and mesoporous structure, respectively, which result from packing and sintering of ceramic particles. Liquid flow in such porous media is convective in nature and the simplest description of permeation flux, J, is given by the Darcy s equation [20] ... 

The bio-heat transfer equation with both of these assumptions has been solved for various tissue geometries and initial and boundary conditions (Shitzer and Eberhart, 1985). Because of scalar treatment of the convective heat transport by blood, the use of the bio-heat transfer equation has been questioned repeatedly (Charny, 1992). Considering tissue as porous media, Wulff (1974, 1980) introduced the blood velocity vector ub, in the bio-heat transfer equation. Unfortunately, the complex nature of the system defies any attempt to specify the circulation vector at the microscopic level. As non-invasive technologies (e.g., MRI) provide improved spatial resolution, it may be possible to incorporate such data numerically (Dutton et al., 1992). 

The combined use of different natural fluorescence techniques, such as steady-state fluorometry, fluorescence anisotropy and time-decay fluorescence, has been revealed to be quite powerfiil. The use of these techniques in an integrated mode for the monitoring of membrane-protein interactions is only in its infancy. These techniques offer not only the possibility to study the interaction of proteins with membranes, under convective and diffusive conditions, but also they may be easily extended to studies involving proteins and other porous materials such as chromatography media. The areas of application of these techniques will range from polypeptide and protein fractionation to the monitoring of hemodialysis systems. 

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