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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [Fi r s [11 3 Lin e 0.3 4 —— No r m PgE [11 3 CHAPTER 15 Porous Media ADRIAN BEJAN Department of Mechanical Engineering and Materials Science Duke University Durham, North Carolina 15.1 Introduction 15.2 Basic principles 15.2.1 Mass conservation 15.2.2 Flow models 15.2.3 Energy conservation 15.3 Conduction 15.4 Forced convection 15.4.1 Plane wall with constant temperature 15.4.2 Sphere and cylinder 15.4.3 Concentrated heat sources 15.4.4 Channels ±lled with porous media 15.4.5 Compact heat exchangers as porous media 15.5 External natural convection 15.5.1 Vertical walls 15.5.2 Horizontal walls 15.5.3 Sphere and horizontal cylinder 15.5.4 Concentrated heat sources 15.6 Internal natural convection 15.6.1 Enclosures heated from the side 15.6.2 Cylindrical and spherical enclosures 15.6.3 Enclosures heated from below 15.6.4 Penetrative convection 15.7 Other con±gurations Nomenclature References 15.1 INTRODUCTION Heat and mass transfer through saturated porous media is an important development and an area of very rapid growth in contemporary heat transfer research. Although the mechanics of fluid flow through porous media has preoccupied engineers and physicists for more than a century, the study of heat transfer has reached the status 1131
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1132 POROUS MEDIA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [113 2 Lin e -2. 5 —— Lon g * PgE n [113 2 of a separate Feld of research during the last three decades (Nield and Bejan, 1999). It has also become an established topic in heat transfer education, where it became a part of the convection course in 1984 (Bejan, 1984, 1995). The reader is directed to a growing number of monographs that outline the fundamentals (Scheiddeger, 1957; Bear, 1972; Bejan, 1987; Kaviany, 1995; Ingham and Pop, 1998, 2002; Vafai, 2000; Pop and Ingham, 2001; Bejan et al., 2004). Porous media and transport are becoming increasingly important in heat exchanger analysis and design. It was pointed out in Bejan (1995) that the gradual miniatur- ization of heat transfer devices leads the flow toward lower Reynolds numbers and brings the designer into a domain where dimensions are considerably smaller and structures considerably more complex than those covered by the single-conFguration correlations developed historically for large-scale heat exchangers. The race toward small scales and large heat fluxes in the cooling of electronic devices is the strongest manifestation of this trend. It is fair to say that the reformulation of heat exchanger analysis and design as the basis of porous medium flow principles is the next area of growth in heat exchanger theory for small-scale applications. The objective of this chapter is to provide a concise and effective review of some of the most basic results on heat transfer through porous media. This coverage is an updated and condensed version of a review presented Frst in Bejan (1987). More detailed and tutorial alternatives were developed subsequently in Bejan (1995, 1999) and Nield and Bejan (1999), to which the interested reader is directed.
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This note was uploaded on 12/03/2010 for the course ECON 089907 taught by Professor Mikey during the Spring '10 term at Nashville State Community College.

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