Heat transfer in porous media

Effectively, Eqs. (86) and (87) describe two interpenetrating continua which are thermally coupled. The value of the heat transfer coefficient a depends on the specific shape of the channels considered suitable correlations have been determined for circular or for rectangular channels [100]. In general, the temperature fields obtained from Eqs. (86) and (87) for the solid and the fluid phases are different, in contrast to the assumptions made in most other models for heat transfer in porous media [117]. Kim et al. [118] have used a model similar to that described here to compute the temperature distribution in a micro channel heat sink. They considered various values of the channel width (expressed in dimensionless form as the Darcy number) and various ratios of the solid and fluid thermal conductivity and determined the regimes where major deviations of the fluid temperature from the solid temperature are found. 

Kaviany, M., Principles of Heat Transfer in Porous Media, Springer-Verlag,... 

Kaviany, M. Principles of Heat Transfer In Porous Media-, Springer-Verlag New York, 1991 p 598. 

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. 

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. 

Vafai. K. and Tien. C.-L.. Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media , Int. J. Heat Mass Transfer, Vol. 24, pp. 195-203, 1981. 

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. 

Udell, K.S. Heat transfer in porous media considering phase change and capillarity... the heat pipe effect. J. Heat Mass Transfer 1985, 28 (2), 485-495. 

Udell K.S. (1983) Heat transfer in porous media heat from above with evaporation, condensation and capillary effects, J. Heat Transfer, vol. 105, pp.485-492. 

Kaviany, Massoud Department of Mechanics and Applied Mechanics Engineering, University of Michigan (chap. 9, Heat Transfer in Porous Media), e-mail kaviany umich.edu... 

For radiation heat transfer in porous media, the same unit-cell approach is used and the particles in each cell are treated as scatterers. The scattering also becomes dependent when the porosity is not close to unity. The radiation properties are related to the optical properties and the porosity. 

As we consider simultaneous fluid flow and heat transfer in porous media, the role of the macroscopic (Darcean) and microscopic (pore-level) velocity fields on the temperature field needs to be examined. Experiments have shown that the mere inclusion of u0 V(T) in the energy equation does not accurately account for all the hydrodynamic effects. The pore-level hydrodynamics also influence the temperature field. Inclusion of the effect of the pore-level velocity nonuniformity on the temperature distribution (called the dispersion effect and generally included as a diffusion transport) is the main focus in this section. 

Summary. In conclusion, some suggestions are made on how to model the problem of radiative heat transfer in porous media. First, we must choose between a direct simulation and a continuum treatment. Wherever possible, continuum treatment should be used because of the lower cost of computation. However, the volume-averaged radiative properties may not be available in which case continuum treatment cannot be used. Except for the Monte Carlo techniques for large particles, direct simulation techniques have not been developed to solve but the simplest of problems. However, direct simulation techniques should be used in case the number of particles is too small to justify the use of a continuum treatment and as a tool to verify dependent scattering models. 

Since in two-phase flow and heat transfer in porous media for any direction, the bulk effective thermal conductivity is generally much smaller than the bulk thermal dispersion, the available studies on Ke are limited. In the following, we briefly discuss the anisotropy of K, and then review the available treatments. 

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