Download e-book for kindle: Handbook of Porous Media by Kambiz Vafai

By Kambiz Vafai

ISBN-10: 0824788869

ISBN-13: 9780824788865

ISBN-10: 0842788867

ISBN-13: 9780842788861

"Presents crucial and up to date examine on the topic of warmth move in porous media, concentrating on useful functions of the newest reports to engineering items and techniques. contains theoretical types of fluid move, capillary results, software of fractal and percolation characterizing porous fabrics, multiphase movement and warmth move, turbulent circulate and warmth move, more advantageous dimension and stream visualization thoughts, and more suitable layout correlations."

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Example text

49) to determine the spatial average temperature, provided that the velocity is known and the thermal sources can be determined. Traditionally, the thermal energy transport equation is represented in terms of the super®cial velocity according to hiCp @hTi ‡ …cp † hv i Á rhTi ˆ r Á …Kà Á rhTi† ‡ av hi  ‡ " hÈ i @t …82† and this means that a closed form of Eq. (39) must be developed in order to determine hv i. The analysis is given elsewhere (Whitaker, 1996), and here we will only list the result known as the Forchheimer equation Q P hv i ˆ À U K T À F Á hv i ÁT rhp i À  g À … =" †r2 hv iU R |‚‚‚‚‚‚‚‚‚‚{z‚‚‚‚‚‚‚‚‚‚}S |‚‚‚‚{z‚‚‚‚}  Brinkman correction …83† Forchheimer correction in which K represents the Darcy's law permeability tensor and F represents the Forchheimer correction tensor.

If one recognizes the dif®culty associated with measuring longitudinal thermal dispersion coef®cients, one concludes that the agreement between theory and experiment is quite reasonable. In addition, the general trends for the two different systems are predicted with reasonable accuracy in the absence of any adjustable parameters. V. TWO-EQUATION MODEL FOR HEAT TRANSFER When the condition of local thermal equilibrium is not valid, we must return to Eqs. (37) and (38) and develop separate equations for hT i and hT i .

The simplicity of the one-equation model and the associated closure problem certainly motivates the use of this form of the volume-averaged thermal energy equation; however, the one-equation model is valid only when the constraints associated with local thermal equilibrium are satis®ed. C. Comparison with Experiment Because of the complexity of Eqs. (141) and (150), the comparison between theory and experiment is probably best done in terms of theoretical and experimental temperature ®elds as opposed to attempting to extract experimental values of the various coef®cients.

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Handbook of Porous Media by Kambiz Vafai


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