Advances in Transport Phenomena in Porous Media by Yehuda Bachmat, Jacob Bear (auth.), Jacob Bear, M. Yavuz

By Yehuda Bachmat, Jacob Bear (auth.), Jacob Bear, M. Yavuz Corapcioglu (eds.)

This quantity includes the lectures awarded on the NATO complex learn INSTITUTE that happened at Newark, Delaware, U. S. A. , July 14-23, 1985. the target of this assembly was once to offer and speak about chosen issues linked to shipping phenomena in porous media. via their very nature, porous media and phenomena of shipping of in depth amounts that ensue in them, are very complicated. the cast matrix could be inflexible, or deformable (elastically, or following another constitutive relation), the void area could be occupied by means of a number of fluid levels. every one fluid section will be composed of multiple part, with a number of the elements in a position to interacting between themselves and/or with the cast matrix. The shipping method can be isothermal or non-isothermal, without or with part alterations. Porous medium domain names within which huge amounts, corresponding to mass of a fluid part, component to a fluid part, or warmth of the porous medium as a complete, are being transported happen within the perform in quite a few disciplines.

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7) By inserting this expression into Eq. 8) 26 . a Assum1ng that PC!. « be approximated by C!. PC!. S of Eq. dS C!. C!. v 3dS J C!. 9) In writing Eq. 9), we have made use of Eq. C!. 10) 6 .. OC!. S of Eq. 3) can be expressed by C!. p C!. g ax. 11) J By inserting Eq. 8), Eq. 9) and Eq. 11) into Eq. 3), we --C!. dTC!. •• 1J _ _ C!. aT ~ ax. 1 a-C!. PC!. (- ax. 1 -Ci + PC!. g az ax. S of Eq. e Ta , appearing in Eq. 13) in terms of the averaged a-a fluid velocIty. 14) J Other types of fluids may be considered by the same methodology.

16) by Ai3 and subtracting the result 42 from Eq. 14), yields -a -S a(6 a (Ga-G S» ax. 17) where Eq. 13) and the relationship 6 a +6 S = 1 were employed. In the particular case AS=O, Eq. 17) reduces to Eq. 11), corresponding to Case A. The same holds when AafAS' but G~ = G~ throughout the entire porous medium domain. 6. APPENDIX B: THE COEFFICIENT I~ The coefficient Ia* ' defined in Eq. 9 ) represents the . stat~c moment of oriented areal elements of Saa , with respect to planes passing through ~o' per unit volume of the a phase within (U o )' * ·, To obtain an estimate of the magnitude of the components Tai consider a spherical REV oL radiusR.

Under such conditions, I~ has still the meaning of a tortuosity of the fluid phase. -f Let us consider the special cases T f reduces to -s Ts . Then Eq. 6 ) which is similar to Eq. ~. This result is obvious since we have no heat exchange (on the average) between the two phases. Hence, Eq. 7 ) where ~ = nA; + (l-n)~= is the thermal conductivity of the saturated porous medium as a whole. 5. APPENDIX A The objective of this Appendix is to develop, following Bachmat and Bear (1) a modified form of the commonly used averaging rule for a spatial derivative ----0.

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