Convective Heat and Mass Transfer in Porous Media by Arthur E. Bergles (auth.), Sadik Kakaç, Birol Kilkiş, Frank

By Arthur E. Bergles (auth.), Sadik Kakaç, Birol Kilkiş, Frank A. Kulacki, Faruk Arinç (eds.)

The quick development of literature on convective warmth and mass move via porous media has introduced either engineering and basic wisdom to a brand new kingdom of completeness and intensity. also, numerous new questions of primary advantage have arisen in different components which undergo direct relation to additional development of easy wisdom and purposes during this box. for instance, the expansion of primary warmth move info and correlations for engineering use for saturated media has now reached the purpose the place the relatives for warmth move coefficients and move parameters are identified good adequate for layout reasons. a number of circulation box regimes in typical convection were pointed out in numerous very important enclosure geometries. New questions have arisen at the nature of equations getting used in theoretical reports, i. e. , the Validity of Darcy assumption is being introduced into query; Wall results in low and high pace stream fields were chanced on to play a job in predicting shipping coefficients; The formula of shipping difficulties in fractured media are being investigated as either an extension of these in a homogeneous medium and for program in engineering platforms in geologic media and difficulties on saturated media are being addressed to figure out their right formula and answer. The lengthy status challenge of the way to effectively formulate and clear up difficulties of multi-phase warmth and mass move in heterogeneous media is necessary within the applied sciences of chemical reactor engineering and more advantageous oil recovery.

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Sample text

F) (66) Energy of a phase For the phase as a whole, the balance equation i. , lead. " =o. (68) (-,) By combining (61) with (51) and (54), we obtain an energy balance equation, written in term. "'f is the chemical potential of the ")'-component. v ..... 'ldw'l. '1 - 8p 8T v,,,,'1' 8u 8T ,,,), = 1. 'l) dw'l. ,. i J. " • " (71) -p vV·Y ,,( I T8s - 8w"l Tv ... 'l - dt (72) in which we have made use of the relationship 1 dv -; dt = V·Y, which follows from the mass balance equation. By inserting (72) in (69), we obtain DT pCvDt (73) 32 or, taking into account the mass balance equation O(P~VT) = -V.

This relationship should be compared with that expressing the relationship between the energy density of a phase and that of the components, given above. With the definition of partial specific values, new weighted velocities may be defined. , (a) an advective jluz, carried at the mass weighted velocity, and (b) a diffiuive jluz, relative to that velocity (36) Examples of interest are: jm jM j& diffusive mass flux of a phase, diffusive momentum. " 24 defined by = p(V - V);: 0, = pV (VM - V) ;: -0', = P(u+ lV2) (ve - V) ;:jH.

W / 8Z} Z, vZ, where (142) is a coefficient related only to macroscopic parameters that describe the geometrical configuration of the void space. It is called the permeability, or intrinsic permeability, of the porous medium (since we have assumed here that the fluid occupies the entire void space). This equation is usually referred to as the generalized Darcy law. s. 2 Advective Huxes in a multiphase How When two immiscible fluids occupy (disjoint) parts of the void space, because of surface tension phenomena, one of the fluids, called the wetting fluid (subscript w), tends to adhere to the solid wall of the void space, while the other, called the n{lnwetting fluid (subscript n); tends' to stay away from the solid wall.

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