By Hari G. Garg, Charles A. Hales
Advances in warmth move is designed to fill the knowledge hole among usually scheduled journals and collage point textbooks via offering in-depth evaluation articles over a broader scope than is allowable in both journals or texts.
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Extra info for Chemistry and Biology of Hyaluronan
Volume averaging theory 17 A. Laminar Flow with Constant Coefficients The transport equations for a ﬂuid phase with linear diffusive terms are *U G:0 (44) *x G *U *U 1 *p * *U G ;S G;U G:9 ; (45) H *x S *x *x *x *t H D H H H * * * * D;U D:D D ;S . (46) H *x D *x *x *t D H H H Here represents any scalar ﬁeld (for example, concentration C) that might be transported into either of the porous medium phases, and the last terms on the right-hand side of (45) and (46) are source terms. In the solid phase, the diffusion equation is * * * Q:D Q ;S .
1s 2( c ) CDD 2 N *t (131) The third term on the right-hand side of (124) plays a different role when the interface between two phases is only a mathematical surface without thickness neglecting the transport within the surface means there is no need to consider this medium separately. When this is the case, this term can be equal for the both phases, simplifying the closure problem. The problem becomes signiﬁcantly more complicated when transport within the interface must be accounted for.
As in numerous other studies of multiphase transport, the major difﬁculties of averaging the terms on the right-hand side were overcome by using assumed closure models for the stress components. As a result, the averaged turbulent momentum equation, for example, has conventional additional resistance terms such as the averaged momentum equation developed by Vafai and Tien  for laminar regime transport in porous medium. A major assumption is the linearity of the ﬂuctuation terms obtained, for example, by neglect of additional terms in the momentum equation.