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Macroscopic equations of non-Newtonian fluid flow and heat transfer in a porous matrix. (English) Zbl 0932.76086

The macroscopic equations that describe the flow of non-Newtonian fluids in porous media are obtained from the corresponding microscopic equations with the method of volume averaging. The energy equation and the continuity equation are the same as those for Newtonian flows in porous media, but the momentum equation contains, in addition to the volume-averaged values, an integral involving the point value of pressure, velocity, and other low-order terms. The presence of this integral in the volume-averaged equation gives rise to an interfacial flux term which is represented in terms of an overall driving force for a flow over dilute arrays of spheres.

MSC:

76S05 Flows in porous media; filtration; seepage
76A05 Non-Newtonian fluids
80A20 Heat and mass transfer, heat flow (MSC2010)
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