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Thermal dispersion in a porous medium. (English) Zbl 0703.76079
Summary: The thermal dispersion conductivity tensor for convection in a porous medium is derived based on the method of volume averaging of the velocity and temperature deviations in the pores. The velocity and temperature deviations are obtained based on flow over a dilute array of spheres, incorporated with a scale analysis. A multiplying constant (i.e. the thermal dispersivity tensor) is introduced to account for the interaction of spheres. Separate considerations are given to the creeping flow at low Reynolds numbers, as well as boundary layer flow and wakes at high Reynolds numbers. It is found that the velocity and porosity dependencies in the thermal dispersion conductivity tensor are different for high Reynolds number and low Reynolds number porous media flows. The value of the transverse thermal dispersivity for a nearly parallel flow at high Reynolds numbers is determined by comparing the predicted heat transfer characteristics with existing experimental results for forced convection of water and air through heated packed channels and cylindrical packed tubes.

MSC:
76S05 Flows in porous media; filtration; seepage
76M25 Other numerical methods (fluid mechanics) (MSC2010)
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