Abstract
Recent advances in mathematical modeling of heat and fluid flow in porous media were discussed starting from an introduction of volume averaging theory and leading to various engineering applications. Mathematical interpretations of tortuosity, thermal dispersion and interstitial heat transfer are provided with their models based on solvable volume averaged quantities. A useful concept “effective porosity” was introduced to account for the tortuosity. Moreover, an inverse relationship between the interstitial heat transfer coefficient and thermal dispersion coefficient was explained, which enables us to estimate the thermal dispersion simply by measuring the interstitial heat transfer using a single blow method. Engineering applications based on the local space sharing concept will be discussed ranging from bioheat transfer to ion transport through a membrane.
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