Theoretical Consideration of the Difference in Interstitial Heat Transfer between Consolidated and Unconsolidated Porous Media

概要

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A theoretical study was made on the interstitial heat transfer coefficients in both consolidated and unconsolidated porous media. Firstly, a boundary layer consideration was introduced to consider heat transfer in unconsolidated porous media. A general Nusselt number correlation was derived using the boundary layer solution for the axisymmetric stagnation thermal boundary layer, which shows its square root dependence of the Reynolds number, and matches fairly well with existing experimental data and correlations. Then, for low-density consolidated porous media, a volume averaging theory was exploited to obtain the set of macroscopic energy equations. The energy equations along with mathematical modeling revealed the reason why the Reynolds number exponent of the Nusselt number expression for the case of low density consolidated porous media is much greater than that of unconsolidated porous media. The present expressions are compared against available experimental data and empirical correlations, and found to be valid for a wide range of the porosity and Reynolds number.