A study on interstitial heat transfer in consolidated and unconsolidated porous media

The Nusselt number expressions are presented for the interstitial heat transfer coefficients for both consolidated and unconsolidated porous media. A boundary layer consideration is made for unconsolidated porous media to derive a general Nusselt number correlation, which shows its square root dependence of the Reynolds number, and matches fairly well with existing experimental data and correlations. As for low density consolidated porous media, rigorous mathematical arguments based oil the volume averaging theory are provided, so as to explain 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 resulting expressions are compared against available experimental data and empirical correlations, and found to be in good accord with them.