A review of models for the stagnant effective thermal conductivity of a saturated porous medium

The prediction of the effective thermal conductivity, k(e), of a saturated porous medium has proven to be a great challenge both theoretically and experimentally. Generally, pore geometry has a substantial influence on k(e) and is important because conduction within the medium is multidimensional. The failure of one-dimensional models when the ratio of solid (k(s)) to fluid (k(f)) conductivity, kappa, is different from unity is evidence that conduction within the medium is not one-dimensional. While heat transfer must thus be three-dimensional, the success of two-dimensional spatially periodic models suggests that a high degree of symmetry exists in the internal temperature fields. However, such models fail for kappa >1000, and this failure is attributed to the predominance of diffusion through particle contact regions. Thus k(e) is dependent on the thermal and mechanical properties of the solid phase. The models of Nozad et al. [1] and Batchelor and O'Brien [2] define two asymptotes for k(e) corresponding to large and small particle contact area models, respectively, Measured values however, diverge from either model when kappa >1000, and there thus remains a need to develop a validated model that accurately represents the thermo-physics of particle contact. There is also a need for more carefully documented measurements for validation, especially when kappa greater than or equal to1.