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, κ, 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 κ> 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 κ> 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 κ>1.