Conduction and Convection

As we discussed in Chapter 8, our knowledge of the pore-level fluid mechanics in two-phase flow through porous media is rather incomplete. In this chapter, we discuss thermal dispersion, i.e., convective heat transfer at the pore level, using the available knowledge about the subject. This knowledge is even more inconclusive. We begin with the local volume averaging of the energy equation, and then we arrive at the effective thermal conductivity tensor and the thermal dispersion tensor for the three-phase system (liquid-gas-solid). The same closure conditions used in the single- phase flow treatments are used. Then we examine the various features of these tensors such as their anisotropy, and we discuss some of the available models and empirical relations for the various elements of these tensors. We conclude by noting that near the bounding surfaces, the phase distribution nonuniformities lead to substantial variations in the magnitude of the components of the effective thermal conductivity and the dispersion tensors.