Non-Darcy flow and thermal radiation in convective embankment modeling

The design of convective embankments generally hinges on the use of numerical models that describe buoyancy-driven flow and heat transfer in porous media. A review of the literature reveals that most of the models used in the study of convective embankments assume that heat transfer occurs by conduction and convection, and that airflow can be described with Darcy’s law. This is inconsistent with recent experimental evidence that suggests that radiative heat transfer is significant, and that Darcy’s law does not adequately describe the relation between superficial flux and gradient in rockfill materials. In response to these shortcomings, a new model is herein derived to account for both radiative heat transfer and non-Darcy effects. After demonstrating its ability to solve fairly complex steady-state problems, the model is used to gain insight into the relative importance of radiative heat transfer and non-Darcy flow on the thermal response of a typical railway embankment. The radiative heat transfer is shown to be greater during the summer months. This increases the temperature at the base of the embankment, which in turn, increases the wintertime convective heat transfer. This additional heat extraction does not counteract the effect of the radiative heat transfer, and the wintertime temperatures below the embankment are shown to be warmer than that computed without radiative and non-Darcy effects.