Thermal dispersion effects on the two-phase zone with evaporation in a porous medium

The one-dimensional steady-state heat transfer in a two-phase zone of a water-saturated porous medium is studied numerically by including thermal dispersion effects. The physical system consists of a porous medium-liquid-vapor mixture that is heated from above and maintaining a fixed temperature on the bottom surface. Under certain conditions, a two-phase zone of both vapor and liquid exists in the middle of the region of the porous medium. A mathematical model for the temperature and the liquid saturation profiles within this two-phase zone is formulated by allowing for explicit temperature dependence for the saturation vapor pressure together with explicit saturation dependence for the capillary pressure. The set of resultant equations is numerically integrated by using a conventional fourth order Runge-Kutta scheme. The results evidence the strong influence of the thermal dispersion, porosity and pore diameter on the two-phase zone. $R_{1} R_{3}$