Frost propagation in wet porous media

A water saturated porous medium freezes when it is chilled. The frost line which separates the frozen part and the unfrozen part is a free surface. Experiments show that a depression pppears on the frost line. Water is thus sucked in through the unfrozen part. It freezes when it reaches the frost line. The problem is a coupled Stefan problem linking the heat and water equations of diffusion. The energy conservation law couples the equations on the frost line. The equations are solved using a new unkown the freezing index and the methods of variationnal inequalities. A numerical example is given.