The heat and mass transfer within a porous structure with partial heating and vaporization on the upper surface is studied numerically. Two models are presented: a continuum (Darcy) model and a pore network model. Both approaches show that the liquid-vapor front enters inside the porous structure. When the structure is characterized by a single pore size, the continuum model and the pore network model lead to the same stationary solution and the liquid-vapor front is smooth. When there exists a pore size distribution, pore network simulations show that the front resembles fractal fronts typical of invasion percolation. Implications of the results to capillary pumped loops (CPL) are discussed. In particular, the results indicate that capillary fingering may limit the operating range of CPL.