Evaporation and steam generation are two of the most vital processes in industry. A new method to advance the efficiency of evaporation involves localizing heat at the water surface where the vapor escapes into the air to minimize energy loss. In this research, we numerically investigate the improvement of a novel evaporation process via solar heat localization in a porous medium. A layer of carbon foam with a combination of interconnected and dead-end pores with a high hydrophilicity surface adjacent to a layer of expanded graphite with known porosity and properties were modeled numerically using a finite volume method. The hydrophilic porous media facilitates the capillary forces for better transportation of the bulk water through the porous media to the top surface of the porous media where the absorbed solar energy is delivered to the water inside the pores for evaporation. Continuity, momentum, heat and mass transfer equations were solved in this modeling effort. The modeling results were validated with the experimental data available in the literature. The findings in this numerical study can shed light on the complex interplay between the fluid dynamics and heat and mass transfer across the porous medium, which are important for efficient evaporation processes.