Phase-Change Transpiration Cooling in a Porous Medium: Determination of the Liquid/Two-Phase/Vapor Interfaces as a Problem of Eigenvalues

In this work, we carry out a theoretical analysis of the transpiration cooling with a liquid coolant phase change in a porous medium. The evaporation of the liquid inside the porous medium causes the appearance of three regions: a liquid region, a two-phase region and a vapor region. This kind of physical problem has been widely studied in the specialized literature and the main contributions are based on the separated phase model or by using the two-phase mixture model. Here, we propose a new model that permits to numerically determine the thickness of the three regions that are formed inside of the porous medium. To analyze this phenomenon, the governing equations were appropriately nondimensionalized, where suitable Péclet numbers for each region appear such that these numbers represent eigenvalues for the mathematical model, and when they are obtained, the relative position of the interfaces between each region is found.