Analysis of boiling heat transfer and two-phase flow in porous media with non-uniform porosity

An analytical model is presented for the two-phase transport which results from bottom heating of a liquid-saturated porous medium whose porosity varies with height. In this model, the difference between the bottom and the ambient porosity levels is assumed to diminish exponentially. Such a distribution may arise, for example, due to non-uniform distribution of particle sizes in a particle bed. The model applies to flows driven by both buoyancy and capillary effects. Numerical solution of the governing equations for a steam-water system indicates that variation of the porosity profile strongly affects the height of the two-phase zone and the temperature difference across the two-phase layer. Decreasing the porosity locally near the heated surface may increase or decrease the length of the two-phase zone depending on the size of the region of decreased porosity. In addition, decreasing the porosity near the surface is found to significantly increase the temperature difference across the two-phase zone, whereas increasing the porosity at the surface has the opposite effect. The lower-limit of heat flux at which capillary forces affect the two-phase transport has also been calculated. The computed results indicate that even when the region of porosity variation is small, this limit can be changed significantly when the porosity profile near the surface is altered.