Thermal analysis of freeze-drying process with mass transfer of water vapor: Volumetric heating approach

The current work deals with a heat and mass transfer problem describing the freeze-drying process of a phase-change material in a one-dimensional semi-infinite porous medium, which is divided into three regions: prefreezing, primary drying, and secondary drying. The effect of convection on drying rate, induced by residual mass transfer of the water vapor within the desorbed region, followed by the convective term driven by mass transfer of the water vapor within the sublimated region, is considered. An internal heat generation in terms of a volumetric heat source is also accounted for. In addition, fixed and time-dependent boundary conditions are the driving functions at the surface $x=0$ that cause freeze-drying to occur. The exact treatment of the mathematical model is carried out via similarity transformation. The present analytical work shows excellent agreement with previous available works. It is found that after the end of the sublimation of the material through a porous medium, only a small amount of water is available for desorption. Moreover, a volumetric heat source produces a faster desorption rate than usual. With the heat flux condition, the Kirpichev number shows a pronounced impact on the temperature field and evolution rate of the sublimation and desorption interfaces.