An analytical study of coupled convective heat and mass transfer with volumetric heating describing sublimation of a porous body under most sensitive temperature inputs: Application of freeze-drying

Abstract

Sublimation heat-mass transfer has great applications in the pharmaceutical and food industries, such as the preservation of biological products, accelerated freeze-drying (AFD), energy storage systems, microwave freeze-drying, and enabling long-time active covid like vaccines. The current technological demand encourages investigators to provide new knowledge for freeze-drying so that it reduces the high economic cost, prevents materials from being denatured, and remains stable for a long time. In connection with this, it is of key interest to analyze the impact of convective heat and mass transfer, the rate of water vaporization, and the volumetric heating source under the most realistic temperature inputs. Despite the available works on sublimation, there is still a lack of mathematical modeling that accounts for these informations together and is presently being considered. This paper presents a heat and mass transfer problem describing sublimation in a half-porous space. The mathematical model accounts for convective heat/mass transfer and a volumetric heat source within dried and frozen regions. In addition, convection driven by the mass transfer of ice crystals within the dried region is also considered. Three different types of temperature input are placed at the surface $x=0$ to obtain the rapid sublimation process without harming the material properties. The exact solution to the problem is obtained successfully by using similarity transformation. The impact of various problem parameters on sublimation is comprehensively studied. In this study, it is found that with a volumetric heating source term $G_0$, material sublimates faster than without one. Furthermore, convective heat transfer in terms of $P{e}_1$ and $P{e}_2$, enhances the temperature within the porous medium, and as a result, material sublimates faster than usual. As the value of the convective term $\beta$ goes up, a reduction in the temperature field is observed. The temperature of the medium rises as the value of the Kirpichev-like number $K_i$ increases. Similar observation is found in the case of Biot like number $B_i$. The concentration profile decreases as the value of the Luikov number $Lu$ increases. It is also found that Newton-type temperature input offers a faster sublimation rate in comparison to constant and flux-type temperature input. The analytical results obtained in this study show excellent agreement with previous available results. These results provide a comprehensive theoretical and mathematical understanding of sublimation heat/mass transfer and are expected to be useful in energy storage systems, food technology, and accelerated freeze drying.