Numerical simulation of a non-linear sublimation process with temperature-dependent permeability and volumetric heat source: A phase change problem

Abstract

Conventional freeze-drying takes a long drying time and makes the process expensive. High-quality biological materials, medicine, and vaccines may not find easy acceptance with this technology. To overcome the operative time, several engineering innovations are carried out. A long drying time during freeze-drying can be minimized by accelerating the sublimation rate. Obtaining a fast drying rate without harming the material properties is the prime focus of the accelerated freeze-drying (AFD) like-techniques. In connection with this, the study of temperature-dependent thermal-physical properties of the medium during sublimation is considered in this study. For example, a temperature-dependent volumetric heat source is assumed within the vapor region. An increase in the temperature field results in higher pressure. Therefore, a temperature-dependent specific heat of vapor pressure is also accounted for. Furthermore, the permeability of the medium and the specific heat of the water vapor are also assumed to be temperature-dependent. Exploring realistic theoretical models with variable-dependent characteristics and convection is essential since the experimental investigation of sublimation in a porous media may be challenging. Despite the previous available studies on sublimation heat and mass transfer, there is still a lack of mathematical modeling of this particular problem. To solve this non-linear sublimation problem, the Genocchi operational matrix of differentiation method ($GOMOD$) method is employed to obtain the numerical results. In case of full non-linear model, results obtained via current numerical technique are verified with finite-difference method (FDM). Furthermore, in a particular case, the accuracy test of the $GOMOD$ method against FDM is presented, and it is found that the current numerical technique is more accurate than FDM. In the current study, it is found that a temperature-dependent heat source offers a faster sublimation rate than a constant one. Similarly, temperature-dependent specific heat of vapor pressure accelerates the pressure distribution within the sublimated region. With temperature-dependent permeability, the concentration distribution within the medium decreases. Moreover, the temperature-dependent specific heat of water vapor delayed the sublimation rate. Results found from this study are expected to aid in AFD techniques, food industry and pharmaceuticals.