An analytical study of coupled heat and mass transfer freeze-drying with convection in a porous half body: A moving boundary problem

Abstract

The freeze-drying of a porous body is the most commonly used process in food technology to capture the coupled heat and mass transfer phenomena which appears in a class of moving boundary problem. The modern technology demand encourages investigators to provide techniques for accelerated food drying (AFD) and preservation of material to be denatured. Experimental study of freeze-drying of a porous body may be difficult and exploration of robust theoretical models with convection is critical. Further, the problem concerning in coupled heat and mass transfer, there is lack of mathematical analysis in the previous literatures which does not accounts the convective heat and mass transfer, convective term due to water vapour and condition for the limitation of sublimation and desorption. It is therefore, essential to develop mathematical formulation to discuss these type of freeze-drying phase change processes. In the current paper, the mathematical work is devoted to study a coupled heat and mass transfer problem describing freeze-drying of a material in a porous half-space. The problem accounts convection in porous frozen, sublimated and desorbed regions and a convective term due to moisture flow of the water vapour in the sublimated region. The exact solution of the proposed problem is obtained via similarity transformation. Condition for the limitation of sublimation and desorption is obtained and illustrated graphically. The effect of various parameters on thermal properties is discussed in detailed. The range values of governing problem parameters are taken as: 0 to 2 for Pe, 0.01 to 1.0 for β, 0.1 to 0.9 for α21, 0.1 to 2.1 for γ1, 0.5 to 2.0 for γ3, 0.2 to 0.8 for ω, 0.01 to 0.85 for (ϵ ‐ ω), 0 to 50 for v and 0.21 to 1.65 for ϵ. In current work, it is shown that the freeze-drying process becomes faster in the presence of convection rather than in the absence of convection. Furthermore, the rate of water vaporization from the surface of the porous body enhanced, as a result freeze-drying process deterred. The current work may be expected aid in accelerated freeze drying (AFD) technology.