Numerical Simulation for Freeze Drying of Skimmed Milk with Moving Sublimation Front using Tri-Diagonal Matrix Algorithm

Abstract

Freeze drying is a highly advanced dehydration technique used for preserving pharmaceuticals, human organs transplanted to others and highly heat sensitive food products. During the freeze drying, there are two layers formed namely dried region and frozen region. In this present work, a numerical model is developed to estimate the temperature distribution of both regions. The sample object considered is skimmed milk. The transient heat conduction equations are solved for both regions of dried and frozen region. The interface layer between the two region is considered as moving sublimation front as same as the realistic case. Radiative boundary condition at the top and convective boundary condition at the bottom are considered. The model has been solved by finite difference method and the scheme used is backward difference in time and central difference in space (implicit scheme), which generates set of finite difference equations forming a Tri-Diagonal Matrix. A computer program is developed in MATLAB to solve the tri-diagonal matrix. The temperature distribution along the length of the product with varying chamber pressures and the sublimation front temperature with time are estimated. The transient effect of sublimation front movement was estimated with different applied chamber pressure. It was noticed that at lower pressure the sublimation rate is very fast.

Developing and solving the mathematical model of transient heat and mass transfer in the freeze-drying of Cordyceps militaris

“…That means that the drying rate increases as the heating shelf temperature increases. This result is also consistent with previously published studies [11,18,19]. However, increasing the heating plate temperature also increased the material temperature.…”