Numerical Simulation of Conjugate Heat and Mass Transfer During Vacuum Freeze-drying of Mare Milk: Validation and Energy-optimisation Study
Rakhmatulina A. Altybay A. Satybaldy S.
October 2025Engineered Science Publisher
Engineered Science
2025#37
Vacuum freeze-drying is a preferred method for converting mare’s milk into a shelf-stable powder while retaining its nutritional and sensory qualities. However, the process remains time-consuming and energy-intensive. This study presents a validated three-dimensional numerical model that simulates conjugate heat- and mass-transfer during vacuum freeze-drying under industrially relevant conditions. The governing equations for heat conduction, water-vapour transport (Darcy’s law), and latent-heat removal were solved in COMSOL Multiphysics 6.3 using the Deformed Geometry interface to track phase-front motion without remeshing. Simulations were performed on a 50 × 45 × 0.7 cm slab frozen to -50 ℃ with a shelf temperature of -20 ℃ and chamber pressure ranging from 15 to 35 Pa. Validation was conducted in a 0.45 m2 pilot dryer using centre-line temperature measurements and gravimetric moisture-loss data. The model reproduced experimental temperature profiles (R2 = 0.96) and predicted sublimation-front motion within 4% of image-based observations. Thinner samples (3 mm vs. 7 mm) and lower pressures (15 Pa vs. 35 Pa) significantly reduced drying time, though gains diminished below 15 Pa. This model offers a practical framework for optimising freeze-drying conditions and is extendable to other porous food and biopharmaceutical products.
Conjugate heat and mass transfer , Energy optimization , Mare milk powder , Numerical Simulation , Sublimation front , Vacuum freeze-drying
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Department of Mechanical Engineering and Robotics, U. Joldasbekov Institute of Mechanics and Engineering, Almaty, 050000, Kazakhstan
Department of Mechanical Engineering, Satbayev University, Almaty, 050000, Kazakhstan
Department of Differential Equations, Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, 9000, Belgium
Department of Computer Science, Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Departments of Technological Machines and Equipment, Satbayev University, Almaty, 050000, Kazakhstan
Department of Mechanical Engineering and Robotics
Department of Mechanical Engineering
Department of Differential Equations
Department of Mathematics: Analysis
Department of Computer Science
Departments of Technological Machines and Equipment
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