3D mathematical modelling to understand atypical heat transfer observed in vial freeze-drying

Highlights: • A 3D mathematical model of heat transfer in freeze-drying is proposed. • The role of several heat transfer mechanisms is explored. • Knudsen effect is considered for conduction inside low-pressure water vapour. • Radiation heat transfer is evaluated using the surface-to-surface model. • Atypical heat transfer is explained mainly by gas conduction rather than radiation. - Abstract: In pharmaceutical freeze-drying, the position of the product container (vial) on the shelf of the equipment constitutes a major issue for the final product quality. Vials located at the shelf edges exhibit higher product temperature than vials located in the centre, which in turn often results in collapsed product. A physics-based model was developed to represent heat transfer phenomena and to study their variation with the distance from the periphery of the shelf. Radiation, conduction between solids, and conduction through low-pressure water vapour were considered. The modelling software package COMSOL Multiphysics was employed in representing these phenomena for a set of five vials located at the border of the shelf, close to the metallic guardrail. Model predictions of heat fluxes were validated against experimental measurements conducted over a broad range of shelf temperatures and chamber pressures representative for pharmaceutical freeze-drying. Conduction through low-pressure water vapour appeared as the dominant mechanism explaining the additional heat transfer to border vials compared to central ones. The developed model constitutes a powerful tool for studying heterogeneity in freeze-drying while reducing experimental costs.