Publisher Summary Melting and freezing are important processes and these processes have played a decisive role in the formation of the Earth. This phase-change phenomena have become an indispensable part of many processes, such as, manufacturing of glass, crystals, and metal alloys; continuous casting of ingots, fabrics, and wires; food preservation and cryopreservation of biological cells; and desalination of seawater and freezing-out separation processes. This chapter reviews the current knowledge on phase-change phenomena, with particular focus on phase-change problems from solid to liquid or to gas. Because of their simplicity, one-dimensional, phase-change problems involving conduction heat transfer are the most frequently used model problems for the development of solution methods. This chapter begins with the consideration of such one-dimensional methods, either exact or approximate, which have been widely used in the literature. The substantial information about the physics of phase-change processes that can, in fact, be learned from studies of these simple models is discussed. The multidimensional conduction phase-change problems as well as the additional physics attributable to geometrical complexities are also reviewed.

Melting and Freezing

Finite-element methods for steady solidification problems

Modeling heat and mass transfer in immersion frying. II, model solution and verification

https://hal.archives-ouvertes.fr/hal-00434481/document

Model predictive control during the primary drying stage of lyophilisation

Dynamic and spatially multi-dimensional mathematical models of the primary and secondary drying stages of the freeze-drying of pharmaceutical crystalline and amorphous solutes in vials, are constructed and presented in this work. The models account for the removal of free and bound water and could also provide the geometric shape of the moving interface and its position. It is proved that the temperature of the moving interface can not be constant if the flux of heat flow to the sides of the vial is not zero. It is also proved that the slope of the free surface (moving interface) at the edge of the vial is always curved downward. The numerical solution of the nonlinear partial differential equations of the models would allow model simulations that could indicate design conditions, operating conditions, and control strategies that could provide high drying rates and could lead to a series of novel experiments in freeze-drying.

Freeze-Drying of Pharmaceutical Crystalline and Amorphous Solutes in Vials: Dynamic Multi-Dimensional Models of the Primary and Secondary Drying Stages and Qualitative Features of the Moving Interface

Michael F. Malone

Papers

Analysis of Two-Dimensional Diffusion-Controlled Moving Boundary Problems