The effects of cake shrinkage on the drying times and energy requirements of the primary and secondary drying stages of the freeze drying process involving the drying of a material in a vial, are estimated through the construction and solution of an extended unsteady state and spatially multidimensional model that accounts for the changes introduced by cake shrinkage on the internal and external mass and heat transfer mechanisms of the freeze drying
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Sadıkoğlu et al. (1999) studied this question.