Abstract
A moving boundary model for food isothermal drying and shrinkage is applied to predict the time decay of water content and sample volume, as well as water diffusivity for chayote discoid slices in the temperature range 40–70°C. The core of the model is the shrinkage velocity v, assumed equal to the water concentration gradient times a shrinkage function α representing the constitutive equation of the food material under investigation. The aim is to provide a case study to analyze and quantify differences and accuracies of two different approaches for determining the shrinkage function α from typical experimental data of moisture content X/X0 vs. rescaled volume V/V0: a fully analytical approach and a shortcut numerical one.
Highlights
Mathematical modeling in chemical engineering historically provided the necessary support for understanding physics and transport phenomena that underlie the chemical processes
A moving boundary model for food isothermal drying and shrinkage is applied to predict the time decay of water content and sample volume, as well as water diffusivity for chayote discoid slices in the temperature range 40–70°C. e core of the model is the shrinkage velocity v, assumed equal to the water concentration gradient times a shrinkage function α representing the constitutive equation of the food material under investigation. e aim is to provide a case study to analyze and quantify differences and accuracies of two different approaches for determining the shrinkage function α from typical experimental data of moisture content X/X0 vs. rescaled volume V/V0: a fully analytical approach and a shortcut numerical one
The comparison between the two approaches developed in [21, 22] for mathematical modeling of food drying with shrinkage is carried out
Summary
Mathematical modeling in chemical engineering historically provided the necessary support for understanding physics and transport phenomena that underlie the chemical processes. Food process engineering represents one of the most promising research fields in chemical engineering that could benefit the enhancements of the theoretical research. It was quite intentionally forgotten, in the past, due to the complexity of food materials and of related transformation processes. The comparison between the two approaches is carried out by using literature experimental data [27] on chayote discoid slices In this case, due to both the regular shape and the aspect ratio of the samples, both approaches can be adopted. Due to both the regular shape and the aspect ratio of the samples, both approaches can be adopted. e aim is to provide a case study to test differences in terms of accuracy of prediction of water content evolution, volume reduction, and other significant physical quantities such as the water diffusivity
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