Mathematical modelling of shrinkage effect during drying of food

Abstract

Shrinkage is one of the major changes taking place during the drying process. Typically, empirical fitting through experiment data is used to find the shrinkage equation. In this paper, the shrinkage equation was developed on the basis of a simple mechanism of volume of water evaporated during drying and is not dependent on data from experiment. The shrinkage equation was put into the model of heat and mass transfer for the prediction of moisture and temperature distributions during drying. A numerical solution technique, based on the method of lines, has been used with local finite difference approximations to the drying interface. Results show that the model incorporating the effect of shrinkage is capable of describing the behaviour of moisture and temperature in food during drying.

Mathematical modelling of cucumber (cucumis sativus) drying

“…Shrinkage equation that is introduced for drying of food [13] will be used to simulate the drying of cucumber. Initially it is assumed that no gas phase (air or vapor) is present and that the material consists only of solid and liquid phases and cellular tissue are incompressible (see for example [14]).…”

“…The problem considered is symmetrically relative to the mid-plane of the cucumber slice. The mathematical formulation introduced in [13], for the drying of food was used to fit with the experiment for the drying of cucumber and is given by …”

“…Experiment data for cucumber was fitted to the selected empirical drying model and also fitted to the numerical solution of a single phase mathematical model with shrinkage that has been developed by Shahari and Hibberd [13]. Then, the best drying curve using the empirical model was compared with the single phase mathematical model for the prediction of moisture during drying.…”

Mathematical modeling of drying process of unripe banana slices

“…An interesting shrinkage approach was published by Shahari;Hibberd (2012), in which, the authors considered the drying process as a simultaneous heat and mass transfer, similarly with this study. They introduced a complex factor for the solution related to a changing region of the sample, with an interface decreasing with drying.…”

“…Source: Adapted from Shahari;Hibberd (2012) During drying, heat is transferred mainly by convection from air to the product surface and by conduction from the surface towards the product center. Such mechanism provides the basis for a simultaneous heat and moisture transfer model.…”