Modelling the Drying Kinetics of Apple (Golab Variety): Fractional Calculus vs Semi-empirical Models

Abstract

In this work, two novel models have been proposed based on semi-empirical and factional calculus incorporating non-integer time derivatives in the Fick’s first law of anomalous diffusion. The experimental data has been collected from literature of 15 kinetics investigated in a convective dryer under the effect of temperatures ranging from 40 to 80 °C at 10 °C interval, and thickness of the slices of 2 to 6 mm at 2 mm interval. The collected experimental dataset was of apple slices (Golab variety). Results from this study were compared with a set of 64 thin-layer drying models previously published in the literature. The fitting capability of the models was compared using the mean of root mean square error MRMSE (%) of all kinetics and the global determination coefficient R2. All models’ constants and coefficients were optimised by dragonfly algorithm programmed in MATLAB software. Results showed that the fractional model is highly capable of describing the drying curve of the apple slices with a determination coefficient (R2) of 0.99981, and average root mean square error (MRMSE) of 0.43 % in comparison to the best empirical models with R2 of 0.99968 and MRMSE of 0.61 %.

Keywords

• thin-layer solar drying
• fractional calculus
• semi-empirical modelling
• apple slices