A model of distributed parameters for non-Fickian diffusion in grain drying based on the fractional calculus approach

Abstract

Diffusion is the mass transfer phenomenon that governs the hot air drying of grain. This study aimed to obtain an equation for the anomalous diffusion of distributed parameters in soybean drying using fractional-order calculus drying techniques for non-ideal processes and with non-local properties. Kinetic data from soybean drying at different temperatures were collected, and classical diffusion models were fitted to the experimental data. They were compared with a lumped parameters from a fractional order model for diffusion in time and with a distributed parameters model obtained by a generalisation of the spatial derivative of the classical Fick model using fractional derivatives. The results indicate that soybean presents anomalous diffusion, and that the fractional model order in time has a better fit than the classic models. This suggests anomalous diffusion, except when temperatures reach 100 °C at which point water vaporisation occurs and whole-order models appear appropriate.