A method to estimate anisotropic diffusion coefficients for cylindrical solids: Application to the drying of carrot

Abstract

In this study, a method to estimate water diffusivity in axial, radial and angular directions during drying of anisotropic cylindrical solids is proposed. The method is based on the analytical solution for non-steady state mass transfer equation in products shaped as longitudinal sections of finite anisotropic cylinders. A sequential approach is applied where radial and axial diffusion coefficients are first estimated from drying curves of whole cylinders with increasing height, while angular diffusivity is obtained thereafter from drying experiments carried out with longitudinal sections of fixed-height cylinders varying cut angle. Developed theory was applied to the analysis of two sets of convective drying data of carrot obtained at 80°C with an air velocity of 2m/s. The first experiment set was conducted with carrot cylinders of 2.2cm diameter and heights of 1, 2,…,10cm, while cylinders in the second set were longitudinally cut as halves, quarters, sixths and eighths with a constant height of 10cm. Under such experimental conditions, identified water diffusivities were in the range of 0.53–2.93×10−9m2/s. Differences in water diffusivity for studied mass transfer directions were significant (p<0.05), with SEM images revealing structural differences between longitudinal and transversal product cuts, thus further supporting numerical results. Present findings suggest that, depending on product, anisotropic diffusion should be included in drying modeling in order to obtain an accurate process description.