Mathematical methodologies for calculating the mass diffusion coefficient of bananas during drying

Abstract

In this work two mathematical methodologies to solve the diffusion differential equation related to the banana drying process were used in order to obtain the mass diffusion coefficient value. A simplified mathematical model was considered that was based on Fick's Law, with initial and boundary conditions according to the experimental procedure carried out for banana drying. The first methodology was performed by using an approximation of the analytical solution and the second by using the numerical simulation according to the implicit scheme of the finite difference method. The calculation was carried out by looking for the minimal value of the norm calculated between the experimental data and the theoretical results obtained using different values of the diffusion coefficient. The algorithms associated with these methodologies were implemented with Matlab. The values of the diffusion coefficient according to the first and second methodologies were 1.65 x 10-6 [m² h-1] and 1.58 x 10-6 [m² h-1] respectively, with the associated minimal residual values of 0.0269 and 0.0257.