Solução numérica da equação de difusão em coordenadas cilíndricas e aplicações em processos de secagem.

Abstract

In this work, a study of the Diffusion Equation was carried out from the perspective of applications, emphasizing the phenomena of transient mass diffusion in solids with a cylindrical geometric shape. The numerical solution of the two-dimensional Diffusion Equation, in cylindrical coordinates, was obtained using the Finite Volume Method, with a fully implicit formulation. The mathematical model used assumes boundary conditions of the third kind and allows the thermophysical parameters to be considered constant or variable. The methodology was applied to estimate the variation in moisture content inside the seeds of a typical Brazilian tree, the pine (Araucaria angustifolia), during the process of continuous and intermittent drying at a temperature of 70°C. Experimental results of the moisture content of in-shell pine nuts over time were compared with values obtained by solving the differential equation to validate the model. A Fortran computer code was used to perform the optimizations/simulations. According to the results of the statistical parameters, the model describes the kinetics of continuous and intermittent drying of pine nuts well. The effect of the adopted considerations regarding diffusivity being constant or variable was observed, and the model adopting the diffusion coefficient dependent on moisture content better describes the kinetics of continuous drying of pine nuts at a temperature of 70°C.