This article aims to study the mass transient diffusion in solids with a cylindrical shape. To this end, the one-dimensional diffusion equation was discretized using the finite volume method with a fully implicit formulation. The solution can be used to simulate diffusive processes and to determine thermophysical parameters via optimization techniques. The computational package developed was applied to study the thin-layer drying of peeled bananas. Three models were used to describe the drying process: (1) the volume V and the effective mass diffusivity D are considered constant; (2) variable V and constant D; (3) V and D are considered variable. For all models, the convective mass transfer coefficient h is considered constant. The statistical indicators show that for the two cases analyzed (low and high temperature), model 3 describes the drying process better than the other models.

The main objective of this article is to describe the drying process of ceramic roof tiles, shaped from red clay, using diffusion models. Samples of the product with initial moisture content of 0.24 (db) were placed inside an oven in the temperatures of 55.6, 69.7, 82.7 and 98.6°C; and the data of the drying kinetics were obtained. The analytical solutions of the diffusion equation for the parallelepiped with boundary conditions of the first and third kinds were used to describe the drying processes. The process parameters were determined using an optimization algorithm based on inverse method coupled to the analytical solutions. The analysis of the results makes it possible to affirm that the boundary condition of the third kind satisfactorily describes the drying processes. The values obtained for the convective mass transfer coefficient were between 8.25 9 10 -7 and 1.64 9 10 -6 m s -1 , and for the effective water diffusivity were between 9.21 9 10 -9 and 1.80 9 10 -8 m 2 s -1 . List of symbolsA n Coefficients of the analytical solution dependent on position (boundary condition of the third kind) B n Coefficients of the analytical solution for the average moisture content (boundary condition of the third kind) Bi Biot number (dimensionless) Bi 1 Biot number for the side of length L 1 (dimensionless) D Effective water diffusivity (m 2 s -1 ) h Convective mass transfer coefficient (m s -1 ) k, m, n Indexes of summations L 1 , L 2 , L 3 Dimensions of a parallelepiped (m) M Moisture content (kg kg -1 , dry basis) M(x, y, z, t) Moisture content at instant t in the position (x, y, z) (kg kg -1 , dry basis) M 0 Initial moisture content (kg kg -1 , dry basis) M eq Equilibrium moisture content (kg kg -1 , dry basis) MðtÞ Average moisture content at instant t (kg kg -1 , dry basis) M exp i Average moisture content of the ith experimental point (kg kg -1 , dry basis) M ana i Average moisture content determined by analytical solution (kg kg -1 , dry basis) R 2 Coefficient of determination (dimensionless) t Time (s) x, y, z Position in Cartesian coordinates (m)Greek symbols v 2 Chi-square or objective function l n Roots of the characteristic equation for boundary condition of the third kind r i Standard deviation of the ith experimental point

Summary To describe water transport in a porous media, a mathematical model is usually used. Among the models available in the literature, empirical and diffusive ones can be cited. In this paper, Page and diffusion models are used to describe drying and soaking of chickpea. In addition, new empirical equation is proposed to describe the mentioned processes. According to the results, the two empirical models well describe drying and soaking, but the proposed one gives the best statistical indicators. The use of the diffusion model to describe the drying process makes it possible to determine the effective diffusivities (7.13 × 10−11, 10.39 × 10−11 and 13.78 × 10−11 m2 s−1 for the drying air at 40, 50 and 60 °C, respectively) and also the activation energy associated with the process (27.9 kJ mol−1).

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