In this article, a mathematical model was developed for the numerical simulation of the water diffusion in an infinite cylinder. A solver for the diffusion equation was created using the finite volume method, with a fully implicit formulation. In order to create such solver, it was assumed that the boundary condition of the first type is adequate to simulate the physical problem. The solver presupposes variable thermophysical properties and radius in the domain. In order to determine the parameters of the expression between the diffusivity and the moisture content, an optimizer was created, based on the inverse method. The developed mathematical model was applied to simulate the drying of banana and rough rice, using experimental data obtained from the literature. The results obtained in this article, considering the variable diffusivity, are better than the results obtained originally in the literature, where the water diffusivity was considered constant.