Numerical Solution of the Three-Dimensional Diffusion Equation in Solids with Arbitrary Geometry for the Convective Boundary Condition: Application in Drying

Abstract

In this work, a numerical solution for the diffusion equation applied to solids with arbitrary shape considering convective boundary condition is presented. To this end, the diffusion equation, written in generalized coordinates, was discretized by the finite-volume method with a fully implicit formulation. The transport parameters and the dimensions of the solids are considered constant during all process. For each time step, the system of equations obtained for a given non-orthogonal structured mesh was solved by the Gauss-Seidel method. One computational code was developed in FORTRAN, using the CFV 6.6.0 Studio, in a Windows platform. The proposed solution was validated using analytical and numerical solutions of the diffusion equation for different geometries (parallelepiped and finite cylinder). The analysis and comparison of the results showed that the proposed solution provides correct results for the cases investigated. In order to verify the potential of the proposed numerical solution, we used experimental data of the drying of ceramic roof tiles for the following temperature: T = 55.6 °C. The analysis of the results and the statistical indicators enables to affirm that the developed numerical solution satisfactorily describes the drying processes in this temperature for the convective boundary condition.