Transporte difusivo em sólidos com forma arbitrária usando coordenadas generalizadas.

Abstract

This work seeks to study the diffusion phenomenon in porous solids with arbitrary geometry, to present the numeric solution of the equation that describes the phenomenon for extrusion solids and to propose a numeric solution for revolution solids. In this sense, the diffusion equation was solved for a bi-dimensional grid which generates extrusion or revolution solids, and it reduces in a significant way the computational effort demanded in the three-dimensional numeric solution. The integral (in the space and time) of the diffusion equation in unsteady state was solved numerically for first, second and third species boundary, using generalized coordinates. The used method was the method of the finite volumes, with a fully implicit formulation. It is presented the necessary study for mesh generation in two dimensions through the Poisson equation, via finite differences; and software in the platform Windows was developed to make possible the generation. Seeking to acquire the points of the boundary of a mesh, it was also developed digitizer software for points, starting from the illustration of a solid contained in a bitmap file. It was created a function parser for the Fortran language to make possible the development of software destined to the drying simulation for individual solid or product in thin layer. Several simulations were accomplished (using the developed codes), involving a great number of physical situations of interest, and all the obtained results were theoretically consistent and coherent with expected values. The developed software was applied in the simulation, starting from experimental data, of the drying of ceramic membranes in the shape of tubes, used as filters, for the following experimental conditions: temperature from 45 up to 105 °C, initial moisture content from 25 up to 30% (db) and relative humidity of the air of 58%. The simulation makes possible to determine an expression for the diffusion coefficient in function of the moisture ratio and of the temperature of the drying air, and also the value of the convective mass transfer coefficient corresponding to each temperature.