Modelado Matemático Del Secado De Madera Subtropical Por Convección De Aire Caliente

Abstract

This work was divided into three parts. In the first part we obtained the experimental drying kinetics for Mexican softwood (Pinus pseudostrobus). In the second part, from experimental data we have developed a semi-empirical model (Characteristic Drying Curve), In the third part we have proposed a phenomenological drying model that involves heat transfer and mass transport during the drying process. To validate the models, we have analyzed the drying experiments. All drying trials were carried out in a drying tunnel (CIIDIR Oaxaca) at different conditions of temperature, keeping constant the ariflow speed. The relative humidity was not controlled. The experiments had an average duration of 70 hours, each of one with its replicate. From experimental data was obtained a model based on the method of the drying characteristic curve (DDC). This model allow to simulate the moisture content evolution. This model takes into account the reduced drying rate, and the identification of drying´s stages. This model considers a drying rate of reference and establishes the assumption of moisture content dependency. During drying process two zones or stage are identified, the first one called the capillary domain, where migration of moisture is strongly influenced by the capillary forces, and the second one, corresponding to diffusion of water and bounded water. The parameters of the proposed model were estimated by reducing the quadratic error between the experimental curves and the theoretical results. The parameters of this model were estimated in Microsoft Excel by using the SOLVER tool. In the third part of this work, a phenomenological formulation was developed. The model describes the mechanisms of heat and mass transport during drying. Wood is a porous medium where the water is present at different states. We consider these states as chemically inert phases. The mass and heat balance are given in the frame of the Representative Volume Element (RVE), which contains the four phases, and it is enough small to consider a local thermodynamic equilibrium. The RVE considers the solid phase (matrix), liquid phase, gaseous phase (vapor and air) and bounded water. The flow of free-water is governed by Darcy's law, the bound water by Fick's law, and water vapor and dry air is a combination of mechanisms convection-diffusion. Then, the model solves 3 unknowns: The moisture content represented in the equation of conservation of moisture, temperature in the heat equation, and air density in the equation of conservation of dry air. These all equations are highly coupled, and the macroscopic scale is coupled to the dryer scale too by means of the boundary conditions. The equations were solved in COMSOL 3.4. The PDE module was used in this approach. The general form for the mass balance and the coefficient form for the heat balance. The thickness of the wood was discretized with 753 degrees of freedom. The system of partial differential equations was solved by numerical factorization by using UMFPACK. UMFPACK solves the linear systems by using a pattern multi frontal non-symmetric method and by factoring sparse matrix. The phenomenological model is able to simulate the spatial profiles of moisture content, density of dry air, temperatures by taking into account the constitutive properties of wood. The two models developed were validated by comparison with the experimental kinetics. The numerical results and experimental measures provide some confidence in the proposed model.