Modeling Simultaneous Heat and Mass Transfer in an Amaranth Grain During Drying: a Finite Element Approach

Abstract

A finite element formulation was used to obtain numerical solutions to the simultaneous equations of heat and mass diffusion that describe the removal of moisture and heat gain during the isothermal drying of amaranth grain, for temperatures from 25 to 70ºC and initial moisture contents between 14.9 and 32.5% db (dry basis). The numerical model was implemented in ANSYS® using the direct analogy of thermal-mass diffusion. Granular particle was considered as homogeneous and isotropic material with negligible volume changes and constant properties evaluated at the initial moisture content. Grain shape was performed using different geometries (sphere, ellipsoid-oblate and volume of revolution). Given the symmetry of the grain, a two-dimensional model was defined taking into account only one quarter of the domain, which was discretized using 6-node triangular elements with characteristics of axial symmetry. As boundary condition, it was assumed that grain surface was instantaneously attained the equilibrium moisture content (i.e., strict internal control during the drying process). The effective coefficients of moisture (Def) were estimated for each drying temperature and initial moisture content, and resulted between 1.538x10-12 m2/s and 4.334x10-11 m2/s when grain shape was modeled by an oblate ellipsoidal, and between 1.850x10-12 m2/s and 5.189x10-11 m2/s when a spherical geometry was considered, being the ratio between these coefficients (Def ellipsoid/Def sphere) equivalent to the amaranth sphericity squared. The simulation results were validated by its contrast with their own experimental data of drying kinetics in thin layers. Best description of the drying curves was obtained when the domain was modeled by ellipsoidal geometry, followed by the spherical model. It was observed an Arrhenius type exponential dependence of the diffusion coefficient with the reciprocal of the absolute temperature, and a linear function of initial moisture content of grain. The activation energy for desorption of water was in the range 18.7–35.6 kJ/mol.
From the finite elements model it was possible to predict the profiles of moisture and temperature distribution inside the grain, allowing obtain the time process for reach the maximum thermal and mass gradients. Temperature profiles ensure the validity of the hypothesis assumed isothermal behavior of the solid during drying, because it was noted that the material quickly reaches equilibrium with the drying air temperature. The parameterized model developed has the flexibility to respond quickly to obtain the average moisture content of grain as a function of time and spatial distribution of moisture inside. Another strength of this simulation technique based on finite element method is that it allows to easily obtain moisture gradients (and, similarly, the thermal gradients) within the grain, in a form directly usable for any analysis stress cracking and can be extended the focus of this work to the study of other biomaterials with different geometries, loading conditions and boundary conditions.