Estimation of the influence of variable boundary conditions when using thin layer equations for grain dryer simulation

Abstract

Most dryer design programs or dryer simulators use “thin layer equations” to predict mass transfer rates in each subdivision of grain beds in dryers. These equations work well under the constant boundary conditions for which their parameters were determined. Considering that the atmosphere surrounding the grains in dryers vary with time and position, a specific study was conducted here to analyse the behaviour of analytical solutions under such variable conditions. This work provides examples for wheat using parameters obtained in previous research conducted in our laboratory, and compares analytical predictions of the diffusion equation with those of a numerical (finite difference) solution of the partial differential equation of diffusion for one grain, which is naturally prepared to predict under either constant or variable boundary conditions. As expected, predictions of the analytical and numerical solutions coincided under constant boundary conditions, and this aspect was important to corroborate the behaviour of the numerical method in the program. Then, simulated data of exhaust air temperature and relative humidity from a dryer were produced by a drying simulator previously validated and, under this variable environment, predictions for a thin layer with the analytically-based model and the numerically-based solution tend to depart, especially after the derivative of the mean grain moisture with time changed sign. The preliminary conclusion is that, at least in positions near the outlet of dryer columns, predictions of the analytical solution-based model might be misleading, and this must be taken into account in future research aimed at developing grain dryer simulators.