Mathematical modelling of low temperature drying of maize: Comparison of numerical methods for solving the differential equations

Abstract

Low temperature/natural drying of grain depends strongly on the climate. Being a slow process, experimental determinations are costly and difficult, so that developing a mathematical model and finding a proper method of solution is of great importance. The dryer model is composed of a first-order, hyperbolic partial differential equation (PDE) system, encompassing four dependent variables: grain moisture content, grain temperature, air temperature and air humidity, plus two independent variables: time and position along the bed depth direction. The bed system requires initial and boundary conditions, the latter of the Dirichlet type. In this work the following numerical methods for solving the set of dryer equations were compared: (1) explicit finite differences (2) implicit finite differences and (3) the method of lines. The performance parameters selected for the comparison were (a) drying time and (b) specific energy consumption. The influence of time and length steps of numerical solutions on such parameters was also assessed through indicators such as relative computing (CPU) time, prediction stability and truncation error. The results indicated that the method of lines was the most adequate to solve the compromise between these indicators.