Heat Transfer in a Silo Containing Rice: Solution by the Explicit Method of the Finite Differences with Approximations of Order 2 and 4 for a One-Dimensional Transient Model

Abstract

Rice is one of the most consumed cereals in the world, and the cultivation of this crop has significant relevance in the southern region of Brazil. When subjected to inadequate conditions of temperature and humidity, rice becomes susceptible to attacks from pests and fungi and, therefore, care in the storage process is of paramount importance, since this is largely responsible for the quality of the harvest. Such care allows the food to arrive without harm to the consumer. In this sense, the mathematical modeling, among numerous possibilities, allows for evaluating the internal temperature of a silo and, through this, taking preventive measures so that the grains maintain their quality. The objective of this work is to model the heat transfer process in a silo prototype containing rice in husk through the explicit finite difference method for a one-dimensional and transient model considering two approaches centered on the spatial derivative: error of order 2 and 4. In addition, the thermal diffusivity of the grain with average value was analyzed. The results obtained by the solutions were analyzed through graphs and statistical indexes comparing with the experimental data of the literature, and the computer simulation was performed through the Google Colab platform. The chosen methodology proved effective for the work, and the predicted temperatures for the approximations of order 2 and 4 denote similarities both graphically and in the precision of the statistical indexes.