Transferência de calor em um silo armazenador de arroz: uma abordagem pelo método explícito das diferenças finitas para dois modelos transientes unidimensional e bidimensional

Abstract

Rice is one of the most consumed cereals in the world, being one of the most important crops in southern Brazil, however, it is a grain susceptible to thermal and mechanical damage and, mainly, to the attack of pests and fungi when subjected to inadequate temperature conditions. and humidity. Because of this, it needs a lot of care in its harvesting and post-harvesting processes, so that it reaches the consumer in good condition. Among these precautions is the need for careful storage in your silo, as poor storage can lead to irreparable damage to producers, such as total or partial loss of grain and, consequently, monetary loss. In this sense, mathematical modeling makes it possible to evaluate and predict within certain parameters, not free of errors, the internal temperature of a silo and, thus, to analyze the best preventive tool for the grain to maintain its ideal physical and nutritional properties. In this sense, through the relations of mathematical models, it is aimed to reduce the damages resulting from the bad conducts of the process related to the storage of the grain. Thus, the main objective of the present work is to model the heat transfer process by the explicit method of finite differences, applied to a prototype of a silo containing grains of paddy rice, and to compare the simulated data with the experimental ones in the literature. Seeking to carry out this comparison, two transient mathematical models will be presented, namely: one-dimensional and two-dimensional. In both models, the thermal diffusivity of the grains will be analyzed with mean and variable value (with grain moisture and temperature). The numerical simulations were obtained through the Google Collaboratory platform and, through these, the graphs between the approximations of order two and four were analyzed for the unidimensional model with thermal diffusivity with average value and, for approximation of order two the one-dimensional models with variable thermal diffusivity and two-dimensional models with mean and variable values. In addition, statistical indices, correlation coefficients and determination between observed and predicted temperatures were analyzed. The chosen methodology proved to be satisfactory, as the data obtained are close to literature data, adapting to the physical process of the system. In this sense, the methodology is of paramount importance for more complex problems, as in the case of variable thermal diffusivity, since for non-linear partial differential equations such resolution is not feasible analytically, which is the differential of the research. Furthermore, the statistical indices are close to the ideal values, with a very strong positive correlation for both cables of the one-dimensional and two-dimensional models (average and variable value).