Comparação entre o método numérico de quarta ordem de Runge-Kutta e a solução analítica da equação diferencial ordenada relativa à lei de resfriamento de Newton, aplicando a linguagem de programação Python: estudo da variação de temperatura de um silo de armazenagem de grão.

Abstract

Temperature and humidity are key factors in preserving the quality of grains during storage. In silos, strict control of these variables is essential to ensure the integrity of the final product. This study aims to perform a comparative analysis between the analytical and numerical solutions — using the fourth-order Runge-Kutta method — of the differential equation representing Newton’s Law of Cooling, applied to the context of heating or cooling grains stored in silos. Specifically, the objectives include understanding the concept of Ordinary Differential Equations (ODEs), modeling the thermal behavior of grains based on Newton’s Law, developing a Python-based computational routine to solve the equation analytically and numerically, and comparing the results through graphical analysis. The study also seeks to highlight the practical and pedagogical applicability of ODEs in everyday contexts, such as food cooling and grain storage. The methodology involves collecting thermal data from silos operated by the Maranata agribusiness group, processing the data in a custom routine developed in the VS Code editor, and analyzing the results through simulation-generated graphs.