Construction of a Mathematical Model derived from the coupling of Newton's Cooling Modeland Linear Expansion

Abstract

This work is the result of the results of a research carried out by the Institutional Program for Scientific Initiation Scholarships (PIBIC), which aimed to determine a mathematical model that would allow the calculation of the time that a given material, expanded in x unit of measurement, took to return to its initial length, after removing the heat source that heats it and leaving it in contact only with the ambient temperature. The proposal was to describe, in a single model, the relationship between the variables time, temperature and length. For that, we tried to couple the linear expansion model to
Newton's cooling model. In carrying out this study, we opted to follow the experimental research method. Initially, it was analyzed whether the material used in the experiments satisfied Newton's cooling law, then we tried to couple the two models mentioned above and, finally, the validation of the model found from the experiments carried out. From the analysis of the data obtained in the
experiments, it was found that the numerical simulations performed presented a good approximation of the real situation. The result of this research (model found) can be a starting point for other research that aims to study the expansion constants of different types of concrete.