A laboratory practice for partial differential equations: conducting heat in a copper bar

Abstract

Considering that practical classes make the teaching and learning process more pleasant and meaningful, as well as, seeking to propose to students a better understanding of the subject partial differential equations, in this work an experiment was carried out involving laboratory tests and the use of differential equations. The research in question addresses a problem of heat conduction, which was developed in two moments, the first was a laboratory test where the heating of a copper bar was carried out. The second analysis of the problem was approached analytically by the mathematical modeling of the heat conduction function, which was obtained by the partial differential equation that describes the heat flow in a bar. Thus, the work, in particular, consists of the thermal study of a copper bar whose ends were isolated, and during the test the bar was initially heated and then cooled to room temperature, thus comparing the empirical and analytical methods. To collect data in the laboratory, temperature sensors were used, and to obtain the results using the heat conduction equation, a Maple computational tool was used. In possession of the results, analyzes of the results and behavior were made, with the aid of Tables and Graphs. The results obtained were satisfactory, with significant similarities between both experiments, thus implying the feasibility of applying the practical task in the development of the discipline.