Modelagem numérica da condução de calor com condutividade térmica dependente da temperatura utilizando python

Abstract

Thermal conductivity is a physical property that represents the ability of a material to conduct heat. In many heat transfer problems, this property is treated as constant due to mathematical simplification, although it may vary with the material temperature. In this work, a numerical methodology was developed to determine thermal conductivity as a function of temperature, considering one-dimensional steady-state heat conduction. The analysis was applied to three metallic materials: copper, aluminum, and brass. For this purpose, the governing equation was discretized using the Finite Difference Method, and the parameters of the 𝑘(𝑇) models were adjusted using deterministic and heuristic optimization methods. Linear, exponential, and quadratic models were evaluated using the Levenberg-Marquardt, Differential Evolution, and Dual Annealing methods. The results allowed the estimation of the coefficients of temperature-dependent thermal conductivity models and the comparison of the performance of the applied models and methods. It was verified that the proposed objectives were achieved, since the developed methodology was able to represent experimental temperature profiles and evaluate the consistency of the adjusted models for the materials studied.