Equação do calor bidimensional com condições de contorno de Neumann: soluções analítica e numérica

• Main Author: Brito, Leandro Wrzecionek de
• Publication Date: 2024
• Format: Bachelor thesis
• Language: por
• Source: Repositório Institucional da UTFPR (da Universidade Tecnológica Federal do Paraná (RIUT))
• Download full: http://repositorio.utfpr.edu.br/jspui/handle/1/35839
• topic: Equações diferenciais parciais; Equação de calor; Problemas de valores de contorno; Differential equations, Partial; Heat equation; Boundary value problems; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this article, we addressed the two-dimensional heat equation with Neumann boundary conditions, which describes the diffusion of heat through a solid. This equation holds significant importance in projects involving thermal systems. We performed the algebraic derivation of the equation, and subsequently, obtained both analytical and numerical solutions. The analytical solution was obtained using the method of separation of variables. On the other hand, to obtain the numerical solution, we applied the Finite Difference Method, which was initially utilized by Leonhard Euler (1707 – 1783) and is widely used in numerical simulations. The results achieved, both numerical and analytical, were implemented using the Python programming language. Finally, we conducted an analysis of the solution through 2D graphs and evaluated the relative error. We conclude that the numerical solution provides a good approximation to the analytical solution.