Equação do calor unidimensional: resolução analítica e computacional

Abstract

In this work, the objective was to carry out a study about a thin rod heat flux problem, applying analytical and numerical solving methods to obtain the solution of the partial differential equation (PDE) that governs the boundary value problem (BVP) analyzed and, thus, make comparisons between the results found. The BVP in question deals with the conduction of heat in a thin heated rod with an initial temperature along its entire length whose ends are kept at zero temperature. This problem is described by a linear second-order parabolic PDE called the one-dimensional heat equation, which determines the change in temperature in a medium over time. To determine the analytical solution of BVP, the variable separation method was used, as for the numerical solution, the finite difference method (FDM) was used, replacing the derivatives of the original equation by finite difference formulas, generating a system of algebraic equations. Based on the solutions obtained, the efficiency of the numerical method was verified by comparing the analytical results with the numerical ones and finding a low relative error between them.