Soluções da equação de difusão de calor em regime transiente: Aprendendo matemática com diferentes métodos de solução

Abstract

Problems involving the dynamics of heating or cooling physical systems submitted to boundary conditions are of great importance in a wide range of technological applications. Transient solutions to the heat diffusion equation, for a series of physical systems, are given by infinity series of analytical functions, which makes the analysis of the various aspects of the solution a not easy task. This work provides solutions to the heat diffusion equation in one-dimensional and homogenous systems when submitted to certain boundary conditions. The influence of the boundary conditions on the temporal evolution of the system is explained and some aspects of the solutions are discussed. By comparison of “apparently” different results obtained by using different mathematical methods, some identities are obtained, proved analytically, or verified using computational help. Also we discuss the possibility to analyze more complex systems by using the present results.