Transient solutions to the heat diffusion equation: Learning mathematic from different solution methods

Transient solutions to the heat diffusion equation: Learning mathematic from different solution methods

Authors

  • Verissimo Manoel de Aquino Universidade Estadual de Londrina
  • Hiromi Iwamoto Universidade Estadual de Londrina
  • Guilherme Augusto Lisboa Nogueira Universidade Estadual de Londrina
  • Ladislau Vieira Teixeira Tavares Universidade estadual de Londrina

DOI:

https://doi.org/10.5433/1679-0375.2016v37n1p13

Keywords:

Transient solutions, Heat diffusion, Series solutions

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.

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Author Biographies

Verissimo Manoel de Aquino, Universidade Estadual de Londrina

Docente do Departamento de Física

Hiromi Iwamoto, Universidade Estadual de Londrina

Docente aposentada do Departamento de Física

Guilherme Augusto Lisboa Nogueira, Universidade Estadual de Londrina

Estudante de graduação do Departamento de Física

Ladislau Vieira Teixeira Tavares, Universidade estadual de Londrina

Estudante de graduação do Departamento de Física

Published

2016-03-16

How to Cite

Aquino, V. M. de, Iwamoto, H., Nogueira, G. A. L., & Tavares, L. V. T. (2016). Transient solutions to the heat diffusion equation: Learning mathematic from different solution methods. Semina: Ciências Exatas E Tecnológicas, 37(1), 13–22. https://doi.org/10.5433/1679-0375.2016v37n1p13

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Original Article
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