SOLUTION OF THE DIFFUSION EQUATION: APPLICATIONS IN MODELING HEAT DIFFUSION IN SOIL

Authors

DOI:

https://doi.org/10.21575/25254782rmetg2026vol11n12437

Keywords:

Heat equation, Duhamel’s principle, Green’s function, Soil heat conduction

Abstract

This work presents an alternative approach for solving an initial and boundary value problem related to the one-dimensional non-homogeneous diffusion equation with constant coefficients, applied to soil heat conduction. Unlike the traditional Fourier variable separation method, the proposed approach is based on the fundamental solution (Green’s function), the antisymmetric extension of the initial condition, and Duhamel’s and superposition principles. The methodology involves analyzing the Cauchy problem for the heat equation in unbounded and semi-infinite domains, employing techniques of variable transformation and integration. Preliminary results indicate that this technique can be effectively applied in future studies on ground-air heat exchangers, aiming at thermal comfort in enclosed environments. This study represents an important initial step toward developing more efficient and accurate solutions to describe soil thermal behavior.

Author Biographies

  • Felipe Matheus Mendes Barbosa, Federal University of Pelotas

    Undergraduate student in Mathematics  at the Federal University of Pelotas (UFPel).

  • Elisiane Cogoy da Silva, Federal University of Pelotas

    She holds a Master’s degree in Mathematical Modeling from UFPel (2024) and has academic training in Mathematics and Pedagogy, with several educational specializations. She has been teaching Mathematics in primary and secondary schools since 2010, working in public and private institutions in Rio Grande do Sul. Since 2024, she has been a member of the INSPIRA research group (UNIPAMPA), focusing on pedagogical practices and Mathematics education.

  • Leslie Darien Pérez-Fernández, Federal University of Pelotas

    He holds a B.Sc. (2001) and M.Sc. (2006) in Mathematics from the University of Havana and a Ph.D. from the Institute of Cybernetics, Mathematics and Physics (2010). He has received awards from the Cuban Academy of Sciences and the Agency of Nuclear Energy and Advanced Technologies. Since 2013, he has been a professor at UFPel and, since 2015, a permanent faculty member of the Graduate Program in Mathematical Modeling. His research focuses on multiscale modeling and simulation of physical and biological phenomena, particularly asymptotic and variational homogenization methods.

  • Ruth da Silva Brum, Federal University of Pelotas

    She is an Associate Professor at the Federal University of Pelotas. With a background in Mathematics, her work spans applied mathematics, engineering, and special education. She holds an M.Sc. in Computational Modeling (FURG), a Ph.D. in Mechanical Engineering (UFRGS), and a postdoctoral fellowship from INSA Toulouse.

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Published

2025-12-15

Issue

Vol. 10 No. 4 (2025): Edição Especial do XII ERMAC RS

Section

Edição Especial do XII ERMAC RS

License

Copyright (c) 2025 Felipe Matheus Mendes Barbosa, Elisiane Cogoy da Silva, Leslie Darien Pérez-Fernández, Ruth da Silva Brum

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This work is licensed under a Creative Commons Attribution 3.0 Unported License.

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