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Mathematical Modeling and Numerical Approximation of Heat Conduction in Three-Phase-Lag Solid

Author

Listed:
  • Anibal Coronel

    (Departamento de Ciencias Básicas—Centro de Ciencias Exactas CCE-UBB, Facultad de Ciencias, Universidad del Bío-Bío, Chillán 3780000, Chile)

  • Esperanza Lozada

    (Departamento de Ciencias Básicas—Centro de Ciencias Exactas CCE-UBB, Facultad de Ciencias, Universidad del Bío-Bío, Chillán 3780000, Chile)

  • Stefan Berres

    (Núcleo de Investigación en Bioproductos y Materiales Avanzados (BioMA), Universidad Católica de Temuco, Temuco 4813302, Chile)

  • Fernando Huancas

    (Departamento de Matemática, Facultad de Ciencias Naturales, Matemáticas y del Medio Ambiente, Universidad Tecnológica Metropolitana, Las Palmeras 3360, Ñuñoa, Santiago 7750000, Chile)

  • Nicolás Murúa

    (Facultad de Ciencias Empresariales, Universidad del Bío-Bío, Chillán 3780000, Chile)

Abstract

In this article, we propose a mathematical model for one-dimensional heat conduction in a three-layered solid considering that an interfacial condition is present for the temperature and heat flux conditions between the layers. The numerical approach is developed by constructing a finite difference scheme to solve the initial boundary–interface problem. The numerical scheme is designed by considering the accuracy of the model on the inner part of each layer, then extending to the interfaces and boundaries by incorporating the continuous interfacial conditions. The finite difference scheme is unconditionally stable, convergent, and easy to implement since it consists of the solution of two algebraic systems. We provide three numerical examples to confirm that our numerical approximation is consistent with the analytical solution and the physical phenomenon.

Suggested Citation

  • Anibal Coronel & Esperanza Lozada & Stefan Berres & Fernando Huancas & Nicolás Murúa, 2024. "Mathematical Modeling and Numerical Approximation of Heat Conduction in Three-Phase-Lag Solid," Energies, MDPI, vol. 17(11), pages 1-23, May.
    • Handle: RePEc:gam:jeners:v:17:y:2024:i:11:p:2497-:d:1399795
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    References listed on IDEAS

    as
    1. Pim Vercoulen & Soocheol Lee & Xu Han & Wendan Zhang & Yongsung Cho & Jun Pang, 2023. "Carbon-Neutral Steel Production and Its Impact on the Economies of China, Japan, and Korea: A Simulation with E3ME-FTT:Steel," Energies, MDPI, vol. 16(11), pages 1-24, June.
    2. Abram Dorfman & Zachary Renner, 2009. "Conjugate Problems in Convective Heat Transfer: Review," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-27, October.
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    Cited by:

    1. Nicolás Murúa & Aníbal Coronel & Alex Tello & Stefan Berres & Fernando Huancas, 2024. "GPU Accelerating Algorithms for Three-Layered Heat Conduction Simulations," Mathematics, MDPI, vol. 12(22), pages 1-22, November.

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