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

Anibal Coronel, Esperanza Lozada (), Stefan Berres, Fernando Huancas and Nicolás Murúa
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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

Energies, 2024, vol. 17, issue 11, 1-23

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.

Keywords: heat conduction; finite difference method; unconditional numerical method; second-order finite difference scheme (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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