Mathematical Modeling and Numerical Approximation of Heat Conduction in Three-Phase-Lag Solid
Date
Authors
Coronel, Aníbal
Lozada, Esperanza
Berres, Stefan
Huancas, Fernando
Murúa, Nicolás
Lozada, Esperanza
Berres, Stefan
Huancas, Fernando
Murúa, Nicolás
Authors
Date
Datos de publicación:
10.3390/en17112497
Keywords
Finite Difference Method - Heat Conduction - Second-order Finite Difference Scheme - Unconditional Numerical Method - Finite Difference Method - Heat Conduction - Heat Flux - Finite Difference Scheme - Finite-difference Methods - Interfacial Conditions - Model Approximations - Numerical Approximations - Second Orders - Second-order Finite Difference Scheme - Three Phase - Three Phasis - Unconditional Numerical Method - Numerical Methods
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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. © 2024 Elsevier B.V., All rights reserved.
Description
Keywords
Finite Difference Method , Heat Conduction , Second-order Finite Difference Scheme , Unconditional Numerical Method , Finite Difference Method , Heat Conduction , Heat Flux , Finite Difference Scheme , Finite-difference Methods , Interfacial Conditions , Model Approximations , Numerical Approximations , Second Orders , Second-order Finite Difference Scheme , Three Phase , Three Phasis , Unconditional Numerical Method , Numerical Methods
Citation
10.3390/en17112497