New Thermal-Conductivity Constitutive Matrix in Fourier’s Law for Heat Transfer Using the Cell Method

González-Domínguez, Pablo Ignacio; Monzón-Verona, José Miguel; García-Alonso, Santiago

doi:10.3390/app9214521

Open AccessArticle

New Thermal-Conductivity Constitutive Matrix in Fourier’s Law for Heat Transfer Using the Cell Method

by

Pablo Ignacio González-Domínguez

^1,2,*,

José Miguel Monzón-Verona

^1,2 and

Santiago García-Alonso

³

¹

Electrical Engineering Department, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain

²

Institute for Applied Microelectronics (IUMA), University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain

³

Department of Electronic Engineering and Automatics (DIEA), University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain

^*

Author to whom correspondence should be addressed.

Appl. Sci. 2019, 9(21), 4521; https://doi.org/10.3390/app9214521

Submission received: 3 October 2019 / Revised: 22 October 2019 / Accepted: 23 October 2019 / Published: 24 October 2019

(This article belongs to the Special Issue Heat and Mass Transfer: Fundamentals and Applications in Thermal Energy)

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Abstract

In this paper, a new constitutive matrix

[M_{τ}]

for thermal conduction, for tetrahedral meshes, in a steady state thermal regime is developed through a new algebraic methodology, using the Cell Method as a computational method, which is included in the finite formulation. The constitutive matrix defines the behavior of solids when they are under a thermal potential. The results are compared with those obtained for the same problem by means of the constitutive matrix

[M_{λ}]

developed previously, taking in both cases with a 2D axisymmetric model as reference, calculated with the finite element method. The errors obtained with the new matrix

[M_{τ}]

are of the order of 0.0025%, much lower than those obtained with the matrix

[M_{λ}]

.

Keywords: analytical method; computational technique; cell method; FEM; heat conduction; thermal constitutive matrix

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MDPI and ACS Style

González-Domínguez, P.I.; Monzón-Verona, J.M.; García-Alonso, S. New Thermal-Conductivity Constitutive Matrix in Fourier’s Law for Heat Transfer Using the Cell Method. Appl. Sci. 2019, 9, 4521. https://doi.org/10.3390/app9214521

AMA Style

González-Domínguez PI, Monzón-Verona JM, García-Alonso S. New Thermal-Conductivity Constitutive Matrix in Fourier’s Law for Heat Transfer Using the Cell Method. Applied Sciences. 2019; 9(21):4521. https://doi.org/10.3390/app9214521

Chicago/Turabian Style

González-Domínguez, Pablo Ignacio, José Miguel Monzón-Verona, and Santiago García-Alonso. 2019. "New Thermal-Conductivity Constitutive Matrix in Fourier’s Law for Heat Transfer Using the Cell Method" Applied Sciences 9, no. 21: 4521. https://doi.org/10.3390/app9214521

APA Style

González-Domínguez, P. I., Monzón-Verona, J. M., & García-Alonso, S. (2019). New Thermal-Conductivity Constitutive Matrix in Fourier’s Law for Heat Transfer Using the Cell Method. Applied Sciences, 9(21), 4521. https://doi.org/10.3390/app9214521

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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New Thermal-Conductivity Constitutive Matrix in Fourier’s Law for Heat Transfer Using the Cell Method

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