An approximate method to estimate thermal expansion in solid materials

Authors

  • Brandon Smith Martínez Costa LSRE-LCM – Laboratory of Separation and Reaction Engineering – Laboratory of Catalysis and Materials, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal https://orcid.org/0000-0002-4834-7711

DOI:

https://doi.org/10.22481/intermaths.v6i1.16934

Abstract

We study an approximate method to estimate linear, surface and volumetric thermal expansion in solid materials. For the development of this method, we rely on the theorem of the real numerical value (TRNV), where the linear, surface and volumetric measurements are interpreted as a derivable function in a real variable. Finally, we compare the numerical stability of the approximate method with respect to the common thermal expansion models.

Downloads

Download data is not yet available.

References

Ries, L. K., Padilha, J. B. ., Bortoluzzi, A. P. ., & Zeitune, A. F. . (2023). “Aplicações da Matemática na Engenharia: obtenção da equação de efciência de motores elétricos utilizando o método dos mínimos quadrados”. Intermaths, 4(1), 67-77. https://doi.org/10.22481/intermaths.v4i1.12102

Hsieh, C. L., & Tuan, W. H. (2007). “Thermal expansion behavior of a model ceramic–metal composite”. Materials Science & Engineering, 460(461), 453–458. https://doi.org/10.1016/j.msea.2007.01.109

Lenain, G. E., McKinstry, H. A., Alamo, J., & Agrawal, D. K. (1987). “Structural model for thermal expansion in MZr2P3O12 (M=Li, Na, K, Rb, Cs)”. Journal of Materials Science, 22(1), 17–22. https://doi.org/10.1007/bf01160546

Jinghui, D., Zhen, W., Tangzhen, W., & Xiaohui, R. (2024). “Thermal expansion behaviors of sandwich structures reinforced by carbon nanotubes using an improved higher-order model”. Arch Appl Mech, 94(4), 1099–1119. https://doi.org/10.1007/s00419-024-02569-7

Dugdale, J. S., & MacDonald, C. (1953). “The Thermal Expansion of Solids”. Physical Review, 89(4), 832–834. https://doi.org/10.1103/physrev.89.832

Novikova, S. I. (1974). Thermal expansion of solids. Moscow Izdatel Nauka. https://ui.adsabs.harvard.edu/abs/1974MoIzN.........N/abstract

Young, H. D, & Freedman, R.A. University Physics Volumen 1 (Pearson Educación, 2009), pp. 576-578.

Martínez Costa., B. S. (2018). “Teorema del valor numérico real de un polinomio en función a las derivadas de orden superior”. MATUA, pp. 29-35 5(1). Available in: https://revistas.uniatlantico.edu.co/index.php/MATUA/article/view/2020. ‌

Thompson, D. (1996). “A simple model of thermal expansion”. European Journal of Physics, 17(2), 85. https://doi.org/10.1088/0143-0807/17/2/009

Martínez Costa., B. S., (2019). Teorema del Valor Numérico Real: introducción y aplicaciones básicas. Editorial Académica Española, pp. 25-37, ISBN-10 6139466164.

Miller, W., Smith, C. W., Mackenzie, D. S., & Evans, K. E. (2009). “Negative thermal expansion: a review. Journal of Materials Science”, 44(20), 5441–5451. ttps://doi.org/10.1007/s10853-009-3692-4

Barrera, G. D., Bruno, J. A. O., Barron, T. H. K., & Allan, N. L. (2005). “Negative thermal expansion”. Journal of Physics: Condensed Matter, 17(4), R217–R252. https://doi.org/10.1088/0953-8984/17/4/r03

D.R. Jackett, T.J. McDougall, M.H. England, A.C. (2000). “Thermal expansion in ocean and coupled general circulation models”. Journal of Climate 13, 1384–1405. https://doi.org/10.1175/1520-0442(2000)013<1384:TEIOAC>2.0.CO;2

Downloads

Published

2025-10-30

How to Cite

MARTÍNEZ COSTA, Brandon Smith. An approximate method to estimate thermal expansion in solid materials . INTERMATHS, Vitória da Conquista, v. 6, n. 1, p. 64–74, 2025. DOI: 10.22481/intermaths.v6i1.16934. Disponível em: https://periodicos2.uesb.br/intermaths/article/view/16934. Acesso em: 19 may. 2026.

Issue

Section

Artigos