Inverse Method for Estimation of Thermophysics Properties of a Bimaterials

Abstract:

The aim of this study is to identify simultaneously the thermal conductivity tensor and the volume heat coefficient of a bimaterial (checkerboard) whose heat conduction obeys Fourier's law. This approach is validated by numerical simulation. The simulated temperature fields are obtained by the direct resolution heat conduction solved numerically by the finite element method formulation. To identify parameters, an inverse method is developed by using the finite element temperature approach (FEU-T) model fitting method based on the Levemberg-Marquardt algorithm. We validated the numerical procedure by using noiseless temperature fields at different time and space steps. The influence of the noise on the temperature fields is also studied and shows the efficiency of the inverse method. The results show that this procedure is not very sensitive to the number of elements (or space steps) and the number of time steps.

• Periodical: Key Engineering Materials (Volume 913)
• Pages: 287-291
• DOI: https://doi.org/10.4028/p-fpnf11
• Online since: March 2022
• Authors: Yao Koumekpo*, Kossi Atchonouglo, Jean Christophe Dupre, Arnaud Germaneau, Laëtitia Caille, Edo-Owodou Ayeleh
• Keywords: Bimaterial, Finite Elements, Heat Transfer, Inverse Problem, Thermal Capacity, Thermal Conductivity Tensor

References

[1] J. C.Elliot, C.J. Wood: Rear-surface integral method for calculating thermal diffusivity: finite pulse time correction and two-layer samples, International Journal of Heat and Mass Transfer, 144 (2019) 118609.

DOI: 10.1016/j.ijheatmasstransfer.2019.118609

[2] N. Tao, X. L. Li, and J. G. Sun: Simultaneous measurement of thermal conductivity and heat capacity by flash thermal imaging methods, Review of scientific Instruments 88, 064903 (2017).

DOI: 10.1063/1.4985633

[3] C-C.Ma , S.W. Chang: Analytical exact solutions of heat conduction problems for anisotropic multi-layered media, International Journal of Heat and Mass Transfer 47 (2004) 1643–1655.

DOI: 10.1016/j.ijheatmasstransfer.2003.10.022

[4] E. E. Rassy , Y. Billaud , D. Saury: A direct method for the simultaneous characterization of thermal diffusivities of a bi-layer material consisting of a thin coating deposited on a substrate, Applied Mathematical Modelling 91 (2021) 614–631.

DOI: 10.1016/j.apm.2020.09.049

[5] B. Sawaf and M. N. Ozisik: An inverse analysis to estimate linearly temperature dependent thermal conductivity components and heat capacity of an orthotropic medium, International Journal of Heat and Mass Transfer,38(16), p.3005–3010, (1995).

DOI: 10.1016/0017-9310(95)00044-a

[6] A.Logg, K,-A.Mardal, G.N. Welles: Automated Solution of Differential Equations by the finite Element Method. Springer,(2012).

[7] T. Pottier: Identification paramétrique par recalage de modèles éléments finis couplée à des mesures de champs cinématiques et thermiques, Thèse de l'Université de Savoie,(2010).

[8] A.G. Chavez Castillo , B. Gaume, Y. Rouizi, O. Quéméner, P. Glouannec: Identification of insulating materials thermal properties by inverse method using reduced order model, International Journal of Heat and Mass Transfer 166(5-6): 120683, (2021).

DOI: 10.1016/j.ijheatmasstransfer.2020.120683

[9] K. Atchonouglo, J.-C. Dupré, A. Germaneau and C. Vallée: Numerical identification of the thermal conductivity tensor and the heat capacity per unit volume of an anisotropic material, Mechanics & Industry 20, 603 (2019).

DOI: 10.1051/meca/2019026