An iterative finite-element algorithm for solving two-dimensional nonlinear inverse heat conduction problems. (November 2018)

• Record Type: Journal Article
• Authors: Bergagio, Mattia; Li, Haipeng; Anglart, Henryk
• Is Part Of: International journal of heat and mass transfer. Volume 126(2018)Part A
• Page Start: 281
• Page End: 292
• Publication Date: 2018-11
• Subjects: Two-dimensional nonlinear inverse heat conduction problem -- Tikhonov regularization -- Finite element -- FEniCS -- Adjoint -- Conjugate gradient; Heat -- Transmission -- Periodicals; Mass transfer -- Periodicals; Chaleur -- Transmission -- Périodiques; Transfert de masse -- Périodiques; Electronic journals; 621.4022
• DOI: 10.1016/j.ijheatmasstransfer.2018.04.104
• Languages: English
• ISSNs: 0017-9310

Abstract

Highlights: An effective method for solving transient nonlinear inverse heat conduction problems on two-dimensional domains is implemented. The corresponding objective function is minimized using the conjugate gradient method with an adjoint problem. Tikhonov regularization is introduced to increase the stability of the reconstructed temperature field. Good agreement between the solutions to the direct and inverse problems. Robustness of the method to random errors and mesh independence of the results are verified. Abstract: It is often useful to determine temperature and heat flux in multidimensional solid domains of arbitrary shape with inaccessible boundaries. In this study, an effective algorithm for solving boundary inverse heat conduction problems (IHCPs) is implemented: transient temperatures on inaccessible boundaries are estimated from redundant simulated measurements on accessible boundaries. A nonlinear heat equation is considered, where some of the material properties are dependent on temperature. The IHCP is reformulated as an optimization problem. The resulting functional is iteratively minimized using a conjugate gradient method together with an adjoint (dual) problem approach. The associated partial differential equations are solved using the finite-element package FEniCS. Tikhonov regularization is introduced to mitigate the ill-posedness of the IHCP. The accuracy of the implemented algorithm is assessed by comparing the solutions to the IHCP with the correct temperature values, on the inaccessible boundaries. The robustness of our method is tested by adding Gaussian noise to the initial conditions and redundant boundary data in the inverse problem formulation. A mesh independence study is performed.