Two-dimensional non-linear inverse heat conduction problem based on the singular value decomposition

García, Juan Andrés Martín; Cabeza, José María Gutiérrez; Rodríguez, Ana Ruiz

doi:10.1016/j.ijthermalsci.2008.09.002

Cited by 31 publications

(7 citation statements)

References 18 publications

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“…China. 2 School of Materials Science and Engineering, Henan Polytechnic University, Jiaozuo, 454003, P.R. China.…”

Section: Competing Interestsmentioning

confidence: 99%

Modified characteristics projection finite element method for time-dependent conduction-convection problems

2015

Bound Value Probl

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In this paper, we give a modified characteristics projection finite element method for the time-dependent conduction-convection problems, which is gotten by combining the modified characteristics finite element method and the projection method. The stability and the error analysis shows that our method is stable and has optimal convergence order. In order to show the effect of our method, some numerical results are presented. From the numerical results, we can see that the modified characteristics projection finite element method can simulate the fluid field, temperature field, and pressure field very well. MSC: 76M10; 65N12; 65N30; 35K61

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“…China. 2 School of Materials Science and Engineering, Henan Polytechnic University, Jiaozuo, 454003, P.R. China.…”

Section: Competing Interestsmentioning

confidence: 99%

Modified characteristics projection finite element method for time-dependent conduction-convection problems

2015

Bound Value Probl

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“…h , which are hoped to be better solutions of the problems. In order to obtain the equations for u 1 h , p 1 h , T 1 h , we use the residual equation 3.2 to rewrite the linear problems 3.3 ; we obtain…”

Section: 3mentioning

confidence: 99%

A Defect‐Correction Mixed Finite Element Method for Stationary Conduction‐Convection Problems

2011

Mathematical Problems in Engineering

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A defect-correction mixed finite element method (MFEM) for solving the stationary conduction-convection problems in two-dimension is given. In this method, we solve the nonlinear equations with an added artificial viscosity term on a grid and correct this solution on the same grid using a linearized defect-correction technique. The stability is given and the error analysis inL2andH1-norm ofu,Tand theL2-norm ofpare derived. The theory analysis shows that our method is stable and has a good precision. Some numerical results are also given, which show that the defect-correction MFEM is highly efficient for the stationary conduction-convection problems.

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“…To overcome this critical task, unavoidably embedded in the inverse problem, several methods established on the processing of the experimental measurements have been proposed and validated in literature [1]. Between the most employed procedure, the Truncated Singular Value Decomposition (TSVD) has shown robust regularization performance to solve IHCP in steady [5] and transient regimes [6]. The stabilizing effect of this technique is based on the removal of the highest modes of the input signal [7].…”

Section: Introductionmentioning

confidence: 99%

Boundary element method for contactless estimation of spatially varying internal heat transfer coefficient in circular pipes

Aimi

Bozzoli

Cattani

et al. 2023

J. Phys.: Conf. Ser.

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In the present study it is proposed a solution approach of the Inverse Heat Conduction Problem (IHCP) intended at assessing the local heat transfer coefficient on the inner wall of a tube, under a forced convection problem. The estimation method is established on the Boundary Element Method (BEM) combined with the Truncated Singular Value Decomposition (TSVD) methodology, employed to manage the ill-conditioned nature of the problem. The numerical results of the direct problem, built by the BEM, are firstly validated, and consequently adopted as synthetic data inputs to resolve the IHCP and corroborate the whole assessment procedure. This approach is also tested with experimental data about forced convection problem in coiled pipes. In these geometries, the convective heat transfer coefficient changes considerably along the wall periphery and for this reason, it constitutes a perfect example to test the ability of the presented method to infer a spatially varying internal heat transfer coefficient distribution.

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Two-dimensional non-linear inverse heat conduction problem based on the singular value decomposition

Cited by 31 publications

References 18 publications

Modified characteristics projection finite element method for time-dependent conduction-convection problems

Modified characteristics projection finite element method for time-dependent conduction-convection problems

A Defect‐Correction Mixed Finite Element Method for Stationary Conduction‐Convection Problems

Boundary element method for contactless estimation of spatially varying internal heat transfer coefficient in circular pipes

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