Time Traveling Regularization for Inverse Heat Transfer Problems

Magalhães, Elisan dos Santos; Anselmo, Bruno de Campos Salles; Silva, Ana Lúcia Fernandes de Lima e; Silva, Sandro Metrevelle Marcondes de Lima e

doi:10.3390/en11030507

Cited by 9 publications

(3 citation statements)

References 26 publications

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“…The QOM developed by Magalhães [26] is an optimization method that allows for the assessment of more than one variable concurrently by minimizing an objective function (F) given by the sum of squares of the difference between the simulated (T') and reference (T) temperatures. Moreover, F is minimized in a future time step rather than the present one to increase F sensitivity through the Future Time Regularization (FTR) [32]. This regularization technique expands the Function Specification Method developed by Beck et al [33].…”

Section: The Inverse Problemmentioning

confidence: 99%

Numerical Estimation of Nonlinear Thermal Conductivity of SAE 1020 Steel

de Oliveira,

Magalhães,

Zilnyk

et al. 2024

Computation

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Thermally characterizing high-thermal conductivity materials is challenging, especially considering high temperatures. However, the modeling of heat transfer processes requires specific material information. The present study addresses an inverse approach to estimate the thermal conductivity of SAE 1020 relative to temperature during an autogenous LASER Beam Welding (LBW) experiment. The temperature profile during LBW is computed with the aid of an in-house CUDA-C algorithm. Here, the governing three-dimensional heat diffusion equation is discretized through the Finite Volume Method (FVM) and solved using the Successive Over-Relaxation (SOR) parallelized iterative solver. With temperature information, one may employ a minimization procedure to assess thermal properties or process parameters. In this work, the Quadrilateral Optimization Method (QOM) is applied to perform estimations because it allows for the simultaneous optimization of variables with no quantity restriction and renders the assessment of parameters in unsteady states valid, thereby preventing the requirement for steady-state experiments. We extended QOM’s prior applicability to account for more parameters concurrently. In Case I, the optimization of the three parameters that compose the second-degree polynomial function model of thermal conductivity is performed. In Case II, the heat distribution model’s gross heat rate (Ω) is also estimated in addition to the previous parameters. Ω [W] quantifies the power the sample receives and is related to the process’s efficiency. The method’s suitability for estimating the parameters was confirmed by investigating the reduced sensitivity coefficients, while the method’s stability was corroborated by performing the estimates with noisy data. There is a good agreement between the reference and estimated values. Hence, this study introduces a proper methodology for estimating a temperature-dependent thermal property and an LBW parameter. As the performance of the present algorithm is increased using parallel computation, a pondered solution between estimation reliability and computational cost is achieved.

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Section: The Inverse Problemmentioning

confidence: 99%

Numerical Estimation of Nonlinear Thermal Conductivity of SAE 1020 Steel

de Oliveira,

Magalhães,

Zilnyk

et al. 2024

Computation

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“…There are various methods to compute the IHCP solution [47,48]. The classical sequential function specification method (SFSM) is chosen because of its efficiency in solving linear inverse problems, having simpler programming and lower computational cost when compared to non-linear sequential methods [49].…”

Section: Heat Flux Estimationmentioning

confidence: 99%

Contact resistance analysis applied to simultaneous estimation of thermal properties of metals

Ramos

Carollo

Silva

2020

Meas. Sci. Technol.

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This work aims to present a method for simultaneously estimating the thermal conductivity, k, and specific heat, c p , in samples of stainless steel 304 and cemented carbide by accounting the imperfect thermal contact at the heater-sample interface. A transient one-dimensional heat conduction model with constant thermal properties is used. The metallic sample is placed in the middle of a polyimide heater and a thermal insulator. A constant heat flux is applied on the specimen upside surface and a thermal insulation condition is maintained on the opposing surface, where a type T thermocouple measures the temperature response. Contact resistance is determined and accounted for as a reducing factor on heat flux. Instead of considering a lumped model, a microscopic approach of the contacting regions is used to describe both the surface roughness and the fluid gap. With the intention of guaranteeing simultaneous and reliable estimates for both thermal properties, sensitivity analysis is used to establish heat flux intensity, experiment duration, time step for data acquisition, and other characteristics of the experiments. To simultaneously achieve both thermal properties, the optimization method BFGS (Broyden-Fletcher-Goldfarb-Shanno) is employed to minimize a least-squares objective function comparing experientially measured and numerically calculated temperatures. The numerical solution for the transient conduction problem is determined with COMSOL, which solves the transient heat diffusion problem by discretizing it applying the finite element method (FEM). The linear system of equations is solved using the PARDISO solver and backward differentiation formula (BDF) method. Heat flux is estimated employing the sequential function specification method (SFSM) as a means of verifying the robustness of parameter estimation and experimental procedure. Moreover, uncertainty analysis is performed to confirm the quality of the results obtained. Finally, the uncertainty analysis outcomes and thermal properties estimated are compared with literature.

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“…Inverse heat transfer problem (IHTP) uses limited measurable temperature information as input to estimate the unknown temperature, heat flux, heat source, geometry, or thermal properties of a heat transfer system. IHTP has been applied widely in engineering [16][17][18][19][20][21][22][23][24], however, it is difficult to solve because it is a classical ill-posed problem, which indicates any small disturbances in the input data may result in large fluctuations and errors in the estimated results. Many valuable methods have been developed for the solution of IHTP [9,17,19,[24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Estimation of the Time-Varying High-Intensity Heat Flux for a Two-Layer Hollow Cylinder

et al. 2018

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Gun barrels are subjected to time-varying high-intensity heat flux under multiple firing, which may damage the material and limit the overall performance of the gun. In order to monitor the thermal state of a gun barrel, an inverse method coupling the finite difference method with the sequential function specification method was developed to estimate the unknown time-varying heat flux imposed on the inner wall of a gun barrel. A two-layer hollow cylindrical tube was assumed with the convection heat transfer boundary condition on the outer wall of the tube. A direct heat transfer model was developed, and was used to estimate the temporal distribution of boundary heat flux in approximately real time based on the measured transient temperature at some positions on the outer wall of the gun barrel. Numerical tests were performed to verify the effectiveness and reliability of this method by investigating the influence of temperature measurement noises and future time step selection. The results show that the proposed method has high precision and efficiency in extracting the time-varying heat flux under one-shot and three-shot firing conditions. When there is a measurement noise, this method has good anti-illness characteristics and can achieve better results by appropriately selecting the value of a future time step.

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Time Traveling Regularization for Inverse Heat Transfer Problems

Cited by 9 publications

References 26 publications

Numerical Estimation of Nonlinear Thermal Conductivity of SAE 1020 Steel

Numerical Estimation of Nonlinear Thermal Conductivity of SAE 1020 Steel

Contact resistance analysis applied to simultaneous estimation of thermal properties of metals

Estimation of the Time-Varying High-Intensity Heat Flux for a Two-Layer Hollow Cylinder

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