An analytical transfer function method to solve inverse heat conduction problems

Fernandes, Ana Paula; Santos, Marcelo Braga dos; Guimarães, Gilmar

doi:10.1016/j.apm.2015.02.012

Cited by 57 publications

(22 citation statements)

References 5 publications

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“…The analysis of inverse problem requires the solution of its corresponding direct problem, which is concerned with the determination of the effect (temperature) from known cause (boundary condition and source term). Although some analytical methods are available for solving the heat conduction equation to establish the relationship between internal temperature and boundary heat flux [15,16,24,48], the analytical solution can hardly be obtained when there exists a nonlinear heat source (temperature-dependent). Fortunately, a number of numerical methods have been employed to deal with such kind of problems [29,31,38,46].…”

Section: Introductionmentioning

confidence: 99%

Determination of the time-dependent reaction coefficient and the heat flux in a nonlinear inverse heat conduction problem

Zhuo

Lesnic

Ismailov

et al. 2018

International Journal of Computer Mathematics

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Diffusion processes with reaction generated by a nonlinear source are commonly encountered in practical applications related to ignition, pyrolysis and polymerization. In such processes, determining the intensity of reaction in time is of crucial importance for control and monitoring purposes. Therefore, this paper is devoted to such an identification problem of determining the time-dependent coefficient of a nonlinear heat source together with the unknown heat flux at an inaccessible boundary of a one-dimensional slab from temperature measurements at two sensor locations in the context of nonlinear transient heat conduction. Local existence and uniqueness results for the inverse coefficient problem are proved when the first three derivatives of the nonlinear source term are Lipschitz continuous functions. Furthermore, the conjugate gradient method (CGM) for separately reconstructing the reaction coefficient and the heat flux is developed. The ill-posedness is overcome by using the discrepancy principle to stop the iteration procedure of CGM when the input data is contaminated with noise. Numerical results show that the inverse solutions are accurate and stable.

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Section: Introductionmentioning

confidence: 99%

Determination of the time-dependent reaction coefficient and the heat flux in a nonlinear inverse heat conduction problem

Zhuo

Lesnic

Ismailov

et al. 2018

International Journal of Computer Mathematics

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“…As mentioned before, the inverse procedure used here is based on the Transfer Function Based on Green's Function (TFBGF) method [13] adapted for heat source estimation. This procedure will be described in this section.…”

Section: The Tfbgf Methodsmentioning

confidence: 99%

“…relation between input and output in the complex variable domain is given by the multiplication shown in (13), that is,…”

Section: X(s) Y(s)mentioning

confidence: 99%

“…Thus, the solution of the inverse problem (in variable ) is obtained in the Laplace domain using (19) or in the time domain using (4) [13]. The input, the heat source ( ) was estimated from the impulse response ( ) and from the temperature measured at any position of the system.…”

Section: (18)mentioning

confidence: 99%

“…This work proposes the estimation of the moving heat source produced during the micromilling process using a modification of the TFBGF technique [13] which is based on analytical solution and transfer function.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of a Moving Heat Source due to a Micromilling Process Using the Modified TFBGF Technique

Ribeiro

Fernandes

Cunha

et al. 2018

Mathematical Problems in Engineering

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Moving heat sources are present in numerous engineering problems as welding and machining processes, heat treatment, or biological heating. In all these cases, the heat input identification represents an important factor in the optimization of the process. The aim of this study is to investigate the heat flux delivered to a workpiece during a micromilling process. The temperature measurements were obtained using a thermocouple at an accessible region of the workpiece surface while micromilling a small channel. The analytical solution is calculated from a 3D transient heat conduction model with a moving heat source, called direct problem. The estimation of the moving heat source uses the Transfer Function Based on Green's Function Method. This method is based on Green's function and the equivalence between thermal and dynamic systems. The technique is simple without iterative processes and extremely fast. From the temperature on accessible regions it is possible to estimate the heat flux by an inverse procedure of the Fast Fourier Transform. A test of micromilling of 6365 aluminium alloy was made and the heat delivered to the workpiece was estimated. The estimation of the heat without use of optimization technique is the great advantage of the technique proposed.

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Neurosurgical Bone Grinding

2019

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An analytical transfer function method to solve inverse heat conduction problems

Cited by 57 publications

References 5 publications

Determination of the time-dependent reaction coefficient and the heat flux in a nonlinear inverse heat conduction problem

Determination of the time-dependent reaction coefficient and the heat flux in a nonlinear inverse heat conduction problem

Estimation of a Moving Heat Source due to a Micromilling Process Using the Modified TFBGF Technique

Neurosurgical Bone Grinding

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