Inverse Heat Transfer Problems

Alifanov, O. M.

doi:10.1007/978-3-642-76436-3

Cited by 845 publications

(572 citation statements)

References 32 publications

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“…These include Tikhonov Regularisation [13], the LevenbergMarquardt method [14,15], the Beck Sequential Function Specification method [16,17], and the Alifanov Iterative Regularisation method [18,19]. Ozisik and Orlande [9] provide a more complete classification of the various solution techniques.…”

Section: Inverse Solution Methodsmentioning

confidence: 99%

“…Alifanov's solution methodology is composed of the following different steps. The first step in the solution methodology is to re-state the inverse problem as an extremal statement [18]. This extremal formulation is used as an optimisation criterion.…”

Section: Alifanov Iterative Regularisation Methodsmentioning

confidence: 99%

“…The solution to the direct problem is denoted T (Ω, t; q), calculated using a given (estimated) value of q (Λ i , t). The inverse problem can be stated as follows [20,18]: find q (Λ i , t) such that:…”

Section: Inverse Problemmentioning

confidence: 99%

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Inverse estimate of heat flux on a plasma discharge tube to steady-state conditions using thermocouple data and a radiation boundary condition

Faoite¹,

Browne²,

Gamboa³

et al. 2014

International Journal of Heat and Mass Transfer

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The heat flux incident upon the inner surface of a plasma discharge tube during a helicon plasma discharge was estimated using an inverse method. Temperature readings were taken from the outer surface of the tube using thermocouples, and the temperature data were interpolated over the tube surface. A numerical inverse procedure based on the Alifanov iterative regularisation method was used to reconstruct the heat flux on the tube inner surface as a function of space and time. In contrast to previously-used inverse models for this application, the current model implements a thermal radiation boundary condition to realistically model the energy exchange in the device. Additionally in these experiments, steady-state operation was reached, and the accurate modelling of the steady-state condition was facilitated by the thermal radiation boundary condition. The variation of heat flux with helicon discharge power, propellant flowrate, and electromagnet current was studied, and it was found that the waste heat flux increased with applied RF power and propellant flowrate, and decreased with current supplied to the electromagnets, over the range of parameter variation tested.

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Section: Inverse Solution Methodsmentioning

confidence: 99%

Section: Alifanov Iterative Regularisation Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Inverse estimate of heat flux on a plasma discharge tube to steady-state conditions using thermocouple data and a radiation boundary condition

Faoite¹,

Browne²,

Gamboa³

et al. 2014

International Journal of Heat and Mass Transfer

View full text Add to dashboard Cite

show abstract

“…[1], [3], [5], [6] and the references therein). The conjugate gradient method (CGM) as an iterative solution algorithm is itself a regularization method where the iteration index plays the role of the regularization parameter.…”

Section: Statement Of the Problemmentioning

confidence: 99%

Multidimensional Inverse Heat Conduction Calculations

Reinhardt¹,

Frohne

Suttmeier

et al. 2006

Proc Appl Math and Mech

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Inverse Heat Conduction Problems (IHCPs) have been extensively studied over the last 50 years. They have numerous applications in many branches of science and technology. The problem consists in determining the temperature and heat flux at inaccessible parts of the boundary of a 2-or 3-dimensional body from corresponding data -called 'Cauchy data' -from accessible parts of the boundary. It is well-known that IHCPs are illposed which means that small perturbations in the data may cause large errors in the solution.In this contribution we give a short overview over our contributions to multidimensional IHCP's and indicate what computational results for which sort of problems we have obtained. Statement of the problemIn [4] we have established the theoretical background for multidimensional inverse heat conduction problems. In this contribution, we outline and refer to several of our 2-d. calculations.The importance of inverse heat conduction problems and appropriate solution algorithms are established in numerous works (see, e.g. In a 2-d. IHCP we want to determine the temperature and the heat flux on an inaccessible part of the boundary of a 2-d. domain from corresponding data on another (accessible) part (s. Fig. 1). The data on the latter are called Cauchy data. The underlying problem is the heat equation which can have the more general form studied in [4]. The solutions of the associated direct problem as well as the inverse problem are understood in weak sense (see [4]). This allows the Cauchy data to be only from L 2 . The initial condition can be given or not. In the latter case, our method is also able to identify the initial temperature distribution.The idea of our method is very simple: since the initial condition v 0 and the heat flux v 1 = ∂u/∂N | S 2 at the inaccessible part Γ 2 of the boundary are not known, we consider them as a control v = (v 0 , v 1 ) to minimize the defecton the accessible part of Γ 1 of the boundary; here, we set S i = Γ i × (0, T ], i = 1, 2, where T > 0 is the final time. In [4] we have proved the existence of the optimal control, and also obtained the gradient of the defect functional by means of an appropriate adjoint problem. Since the optimal control problem is still unstable, we have to use a regularization method for it. RegularizationWe solve the underlying inverse problem by discretization in combination with Tikhonov's regularization using a zeroth order penalty term as well as iterative regularization via an appropriate stopping rule.As the underlying operator we choose the Neumann-to-Dirichlet mapping A :which maps the (unknown) initial function v 0 and the heat flux v 1 = ∂u/∂N |S 2 to u| S 1 where u is the solution of the heat equation in weak form.The minimizing functional to determine v = (v 0 , v 1 ),is differentiable with gradient

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“…Such account inevitably leads to the necessity of solving inverse heat conduction problems [18], as well as to the problems of eliminating (correction) the impact of measuring system instrumental function. It should be noted that methods of inverse problems solution for processing signals of the dynamic weight and pressure measurements are used for a long time and more often than in the interpretation of thermocouple signals.…”

Section: Introductionmentioning

confidence: 99%