An inverse method for estimation of the initial temperature profile and its evolution in polymer processing

Nguyen, K. T.; Prystay, M.

doi:10.1016/s0017-9310(98)00297-x

Cited by 22 publications

(13 citation statements)

References 16 publications

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“…We would like to note that this inverse problem of the initial temperature reconstruction only from boundary measurements has been relatively ignored in the literature. In the case of the linear heat equation, we are aware only of the engineering works [21,22]. As it is pointed out in [21], in the existing publications concerning the initial temperature reconstruction one usually uses some additional temperature measurements inside the material.…”

Section: Initial Temperature Reconstruction For a Nonlinear Heat Equamentioning

confidence: 99%

Regularized fixed-point iterations for nonlinear inverse problems

Pereverzyev¹,

Pinnau²,

Siedow³

2005

Inverse Problems

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In this paper we introduce a derivative-free, iterative method for solving nonlinear illposed problems F x = y, where instead of y noisy data y δ with y − y δ ≤ δ are given and F : D(F ) ⊆ X → Y is a nonlinear operator between Hilbert spaces X and Y . This method is defined by splitting the operator F into a linear part A and a nonlinear part G, such that F = A + G. Then iterations are organized as Au k+1 = y δ − Gu k . In the context of ill-posed problems we consider the situation when A does not have a bounded inverse, thus each iteration needs to be regularized. Under some conditions on the operators A and G we study the behavior of the iteration error. We obtain its stability with respect to the iteration number k as well as the optimal convergence rate with respect to the noise level δ, provided that the solution satisfies a generalized source condition. As an example, we consider an inverse problem of initial temperature reconstruction for a nonlinear heat equation, where the nonlinearity appears due to radiation effects. The obtained iteration error in the numerical results has the theoretically expected behavior. The theoretical assumptions are illustrated by a computational experiment.

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Section: Initial Temperature Reconstruction For a Nonlinear Heat Equamentioning

confidence: 99%

Regularized fixed-point iterations for nonlinear inverse problems

Pereverzyev¹,

Pinnau²,

Siedow³

2005

Inverse Problems

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“…Further details concerning the importance of the temperature measurements can be also found in [37,38].…”

Section: Introductionmentioning

confidence: 99%

Industrial low cost temperature measurement in permanent electro-magnetic platens

Faranda

Lazzaroni

2013

Measurement

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“…Gejadze and Jarny [9] have presented a detailed analysis of IHCP coupled problem, when the velocity field depends on temperature field through viscosity and Navier-Stokes equations for a non-Newtonian fluid. Recently, Nguyen and Prystay [10] estimated the initial temperature profile and its evolution in polymer processing using the surface temperature measurement and the conjugate gradient method was employed to search for the minimum of the functional. In a previous work [11] the authors studied the numerical resolution of such an inverse heat convection-conduction problem to estimate the temperature field within the polymer flow from temperature measurements taken inside the die wall.…”

Section: Introductionmentioning

confidence: 99%

Temperature profile within a plane channel of an experimental extrusion die under polymer processing conditions

Karkri

Jarny

Mousseau

2009

Inverse Problems in Science and Engineering

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The flow of melted polyethylene (Dowlex 2042 E ) through an extrusion die is investigated both experimentally and numerically. This article deals with the reconstruction of thermal history of the melted polymer in the channel die and the influence of the extrusion parameters on the inlet temperature profile. The inverse heat transfer problem is formulated as an optimization problem by considering both the heat transfer and Navier-Stokes equations. It is solved by using the classical conjugate gradient algorithm. Experimental results are presented and the article focuses on the importance of checking the adequacy of the modelling equations in experimental data processing in order to avoid convergence of the inverse algorithm toward solutions which have no physical significance. The effects of the pressure drop combined with the viscous dissipation effect along the channel die are then discussed. Nomenclature C p heat capacity (J kg À1 C À1 ) F source term of energy (Pa s À3 ) J functional to be minimized ( C 2 ) l c length of the die connector (m) l b width of the zone (m) l p perimeter (m) L hp length of the heating-plate (m)axial and radial velocities (m s À1 ) Y measure temperatures ( C) Subscripts and Superscripts c connector m, p sensor locations 0 inlet extrusion die hp heating plate melt melted polymer n iteration number n vector normal p polymer s outlet extrusion die w die wall Greek symbols " shear rate (s À2 ) dynamic viscosity (Pa s) conductivity (W m À1 C À1 ) density (kg m À3 ) adjoint variable sensitivity variable Dirac delta function O spatial domain IntroductionDuring polymer extrusion, even after the melting zone, heat transfer takes an important place at the outlet of the extruder [1,2]. Due to high viscous dissipation and very low heat conductivity, the temperature profile within the channel die can be quite sharp. Overheated areas can be generated and degradation of the polymer could occur. For such creeping flow the temperature field is affected far downstream from the entrance of the die, so to predict accurately and to control the temperature rise, the inlet temperature profile has to be taken into account. However, due to the history in the extruder, the material temperature at the die entrance is rarely uniform. Hence, the determination of this temperature profile is referred to as a boundary inverse heat convection-conduction problem. There are numerous works on the initial temperature profile restoration, for example, in [3] the inlet temperature profile is estimated in the laminar duct flow and subsequent investigations [4-6] examine various aspects of this problem. Recently, Hsu et al. [7] presented a two-dimensional inverse least squares method to estimate both inlet temperature and wall heat flux in a steady laminar flow in a circular duct. Huang and Chen [8] have solved a non-stationary Navier-Stokes equation, to provide coefficients for energy equation, but the velocity field does not depend on temperature. Gejadze and Jarny [9] have presented a detailed analysis of IHCP coupled ...

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An inverse method for estimation of the initial temperature profile and its evolution in polymer processing

Cited by 22 publications

References 16 publications

Regularized fixed-point iterations for nonlinear inverse problems

Regularized fixed-point iterations for nonlinear inverse problems

Industrial low cost temperature measurement in permanent electro-magnetic platens

Temperature profile within a plane channel of an experimental extrusion die under polymer processing conditions

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