Modelling of Heat Transfer in Stable Wavy Film Flow Based on Effective Thermal Diffusivity

Dietze, Georg F.; Lel, Viatcheslav Vladimirovich; Kneer, Reinhold

doi:10.1615/ihtc13.p25.130

Cited by 2 publications

(3 citation statements)

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“…This reduction is compensated by the introduction of spaceand time-dependent effective transport coefficients [9,15,44], which capture waveinduced transport enhancing effects in this flat film geometry.…”

Section: Numerical Case Studymentioning

confidence: 99%

Identification of Transport Coefficient Models in Convection-Diffusion Equations

Karalashvili¹,

Groß²,

Marquardt³

et al. 2011

SIAM J. Sci. Comput.

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A rigorous method is presented for the systematic identification of the structure and the parameters of transport coefficient models in three-dimensional, transient convection-diffusion systems using high resolution measurement data. The transport is represented by a convection term with known convective velocity and a diffusion term with an unknown, generally state-dependent, transport coefficient. The identification of a transport coefficient model constitutes an ill-posed, highly nonlinear inverse problem. In our previous work [29], we presented a novel incremental identification method, which decomposes this inverse problem into easier to handle inverse subproblems. This way, the incremental identification method not only allows for the identification of the structure and the parameters of the model, but also supports the rigorous decision making on the best suited transport model structure. Due to the decomposition approach, the identified transport model structure and parameters are subject to errors. To cope with the error propagation inherent to the incremental method, the present work suggests a model correction procedure as a supplement to the incremental identification method [29], which results in a transport model of higher precision. The correction refers to both, the model structure and parameters. No a priori knowledge on the unknown transport model structure is necessary. The identification approach is numerically illustrated for a three-dimensional, transient convection-diffusion equation which has its origin in the modeling and simulation of energy transport in a laminar wavy film flow.

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Section: Numerical Case Studymentioning

confidence: 99%

Identification of Transport Coefficient Models in Convection-Diffusion Equations

Karalashvili¹,

Groß²,

Marquardt³

et al. 2011

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

show abstract

“…This reduction is compensated by the introduction of a space-and time-dependent effective transport coefficient a eff (x, t) [8,12,30] to capture all wave-induced transport effects in this flat film geometry.…”

Section: Illustrative Case Studymentioning

confidence: 99%

“…In Section 4 we present results of extensive numerical experiments for the identification of a model for the transport coefficient in a three-dimensional convection-diffusion problem of type (1.1). This model problem is motivated by research on energy transport in wavy films, using effective transport coefficients [8,12,30]. Section 5 contains some conclusions and remarks concerning future work.…”

mentioning

confidence: 99%

Incremental Identification of Transport Coefficients in Convection-Diffusion Systems

Karalashvili¹,

Groß²,

Mhamdi³

et al. 2008

SIAM J. Sci. Comput.

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Abstract. In this paper, an incremental approach for the identification of a model for transport coefficients in convection-diffusion systems on the basis of high-resolution measurement data is presented. The transport is represented by a convection term with known convective velocity and by a diffusion term with an unknown, generally state-dependent transport coefficient. The identification of the transport model for this transport coefficient constitutes an ill-posed nonlinear inverse problem. We present a novel decomposition approach in which this inverse problem is split into a sequence of inverse subproblems. In the first identification step of this incremental approach a source is estimated by solving an affine-linear inverse problem by means of the conjugate gradient method. In the second identification step a nonlinear inverse problem has to be solved in order to reconstruct a transport coefficient. A Newton-type method using the conjugate gradient method in its inner iteration is used to solve this nonlinear inverse problem of coefficient estimation. Finally, in the third identification step a transport model structure is proposed and identified on the basis of the model-free transport coefficient reconstructed in the two previous steps. The ill-posedness of each inverse problem is examined by using artificially perturbed transient simulation data and appropriate regularization techniques. The identification methodology is illustrated for a three-dimensional convection-diffusion equation which has its origin in the modeling and simulation of energy transport in a laminar wavy film flow.

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Modelling of Heat Transfer in Stable Wavy Film Flow Based on Effective Thermal Diffusivity

Cited by 2 publications

References 0 publications

Identification of Transport Coefficient Models in Convection-Diffusion Equations

Identification of Transport Coefficient Models in Convection-Diffusion Equations

Incremental Identification of Transport Coefficients in Convection-Diffusion Systems

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