Determination of a time-dependent heat transfer coefficient in a nonlinear inverse heat conduction problem

Slodička, Marián; Lesnic, D.; Onyango, T. T. M.

doi:10.1080/17415970903234273

Cited by 30 publications

(18 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(4). When generating simulated temperature measurements Y(x s , t) with a predefined h(t), the direct problem is solved with implicit finite difference method, (5) where T i j is the temperature at the j th time step along the i th grid point. Δx is the mesh size, Δt is the time incremental size.…”

Section: T(x T)mentioning

confidence: 99%

“…Chen and Wu [4] applied a hybrid scheme of Laplace transform, finite difference and least-square method in conjunction with a sequential-in-time concept, cubic spline and temperature measurements is applied to predict the heat transfer coefficient distribution on a boundary surface. Slodicka [5] used boundary element method and Tikhonov regularization to construct the time-dependent heat transfer coefficient. Chantasiriwan [6] used the sequential function specification method with the linear basis function and an assumption of linearly varying future boundary heat flux or temperature components to estimate the time-dependent Biot number.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Estimation of Heat Transfer Coefficient in Inverse Heat Conduction Problem Using Quantum-Behaved Particle Swarm Optimization with Tikhonov Regularization

Tian

Zhu²,

Chen

2014

Journal of Algorithms & Computational Technology

View full text Add to dashboard Cite

The quantum-behaved particle swarm optimization (QPSO) with Tikhonov regularization is used to solve the inverse heat conduction problem of estimating the time dependent heat transfer coefficient of a flat plate. The prior information about the functional form of the unknown is unavailable. The estimation is based on transient temperature measurements taken by the sensors imbedded in the plate, which are used in the least square model, minimized by QPSO. The detail of choosing the best regularization parameter by L-curve method is presented. Numerical experiments are performed to test the proposed method. Effects of the location and number of sensors are also investigated. Comparison with conjugate gradient method is given as well.

show abstract

Section: T(x T)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Estimation of Heat Transfer Coefficient in Inverse Heat Conduction Problem Using Quantum-Behaved Particle Swarm Optimization with Tikhonov Regularization

Tian

Zhu²,

Chen

2014

Journal of Algorithms & Computational Technology

View full text Add to dashboard Cite

show abstract

“…However, Cauchy data measurements may experience some practical difficulties, for example, in the case of high temperature hostile environments. Thus, in a more realistic model, we allow for the convective Robin boundary condition to be prescribed over the whole boundary and the linkage between the boundary temperature and heat flux be made through unknown heat transfer coefficient which varies with time [12,13].…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of a Robin Coefficient by a Predictor-Corrector Method

2015

Mathematical Problems in Engineering

View full text Add to dashboard Cite

The present paper is devoted to solving a nonlinear inverse problem of identifying a Robin coefficient from boundary temperature measurement. A numerical algorithm on the basis of the predictor-corrector method is designed to restore the approximate solution and the performance of the method is verified by simulating several examples. The convergence with respect to the amount of noise in the data is also investigated.

show abstract

“…However, spatial discretization, which is necessary for practical computations, was not considered. Recently, Slodička et al [SLO10] extended the analysis to estimating a temporally-dependent Robin coefficient in a nonlinear boundary condition for one-dimensional heat equation, and showed the existence and uniqueness of the solution.…”

Section: Introductionmentioning

confidence: 99%

Numerical identification of a Robin coefficient in parabolic problems

Jin

2012

Math. Comp.

View full text Add to dashboard Cite

Abstract. This paper studies a regularization approach for an inverse problem of estimating a spatially-and-temporally dependent Robin coefficient arising in the analysis of convective heat transfer. The parameter-to-state map is analyzed, especially a differentiability result is established. A regularization approach is proposed, and the properties, e.g., existence and optimality system, of the functional are investigated. A finite element method is adopted for discretizing the continuous optimization problem, and the convergence of the finite element approximations as the mesh size and temporal step size tend to zero is established. Numerical results by the conjugate gradient method for one-and two-dimensional problems are presented.

show abstract

Determination of a time-dependent heat transfer coefficient in a nonlinear inverse heat conduction problem

Cited by 30 publications

References 18 publications

Estimation of Heat Transfer Coefficient in Inverse Heat Conduction Problem Using Quantum-Behaved Particle Swarm Optimization with Tikhonov Regularization

Estimation of Heat Transfer Coefficient in Inverse Heat Conduction Problem Using Quantum-Behaved Particle Swarm Optimization with Tikhonov Regularization

Reconstruction of a Robin Coefficient by a Predictor-Corrector Method

Numerical identification of a Robin coefficient in parabolic problems

Contact Info

Product

Resources

About