Transient inverse heat conduction problem solutions via Newton's method

“…) of surface heat flux is assumed to apply between time steps (Beck et al 1996;Lin et al 2004). Other approaches utilize Newton's method (Dorai and Tortorelli 1997), the Laplace transform technique (Monde et al 2003), singular value decomposition of an operator matrix (Shenefelt et al 2002;Lagier et al 2004), the boundary element method (Lesnic et al 1996) and the conjugate gradient method (Huang and Yeh 2002). These citations are only examples, as the literature on these methods and others is extensive.…”

Section: Introductionmentioning

confidence: 99%

An inverse method to estimate stem surface heat flux in wildland fires

Bova

Dickinson

2009

Int. J. Wildland Fire

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Abstract. Models of wildland fire-induced stem heating and tissue necrosis require accurate estimates of inward heat flux at the bark surface. Thermocouple probes or heat flux sensors placed at a stem surface do not mimic the thermal response of tree bark to flames. We show that data from thin thermocouple probes inserted just below the bark can be used, by means of a one-dimensional inverse heat conduction method, to estimate net heat flux (inward minus outward heat flow) and temperature at the bark surface. Further, we estimate outward heat flux from emitted water vapor and bark surface re-radiation. Estimates of surface heat flux and temperature made by the inverse method confirm that surface-mounted heat flux sensors and thermocouple probes overestimate surface heat flux and temperature. As a demonstration of the utility of the method, we characterized uneven stem heating, due to leeward, flame-driven vortices, in a prescribed surface fire. Advantages of using an inverse method include lower cost, ease of multipoint measurements and negligible effects on the target stem. Drawbacks of the simple inverse model described herein include inability to estimate heat flux in very moist bark and uncertainty in estimates when extensive charring occurs.

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“…The main difficulty of the IHCP is that its solution is very sensitive to changes in the input data resulting from measurement errors [1][2][3]. To date, various methods [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], such as the regularization, least-squares, sequential, conjugate gradient, function specification, Kalman filter, group-preserving, and hybrid inverse methods, have been developed for solving the IHCP. Most of the previous works were confined to problems with constant thermal properties.…”

Section: Introductionmentioning

confidence: 99%

“…Under this circumstance, the conduction problem will become nonlinear. It can be found from [5][6][7][8][9][10][11] that the estimation of the unknown surface conditions for the nonlinear IHCP is more difficult than those for the linear IHCP.…”

Section: Introductionmentioning

confidence: 99%

Estimation of Surface Conditions for Nonlinear Inverse Heat Conduction Problems Using the Hybrid Inverse Scheme

Chen

2007

Numerical Heat Transfer, Part B: Fundamentals

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A hybrid numerical method involving the Laplace transform technique and finite-difference method in conjunction with the least-squares method and actual experimental temperature data inside the test material is proposed to estimate the unknown surface conditions of inverse heat conduction problems with the temperature-dependent thermal conductivity and heat capacity. The nonlinear terms in the differential equations are linearized using the Taylor series approximation. In this study, the functional form of the surface conditions is unknown a priori and is assumed to be a function of time before performing the inverse calculation. In addition, the whole time domain is divided into several analysis subtime intervals and then the unknown estimates on each subtime interval can be predicted. In order to show the accuracy and validity of the present inverse scheme, a comparison among the present estimates, direct solution, and actual experimental temperature data is made. The effects of the measurement errors, initial guesses, and measurement location on the estimated results are also investigated. The results show that good estimation of the surface conditions can be obtained from the present inverse scheme in conjunction with knowledge of temperature recordings inside the test material.

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Transient inverse heat conduction problem solutions via Newton's method

Cited by 27 publications

References 25 publications

A new inverse analysis method based on a relaxation factor optimization technique for solving transient nonlinear inverse heat conduction problems

A new inverse analysis method based on a relaxation factor optimization technique for solving transient nonlinear inverse heat conduction problems

An inverse method to estimate stem surface heat flux in wildland fires

Estimation of Surface Conditions for Nonlinear Inverse Heat Conduction Problems Using the Hybrid Inverse Scheme

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