Solving the Inverse Heat Conduction Problem with Multi-Variables

2010 ◽  
Vol 168-170 ◽  
pp. 195-199
Author(s):  
Qi Wen Xue ◽  
Xiu Yun Du ◽  
Ga Ping Wang
Keyword(s):  
Sensitivity Analysis ◽  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Least Square ◽  
Inhomogeneous Distribution ◽  
Inverse Heat Conduction ◽  
Numerical Examples ◽  
Inverse Heat Conduction Problems ◽  
Direct Problems

This paper presents a general numerical model to solve non-linear inverse heat conduction problems with multi-variables which include thermal parameters and boundary conditions, and can be identified singly or simultaneously. The direct problems are numerically modeled via FEM, facilitating to sensitivity analysis that is required in solving inverse problems via a least-square based CGM (Conjugate Gradient Method). Inhomogeneous distribution of parameters is considered, and a number of numerical examples are given to illustrate the work proposed.

Analysis of Order of the Sequential Regularization Solutions of Inverse Heat Conduction Problems

1989 ◽  
Vol 111 (2) ◽  
pp. 218-224 ◽  
Author(s):  
E. P. Scott ◽  
J. V. Beck
Keyword(s):  
Heat Conduction ◽  
Regularization Method ◽  
Heat Conduction Problem ◽  
Regularization Parameter ◽  
Inverse Heat Conduction Problem ◽  
Regularization Methods ◽  
Inverse Heat Conduction ◽  
Random Errors ◽  
Internal Temperature ◽  
Inverse Heat Conduction Problems

Various methods have been proposed to solve the inverse heat conduction problem of determining a boundary condition at the surface of a body from discrete internal temperature measurements. These include function specification and regularization methods. This paper investigates the various components of the regularization method using the sequential regularization method proposed by Beck and Murio (1986). Specifically, the effects of the regularization order and the influence of the regularization parameter are analyzed. It is shown that as the order of regularization increases, the bias errors decrease and the variance increases. Comparatively, the zeroth regularization has higher bias errors and the second-order regularization is more sensitive to random errors. As the regularization parameter decreases, the sensitivity of the estimator to random errors is shown to increase; on the other hand, the bias errors are shown to decrease.

On Elliptic Inverse Heat Conduction Problems

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
M. Tadi
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Initial Guess ◽  
Unknown Boundary ◽  
Inverse Heat Conduction ◽  
Robustness To Noise ◽  
Inverse Heat Conduction Problems ◽  
New Feature

This note is concerned with a new method for the solution of an elliptic inverse heat conduction problem (IHCP). It considers an elliptic system where no information is given at part of the boundary. The method is iterative in nature. Starting with an initial guess for the missing boundary condition, the algorithm obtains corrections to the assumed value at every iteration. The updating part of the algorithm is the new feature of the present algorithm. The algorithm shows good robustness to noise and can be used to obtain a good estimate of the unknown boundary condition. A number of numerical examples are used to show the applicability of the method.

scholarly journals FEATURES OF THE APPLICATION OF THE IQLAB PROGRAM FOR SOLVING THE INVERSE HEAT CONDUCTION PROBLEM FOR CHROMIUM-NICKEL CYLINDRICAL THERMOSONDES

2018 ◽  
Vol 40 (3) ◽  
pp. 91-96
Author(s):  
E.N. Zotov ◽  
A.A. Moskalenko ◽  
O.V. Razumtseva ◽  
L.N. Protsenko ◽  
V.V. Dobryvechir
Keyword(s):  
Heat Conduction ◽  
Surface Temperature ◽  
Computational Study ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Time Step ◽  
Correct Operation ◽  
Inverse Heat Conduction Problems ◽  
Variable Time Step

The paper presents an experimental-computational study of the results of using the IQLab program to solve inverse heat conduction problem and restore the surface temperature of cylindrical thermosondes from heat-resistant chromium-nickel alloys while cooling them in liquid media. The purpose of this paper is to verify the correct operation of the IQLab program when restoring the surface temperature of thermosondes with 1-3 thermocouples. The IQLab program is also designed to solve one-dimensional nonlinear direct lines and inverse heat conduction problems with constant initial and boundary conditions specified as a function of time in a tabular form with a constant and variable time step. A finite-difference method is used to solve the heat equation. Experiments were carried out on samples D = 10-50 mm in liquids with different cooling capacities such as aqueous solutions of  NaCl and Yukon-E polymer, rapeseed oil and I-20A mineral oil. For the calculation we used the readings of thermocouples installed at internal points of cylindrical thermosondes. The advantages of solving inverse heat conduction problems with the IQLab program include the possibility of restoring the surface temperature for cylindrical samples with a diameter of 10 mm to 50 mm with practical accuracy according to the indications of a single thermocouple located in the geometrical center of the thermosonde, which simplifies the manufacture of the probe. For larger dimensions with a diameter D ≥ 50 mm, it is necessary to install control intermediate thermocouples and perform additional tests. The solution of inverse heat conduction problems and restoration of the surface temperature of the sample makes it possible to calculate other important characteristics of the cooling process: the heat flux density and the heat transfer coefficient.

A Maximum Entropy Solution for a Two-Dimensional Inverse Heat Conduction Problem

2003 ◽  
Vol 125 (6) ◽  
pp. 1197-1205 ◽  
Author(s):  
Sun Kyoung Kim ◽  
Woo Il Lee
Keyword(s):  
Heat Conduction ◽  
Maximum Entropy ◽  
Optimization Problem ◽  
Entropy Solution ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Measured Temperature ◽  
Two Dimensional ◽  
Inverse Heat Conduction ◽  
Inverse Heat Conduction Problems

A solution scheme based on the maximum entropy method (MEM) for the solution of two-dimensional inverse heat conduction problems is established. MEM finds the solution which maximizes the entropy functional under the given temperature measurements. The proposed method converts the inverse problem to a nonlinear constrained optimization problem. The constraint of the optimization problem is the statistical consistency between the measured temperature and the estimated temperature. Successive quadratic programming (SQP) facilitates the numerical estimation of the maximum entropy solution. The characteristic feature of the proposed method is investigated with the sample numerical results. The presented results show considerable enhancement in resolution for stringent cases in comparison with a conventional method.

scholarly journals Influence of Errors in Known Constants and Boundary Conditions on Solutions of Inverse Heat Conduction Problem

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3313
Author(s):  
Sun Kyoung Kim
Keyword(s):  
Exact Solution ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Material Properties ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
One Dimensional ◽  
Boundary Location ◽  
Inverse Heat Conduction Problems

This work examines the effects of the known boundary conditions on the accuracy of the solution in one-dimensional inverse heat conduction problems. The failures in many applications of these problems are attributed to inaccuracy of the specified constants and boundary conditions. Since the boundary conditions and material properties in most thermal problems are imposed with uncertainty, the effects of their inaccuracy should be understood prior to the inverse analyses. The deviation from the exact solution has been examined for each case according to the errors in material properties, boundary location, and known boundary conditions. The results show that the effects of such errors are dramatic. Based on these results, the applicability and limitations of the inverse heat conduction analyses have been evaluated and discussed.

A Meshless Manifold Method for Solving the Inverse Heat Conduction Problems

2013 ◽  
Vol 749 ◽  
pp. 131-136
Author(s):  
Hong Fen Gao ◽  
Gao Feng Wei
Keyword(s):  
Differential Equation ◽  
Finite Element Method ◽  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Problem Domain ◽  
Computation Cost ◽  
Inverse Heat Conduction Problems ◽  
Element Method

In this paper the meshless manifold method is used to obtain the solution of an inverse heat conduction problem with a source parameter. Compared with the numerical methods based on mesh, such as finite element method and boundary element method, the meshless manifold method only needs the scattered nodes instead of meshing the domain of the problem when the trial function is formed. The meshless manifold method is used to discretize the governing partial differential equation, and boundary conditions can be directly enforced without numerical integration in the problem domain. This reduces the computation cost greatly. A numerical example is given to show the effectiveness of the method.

A NUMERICAL AND EXPERIMENTAL STUDY OF A ONE-DIMENSIONAL SPACE BOUNDARY INVERSE HEAT CONDUCTION PROBLEM

1999 ◽  
Vol 23 (2) ◽  
pp. 267-274
Author(s):  
T-F. Chen ◽  
S. Lin ◽  
J.C.-Y. Wang
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Dimensional Space ◽  
Large Error ◽  
Inverse Heat Conduction Problem ◽  
Small Error ◽  
Inverse Heat Conduction ◽  
Ill Posed ◽  
Inverse Heat Conduction Problems ◽  
Space Boundary

Inverse Heat Conduction Problems (IHCPs) are not the same as direct heat conduction problems which are “well-posed”. The difficulty of the “ill-posed” IHCP is that a small error perturbation in the data will lead to a large error in the reconstructed solution. An inverse procedure for solving an IHCP should have the ability to handle the required information obtained from measurements containing noise. In the present work, a stable, accurate and reliable inversion solver is used with interior temperature measurements to predict surface temperatures at the both sides of a brick Numerical results in comparison with experimental data are presented.

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