scholarly journals Semidiscrete central difference method in time for determining surface temperatures

2005 ◽  
Vol 2005 (3) ◽  
pp. 393-400 ◽  
Author(s):  
Zhi Qian ◽  
Chu-Li Fu ◽  
Xiang-Tuan Xiong
Keyword(s):  
Difference Method ◽  
Heat Conduction Problem ◽  
A Priori ◽  
Inverse Heat Conduction Problem ◽  
The Body ◽  
Temperature History ◽  
Measured Temperature ◽  
Central Difference ◽  
Approximation Solution ◽  
Computational Effect

We consider an inverse heat conduction problem (IHCP) in a quarter plane. We want to know the distribution of surface temperature in a body from a measured temperature history at a fixed location inside the body. This is a severely ill-posed problem in the sense that the solution (if exists) does not depend continuously on the data. Eldén (1995) has used a difference method for solving this problem, but he did not obtain the convergence atx=0. In this paper, we gave a logarithmic stability of the approximation solution atx=0under a stronger a priori assumption‖u(0,t)‖p≤Ewithp>1/2. A numerical example shows that the computational effect of this method is satisfactory.

scholarly journals A Mollification Regularization Method for a Fractional-Diffusion Inverse Heat Conduction Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Zhi-Liang Deng ◽  
Xiao-Mei Yang ◽  
Xiao-Li Feng
Keyword(s):  
Regularization Method ◽  
Heat Conduction Problem ◽  
A Priori ◽  
Dirichlet Kernel ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Linear Diffusion ◽  
Ill Posed ◽  
Transient Data ◽  
Parameter Choice Rules

The ill-posed problem of attempting to recover the temperature functions from one measured transient data temperature at some interior point of a one-dimensional semi-infinite conductor when the governing linear diffusion equation is of fractional type is discussed. A simple regularization method based on Dirichlet kernel mollification techniques is introduced. We also proposea priorianda posterioriparameter choice rules and get the corresponding error estimate between the exact solution and its regularized approximation. Moreover, a numerical example is provided to verify our theoretical results.

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.

Modelling, Identification and Control of Thermal Deformation of Machine Tool Structures, Part 3: Real-Time Estimation of Heat Sources

1999 ◽  
Vol 121 (3) ◽  
pp. 501-508 ◽  
Author(s):  
S. Fraser ◽  
M. H. Attia ◽  
M. O. M. Osman
Keyword(s):  
Real Time ◽  
Time Domain ◽  
Measurement Errors ◽  
Thermal Deformation ◽  
Heat Conduction Problem ◽  
Time Estimation ◽  
Inverse Heat Conduction Problem ◽  
Dimensional Structure ◽  
Measured Temperature ◽  
Real Time Estimation

Compensation of thermal deformation of machine tools requires real-time estimation of the heat input to the structure in order to fully describe its thermoelastic response. Available solutions of the inverse heat conduction problem IHCP are not suitable for real-time feedback control applications, since they are too slow and/or rely on future data to stabilize the solution. A new real-time IHCP solver is derived in the form of a convolution integral of the inverse thermal transfer function G−1(s) and the measured temperature difference at two points near the heat source. An expression for G−1(s) is derived for multi-dimensional structural components. To transform G−1(s) to the time domain, a special consideration is given to the treatment of its complex singularity functions. Analytical approach was followed to identify these functions and to determine their time-domain representation. Computer-simulation test cases were conducted using a finite element model of a three-dimensional structure. The random temperature measurement errors, which can lead to non-uniqueness and instability problems, have also been simulated. The test results showed that the computation time can significantly be improved to achieve a control cycle of less than one second, without compromising the accuracy and stability requirements.

An Algorithm Study on Inverse Identification of Interfacial Configuration in a Multiple Region Domain

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Chunli Fan ◽  
Fengrui Sun ◽  
Li Yang
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Identification Problem ◽  
Accurate Method ◽  
Correction Method ◽  
Inverse Heat Conduction Problem ◽  
Measured Temperature ◽  
Inverse Heat Conduction ◽  
Obvious Effect ◽  
One Dimensional

A two-dimensional inverse heat conduction problem to determine the interfacial configuration of a multiple region domain is solved by utilizing temperature readings on the outer surface of the whole domain. The method used is the modified one-dimensional correction method (MODCM) along with the finite element method. The MODCM is a simple but very accurate method, which first solves the multidimensional inverse heat conduction problem based on the simplified one-dimensional model, and the discrepancy in the result caused by this one-dimensional simplification is corrected afterward by an iterative process. A series of numerical experiments is conducted in order to verify the effectiveness of the algorithm. The method can identify the interfacial configuration of the multiple region domain with high accuracy. The average relative error of the identification result is not more than 10.4% when the standard deviation of the temperature measurement is less than 2.0% of the average measured temperature for the cases tested. The number of the measurement points of the inspection surface can be reduced with no obvious effect on the estimation results as long as it is still sufficient to describe the exact interfacial configuration. The method is proved to be a simple, fast, and accurate one that can solve successfully this interfacial configuration identification problem.

Analysis of the Heat Transfer Coefficients on the Top of a Marine Diesel Piston Using the Inverse Heat Conduction Method

2011 ◽  
Vol 291-294 ◽  
pp. 1657-1661 ◽  
Author(s):  
Tao He ◽  
Xi Qun Lu ◽  
Yi Bin Guo
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Optimization Problem ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Measured Temperature ◽  
Inverse Heat Conduction ◽  
Transfer Coefficients ◽  
Conduction Model ◽  
Marine Diesel

An efficient method utilizing the concept of inverse heat conduction is presented for the thermal analysis of pistons based on application to the piston head of a marine diesel engine. An inverse heat conduction problem is established in the form of an optimization problem. In the optimization problem, the convection heat transfer coefficient（HTC）on the top side of the piston is defined as the design variable, while the error between the measured and analysed temperatures is defined as objective function. For the optimization, an axi-symmetrical finite element conduction model is presented. The optimum distribution of the HTC at the top side of piston is successfully determined through a numerical implementation. The temperature obtained via an analysis using the optimum HTC is compared with the measured temperature, and reasonable agreement is obtained. The present method can be effectively utilized to analyze the temperature distribution of engine pistons.

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