scholarly journals Application of the RBF Method to the Estimation of Temperature on the External Surface in Laminar Pipe Flow

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Shiqin Lyu ◽  
Can Wu ◽  
Sufang Zhang
Keyword(s):  
Inverse Problem ◽  
Direct Problem ◽  
External Surface ◽  
Heat Conduction Problem ◽  
Main Idea ◽  
Inverse Heat Conduction Problem ◽  
Laminar Flows ◽  
Temperature Measurements ◽  
Control Technique ◽  
Unknown Boundary

The inverse heat conduction problem on the heat transfer characteristics of cooled/heated laminar flows through finite length thick-walled circular tubes is studied, using temperature measurements taken at several different locations within the fluid in this paper. The method of radial basis functions is coupled with the boundary control technique to estimate the unknown temperature on the external surface of the circular pipe. The main idea of the proposed method is to solve the direct problem instead of solving the inverse problem directly. The temperature data obtained from the direct problem are used to simulate the temperature measurement for the inverse problem, and during the calculation, the Tikhonov regularization and L-curve methods are employed to solve the inverse problem. Therefore, this study also considers the influence of errors in these measurements upon the precision of the estimated results as well as the influence of the locations and number of sensors used upon the accuracy of the estimated results. The results indicate that the accuracy of the estimated results is improved by taking temperature measurements in locations close to the the unknown boundary. Finally, the results confirm that the proposed method is capable of yielding accurate results even when errors in the temperature measurements are present.

Solution of the Inverse Heat Conduction Problem From Thermal Strain Measurements

1996 ◽  
Vol 118 (4) ◽  
pp. 842-849 ◽  
Author(s):  
G. Blanc ◽  
M. Raynaud
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Thermal Strain ◽  
Sensitivity Coefficient ◽  
Inverse Heat Conduction Problem ◽  
Temperature Measurements ◽  
Unknown Boundary ◽  
Inverse Heat Conduction ◽  
Numerical Predictions ◽  
Unknown Boundary Conditions

Another approach for the solution of the inverse heat conduction problem is presented. The unknown boundary conditions are recovered from thermal strain and temperature measurements instead of temperature measurements only. It is required to calculate both the temperature field and the strains induced by this field. The sensitivity coefficient analysis and the results of two benchmark test cases show that it is possible to recover higher temporal frequencies when the inversion is done from strains instead of temperatures. An experimental setup was specially designed to validate the numerical results. The numerical predictions are verified. Special attention is given to the strain gage measurements.

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.

BEM Solution With Minimal Energy Technique for the Geometrical Inverse Heat Conduction Problem in a Doubly Connected Domain

2003 ◽  
Vol 125 (1) ◽  
pp. 109-117 ◽  
Author(s):  
Chang-Yong Choi ◽  
Jong Chull Jo
Keyword(s):  
Heat Conduction ◽  
Boundary Element ◽  
Measurement Errors ◽  
Heat Conduction Problem ◽  
Boundary Surface ◽  
Inverse Heat Conduction Problem ◽  
Unknown Boundary ◽  
Inverse Heat Conduction ◽  
Minimal Energy ◽  
Element Analysis

This article addresses the use of boundary element method in conjunction with minimal energy technique for solving a geometrical inverse heat conduction problem. The problem considered in this study is to estimate the unknown inner boundary position in an irregular-shaped hollow body of which the inner boundary surface is subjected to a specified temperature condition. For solving the problem, first boundary element equations are converted into the quadratic programming problem by minimizing the energy functional with a constraint, next a hypothetical inner boundary is defined such that the actual inner boundary is located interior of the hypothetical solution domain, then temperatures at hypothetical inner boundary are determined to meet the constraints of measurement error in inner surface temperatures, and finally boundary element analysis is performed for the position of an unknown boundary. Based on these main solution procedures, an effective detection algorithm is provided. In addition, the solution method is numerically tested to investigate the effects of measurement errors on the accuracy of estimation.

Application of discrete Fourier transform to inverse heat conduction problem regularization

2018 ◽  
Vol 28 (1) ◽  
pp. 239-253 ◽  
Author(s):  
Andrzej Frąckowiak ◽  
Michał Ciałkowski
Keyword(s):  
Inverse Problem ◽  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Heat Conduction Problem ◽  
Outer Boundary ◽  
Turbine Blades ◽  
Stable Solution ◽  
Inverse Heat Conduction Problem ◽  
Content Type ◽  
Cooling Channels

Purpose This paper aims to present the Cauchy problem for the Laplace’s equation for profiles of gas turbine blades with one and three cooling channels. The distribution of heat transfer coefficient and temperature on the outer boundary of the blade are known. On this basis, the temperature on inner surfaces of the blade (the walls of cooling channels) is determined. Design/methodology/approach Such posed inverse problem was solved using the finite element method in the domain of the discrete Fourier transform (DFT). Findings Calculations indicate that the regularization in the domain of the DFT enables obtaining a stable solution to the inverse problem. In the example under consideration, problems with reconstruction constant temperature, assumed on the outer boundary of the blade, in the vicinity of the trailing and leading edges occurred. Originality/value The application of DFT in connection with regularization is an original achievement presented in this study.

Identification of Contact Failures in Multi-Layered Composites

2011 ◽  
Author(s):  
L. A. Abreu ◽  
H. R. B. Orlande ◽  
C. P. Naveira-Cotta ◽  
J. N. N. Quaresma ◽  
R. M. Cotta ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Monte Carlo ◽  
Markov Chain ◽  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Layered Composites ◽  
Simulated Temperature ◽  
Prior Models

This paper deals with the solution of an inverse heat conduction problem, aiming at the identification of contact failures in composites formed by layers of different materials. The inverse problem is solved within the Bayesian framework, with a Markov chain Monte Carlo method. The effects of the prior models, for the unknown contact conductance at the interface of a plate with two layers, are examined. The solution of the inverse problem is performed with simulated temperature measurements.

Aluminum Sand Casting Interfacial Heat Flux Estimation Based on Corrected Temperature Measurements

2008 ◽  
Author(s):  
Jonathan W. Woolley ◽  
Keith A. Woodbury
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Conduction ◽  
Kernel Method ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Temperature Measurements ◽  
Inverse Heat Conduction ◽  
Interfacial Heat Transfer ◽  
Interfacial Heat Flux

The estimation of the heat flux at the interface between a solidifying metal casting and mold is a frequently investigated topic. Accurate knowledge of the interfacial heat transfer can be used in solidification simulation to reduce the time and cost of the casting design process. A common and well-established approach to estimating the interfacial heat flux is the solution of the inverse heat conduction problem. Temperature measurements from thermocouples imbedded in the sand mold are used as inputs to the inverse solver. It is well-documented that imbedded thermocouples which are subjected to high temperature gradients will yield biased temperature measurements. By accounting for the sensor dynamics with an appropriate model, the measured temperatures can be corrected to mitigate the effect of the bias error in the estimation of the heat flux. In a previous work, experimentally measured temperatures were obtained from aluminum sand castings and the interfacial heat transfer was evaluated. In other works, the temperature measurement error was demonstrated and the kernel method for correcting measured temperatures was demonstrated with a numerical experiment. In this paper, the simulation of the response of a thermocouple with a three-dimensional computational model is used with the kernel method to correct the experimentally measured temperatures. The previous interfacial heat flux estimates are updated by solving the inverse heat conduction problem with the corrected temperatures as the inputs.

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