An application of the generalized least squares method to the analysis of the heat transfer process with supplementary data

Anna Sciazko, Yosuke Komatsu, Shinji Kimijima, Zygmunt Sz Kolenda, Janusz S. Szmyd

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Most theoretical approaches for analysing heat transfer processes yield a unique solution from a specified set of governing equations, boundary and initial conditions and thermophysical properties of fluids and materials. This deterministic approach does not include uncertainties connected with the inaccuracy of directly measured variables and model simplifications. This study presents the idea of evaluating the most probable value obtained in a theoretical solution and a measure of its uncertainty. The proposed methodology - the Generalized Least Squares (GLS) method - allows for including additional data, which are commonly used for validation purposes, in the mathematical model as the supplementary variables. Theoretical considerations are then illustrated by applying the proposed methodology to the steady-state heat conduction process. On the basis of a formal mathematical model with the implementation of the GLS method, the computer program was prepared and applied to an analysis of several different cases, which demonstrate that the GLS methodology can be adopted for both: the process of planning experiments and the analysis of overdetermined problems. The advantages of the proposed method ensure obtaining optimal solutions to the problems of finding the proper position of the probe in the experiment design process, the determination of the empirical parameters and calculating the temperature distribution. The presented results proved that the proposed method is useful in verifying the incorrectly defined models as well as in identifying faulty measurement devices. The analysis pointed out that the experimental inaccuracy can be reduced and the most probable values of all unknown variables can be calculated.

Original languageEnglish
Title of host publicationProceedings of the 15th International Heat Transfer Conference, IHTC 2014
PublisherBegell House Inc.
Publication statusPublished - 2014
Event15th International Heat Transfer Conference, IHTC 2014 - Kyoto, Japan
Duration: 2014 Aug 102014 Aug 15

Other

Other15th International Heat Transfer Conference, IHTC 2014
CountryJapan
CityKyoto
Period14/8/1014/8/15

Fingerprint

least squares method
heat transfer
methodology
Mathematical models
Heat transfer
mathematical models
Heat conduction
Computer program listings
Temperature distribution
Thermodynamic properties
experiment design
Experiments
thermophysical properties
simplification
Planning
conductive heat transfer
Fluids
planning
temperature distribution
boundary conditions

Keywords

  • Computational methods
  • Conduction
  • Measurement and instrumentation
  • Optimal experiment planning
  • The Generalized Least Squares Method
  • The validation of mathematical models
  • Uncertainty evaluation

ASJC Scopus subject areas

  • Mechanical Engineering
  • Condensed Matter Physics

Cite this

Sciazko, A., Komatsu, Y., Kimijima, S., Kolenda, Z. S., & Szmyd, J. S. (2014). An application of the generalized least squares method to the analysis of the heat transfer process with supplementary data. In Proceedings of the 15th International Heat Transfer Conference, IHTC 2014 Begell House Inc..

An application of the generalized least squares method to the analysis of the heat transfer process with supplementary data. / Sciazko, Anna; Komatsu, Yosuke; Kimijima, Shinji; Kolenda, Zygmunt Sz; Szmyd, Janusz S.

Proceedings of the 15th International Heat Transfer Conference, IHTC 2014. Begell House Inc., 2014.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Sciazko, A, Komatsu, Y, Kimijima, S, Kolenda, ZS & Szmyd, JS 2014, An application of the generalized least squares method to the analysis of the heat transfer process with supplementary data. in Proceedings of the 15th International Heat Transfer Conference, IHTC 2014. Begell House Inc., 15th International Heat Transfer Conference, IHTC 2014, Kyoto, Japan, 14/8/10.
Sciazko A, Komatsu Y, Kimijima S, Kolenda ZS, Szmyd JS. An application of the generalized least squares method to the analysis of the heat transfer process with supplementary data. In Proceedings of the 15th International Heat Transfer Conference, IHTC 2014. Begell House Inc. 2014
Sciazko, Anna ; Komatsu, Yosuke ; Kimijima, Shinji ; Kolenda, Zygmunt Sz ; Szmyd, Janusz S. / An application of the generalized least squares method to the analysis of the heat transfer process with supplementary data. Proceedings of the 15th International Heat Transfer Conference, IHTC 2014. Begell House Inc., 2014.
@inproceedings{8afa6783ed4841cd82d25156dca7ef74,
title = "An application of the generalized least squares method to the analysis of the heat transfer process with supplementary data",
abstract = "Most theoretical approaches for analysing heat transfer processes yield a unique solution from a specified set of governing equations, boundary and initial conditions and thermophysical properties of fluids and materials. This deterministic approach does not include uncertainties connected with the inaccuracy of directly measured variables and model simplifications. This study presents the idea of evaluating the most probable value obtained in a theoretical solution and a measure of its uncertainty. The proposed methodology - the Generalized Least Squares (GLS) method - allows for including additional data, which are commonly used for validation purposes, in the mathematical model as the supplementary variables. Theoretical considerations are then illustrated by applying the proposed methodology to the steady-state heat conduction process. On the basis of a formal mathematical model with the implementation of the GLS method, the computer program was prepared and applied to an analysis of several different cases, which demonstrate that the GLS methodology can be adopted for both: the process of planning experiments and the analysis of overdetermined problems. The advantages of the proposed method ensure obtaining optimal solutions to the problems of finding the proper position of the probe in the experiment design process, the determination of the empirical parameters and calculating the temperature distribution. The presented results proved that the proposed method is useful in verifying the incorrectly defined models as well as in identifying faulty measurement devices. The analysis pointed out that the experimental inaccuracy can be reduced and the most probable values of all unknown variables can be calculated.",
keywords = "Computational methods, Conduction, Measurement and instrumentation, Optimal experiment planning, The Generalized Least Squares Method, The validation of mathematical models, Uncertainty evaluation",
author = "Anna Sciazko and Yosuke Komatsu and Shinji Kimijima and Kolenda, {Zygmunt Sz} and Szmyd, {Janusz S.}",
year = "2014",
language = "English",
booktitle = "Proceedings of the 15th International Heat Transfer Conference, IHTC 2014",
publisher = "Begell House Inc.",

}

TY - GEN

T1 - An application of the generalized least squares method to the analysis of the heat transfer process with supplementary data

AU - Sciazko, Anna

AU - Komatsu, Yosuke

AU - Kimijima, Shinji

AU - Kolenda, Zygmunt Sz

AU - Szmyd, Janusz S.

PY - 2014

Y1 - 2014

N2 - Most theoretical approaches for analysing heat transfer processes yield a unique solution from a specified set of governing equations, boundary and initial conditions and thermophysical properties of fluids and materials. This deterministic approach does not include uncertainties connected with the inaccuracy of directly measured variables and model simplifications. This study presents the idea of evaluating the most probable value obtained in a theoretical solution and a measure of its uncertainty. The proposed methodology - the Generalized Least Squares (GLS) method - allows for including additional data, which are commonly used for validation purposes, in the mathematical model as the supplementary variables. Theoretical considerations are then illustrated by applying the proposed methodology to the steady-state heat conduction process. On the basis of a formal mathematical model with the implementation of the GLS method, the computer program was prepared and applied to an analysis of several different cases, which demonstrate that the GLS methodology can be adopted for both: the process of planning experiments and the analysis of overdetermined problems. The advantages of the proposed method ensure obtaining optimal solutions to the problems of finding the proper position of the probe in the experiment design process, the determination of the empirical parameters and calculating the temperature distribution. The presented results proved that the proposed method is useful in verifying the incorrectly defined models as well as in identifying faulty measurement devices. The analysis pointed out that the experimental inaccuracy can be reduced and the most probable values of all unknown variables can be calculated.

AB - Most theoretical approaches for analysing heat transfer processes yield a unique solution from a specified set of governing equations, boundary and initial conditions and thermophysical properties of fluids and materials. This deterministic approach does not include uncertainties connected with the inaccuracy of directly measured variables and model simplifications. This study presents the idea of evaluating the most probable value obtained in a theoretical solution and a measure of its uncertainty. The proposed methodology - the Generalized Least Squares (GLS) method - allows for including additional data, which are commonly used for validation purposes, in the mathematical model as the supplementary variables. Theoretical considerations are then illustrated by applying the proposed methodology to the steady-state heat conduction process. On the basis of a formal mathematical model with the implementation of the GLS method, the computer program was prepared and applied to an analysis of several different cases, which demonstrate that the GLS methodology can be adopted for both: the process of planning experiments and the analysis of overdetermined problems. The advantages of the proposed method ensure obtaining optimal solutions to the problems of finding the proper position of the probe in the experiment design process, the determination of the empirical parameters and calculating the temperature distribution. The presented results proved that the proposed method is useful in verifying the incorrectly defined models as well as in identifying faulty measurement devices. The analysis pointed out that the experimental inaccuracy can be reduced and the most probable values of all unknown variables can be calculated.

KW - Computational methods

KW - Conduction

KW - Measurement and instrumentation

KW - Optimal experiment planning

KW - The Generalized Least Squares Method

KW - The validation of mathematical models

KW - Uncertainty evaluation

UR - http://www.scopus.com/inward/record.url?scp=84964461963&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84964461963&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84964461963

BT - Proceedings of the 15th International Heat Transfer Conference, IHTC 2014

PB - Begell House Inc.

ER -