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1

Determination of thermal diffusivity values based on the inverse problem of heat conduction - numerical analysis

Adamowicz Adam

Acta Mechanica et Automatica

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2022

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Vol. 16, no. 4

399--407

EN

This paper presents a discussion on the accuracy of the method of determining the thermal diffusivity of solids using the solution of the inverse heat conduction equation. A new measurement data processing procedure was proposed to improve the effectiveness of the method. Using the numerical model, an analysis of the sensitivity of the method of thermal diffusivity determination to changes in operational and environmental parameters of the test was carried out. The obtained results showed that the method was insensitive to the parameters of the thermal excitation impulse, the thickness of the tested sample, and the significant influence of convection cooling on its accuracy. The work was completed with the formulation of general conclusions concerning the conditions for determining the thermal diffusivity of materials with the use of the described method.

2

The application of Beck’s method combined with FEM and Trefftz functions to determine the heat transfer coefficient in a minichannel

Maciejewska B.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 1

103--116

EN

The aim of this study is to determine the heat transfer coefficient between the heated surface and the boiling fluid flowing in a minichannel on the basis of experimental data. The calculation model is based on Beck’s method coupled with the FEM and Trefftz functions. The Trefftz functions used in the Hermite interpolation are employed to construct the shape functions in the FEM. The unknown local values of the heat transfer coefficient at the foil- -fluid contact surface are calculated from Newton’s law. The temperature of the heated foil and the heat flux on the foil surface are determined by solving a two-dimensional inverse heat conduction problem. The study is focused on the identification of the heat transfer coefficients in the subcooled boiling region and the saturated nucleate boiling region. The results are compared with the data obtained through the one-dimensional method. The investigations also reveal how the smoothing of measurement data affects calculation results.

3

Heating source localization in a reduced time

Beddiaf S., Autrique L., Perez L., Jolly J. C.

International Journal of Applied Mathematics and Computer Science

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2016

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Vol. 26, no. 3

623--640

EN

Inverse three-dimensional heat conduction problems devoted to heating source localization are ill posed. Identification can be performed using an iterative regularization method based on the conjugate gradient algorithm. Such a method is usually implemented off-line, taking into account observations (temperature measurements, for example). However, in a practical context, if the source has to be located as fast as possible (e.g., for diagnosis), the observation horizon has to be reduced. To this end, several configurations are detailed and effects of noisy observations are investigated.

4

Identyfikacja współczynnika wnikania ciepła na zewnętrznej powierzchni termometru do wyznaczania nieustalonej temperatury płynu

Taler J., Jaremkiewicz M.

Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika

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2015

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z. 87 [291], nr 3

251--260

PL

Opracowano metodę wyznaczania współczynnika wnikania ciepła na powierzchni zewnętrznej termometru służącego do pomiaru temperatury czynnika przepływającego pod wysokim ciśnieniem. Metoda opiera się na rozwiązaniu odwrotnego zagadnienia przewodzenia ciepła. Współczynnik wnikania ciepła jest określany na podstawie pomiaru temperatury w środku metalowego cylindrycznego termometru oraz na podstawie pomiaru temperatury ścianki cylindrycznego rurociągu, który jest izolowany cieplnie. Dodatkowo jest wyznaczany współczynnik wnikania ciepła na wewnętrznej powierzchni rurociągu. Korelacje na liczby Nusselta, z których są wyznaczane współczynniki wnikania ciepła na zewnętrznej powierzchni termometru i wewnętrznej powierzchni rurociągu, zawierają nieznane współczynniki, które wyznacza się metodą najmniejszych kwadratów. Wyznaczone współczynniki wykazują dobrą zgodność ze współczynnikami przyjętymi podczas rozwiązywania zagadnienia bezpośredniego.

EN

The aim of the study was to develop a method of determining the heat transfer coefficient on the outer surface of the thermometer with the large diameter casing, which is used for measuring the temperature of the fluid flowing under high pressure. The method is based on solving the inverse heat conduction problems. The heat transfer coefficient is determined based on measuring the temperature in the middle of the solid cylinder and the temperature of the pipeline wall which is thermally insulated. The heat transfer coefficient on the inner surface of the pipeline is calculated using the known correlation for the Nusselt number. The correlation for the Nusselt number contains one unknown coefficient which is determined using the least squares method. Several time points are taken into account in the sum of temperature difference squares. The estimated coefficients are in good agreement with the input values used for the solution of the inverse problem.

5

Infrared image filtering applied to the restoration of the convective heat transfer coefficient distribution in coiled tubes

Bozzoli F., Cattani L., Pagliarini G., Rainieri S.

Opto-Electronics Review

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2015

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Vol. 23, No. 1

107-115

EN

This paper presents and assesses an inverse heat conduction problem (IHCP) solution procedure which was developed to determine the local convective heat transfer coefficient along the circumferential coordinate at the inner wall of a coiled pipe by applying the filtering technique approach to infrared temperature maps acquired on the outer tube’s wall. The data-processing procedure filters out the unwanted noise from the raw temperature data to enable the direct calculation of its Laplacian which is embedded in the formulation of the inverse heat conduction problem. The presented technique is experimentally verified using data that were acquired in the laminar flow regime that is frequently found in coiled-tube heat-exchanger applications. The estimated convective heat transfer coefficient distributions are substantially consistent with the available numerical results in the scientific literature.

6

Optimum heating of boiler drums

Dzierwa P.

Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika

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2014

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z. 86 [290], nr 2

199--206

EN

W pracy przedstawiono sposób wyznaczania optymalnych zmian temperatury czynnika. Nagrzewanie elementów ciśnieniowych jest prowadzone w taki sposób, aby obwodowe naprężenie na krawędzi otworu w punkcie koncentracji wywołane ciśnieniem i zmianami temperatury czynnika, nie przekraczały wartości dopuszczalnej. W przeciwieństwie do aktualnych norm, analizowany jest rozkład naprężeń w dwóch punktach na krawędzi otworu. Optymalne zmiany temperatury płynu przybliżane są w formie prostych funkcji czasu. Temperatura czynnika na początku procesu nagrzewania zmienienia się skokowo a następnie wzrasta ze stałą prędkością. Temperatura czynnika na początku procesu nagrzewania zmienienia się skokowo, a następnie wzrasta ze stałą prędkością.

7

Analysis of the possibility of determining the internal structure of composite material by estimating its thermal diffusivity

Kucypera S.

Archives of Thermodynamics

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2014

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Vol. 35, no. 1

3--15

EN

The aim of this paper is analysis of the possibility of determining the internal structure of the fibrous composite material by estimating its thermal diffusivity. A thermal diffusivity of the composite material was determined by applying inverse heat conduction method and measurement data. The idea of the proposed method depends on measuring the timedependent temperature distribution at selected points of the sample and identification of the thermal diffusivity by solving a transient inverse heat conduction problem. The investigated system which was used for the identification of thermal parameters consists of two cylindrical samples, in which transient temperature field is forced by the electric heater located between them. The temperature response of the system is measured in the chosen point of sample. One dimensional discrete mathematical model of the transient heat conduction within the investigated sample has been formulated based on the control volume method. The optimal dynamic filtration method as solution of the inverse problem has been applied to identify unknown diffusivity of multi-layered fibrous composite material. Next using this thermal diffusivity of the composite material its internal structure was determined. The chosen results have been presented in the paper.

8

Identification of the thermal conductivity coefficient by using the Artificial Bee Colony algorithm

Hetmaniok E., Słota D., Zielonka A.

Hutnik, Wiadomości Hutnicze

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2012

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Vol. 79, nr 1

41--44

EN

Aim of this paper is to present the numerical method of identification of the thermal conductivity parameter of a material in course of the ingot cooling. Mathematical model of the direct problem is the heat conduction equation with boundary conditions of the second and third kind. Presented approach is based on application of the Artificial Bee Colony algorithm for minimizing the appropriate functional expressing the error of approximate solution. Proposed procedure is investigated with regard to the velocity of working and the precision of obtained results.

PL

Celem pracy jest prezentacja numerycznej metody identyfikacji współczynnika przewodności cieplnej materiału podczas stygnięcia wlewka. Modelem matematycznym zagadnienia bezpośredniego jest równanie przewodnictwa ciepła z warunkami brzegowymi drugiego i trzeciego rodzaju. Idea metody polega na wykorzystaniu algorytmu kolonii sztucznych pszczół (Artificial Bee Colony algorithm) do minimalizacji odpowiedniego funkcjonału, wyrażającego błąd rozwiązania przybliżonego. Proponowana metoda zbadana została ze względu na szybkość działania oraz dokładność uzyskanych wyników.

9

Application of swarm intelligence algorithms in solving the inverse heat conduction problem

Hetmaniok E., Słota D., Zielonka A.

Computer Assisted Methods in Engineering and Science

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2012

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Vol. 19, no. 4

361-367

EN

In the paper a proposal of using selected swarm intelligence algorithms for solving the inverse heat conduction problem is presented. The analyzed problem consist s in reconstructing temperature distribution in the given domain and the form of heat transfer coefficient ap pearing in the boundary condition of the third kind. The investigated approaches are based on the Art ificial Bee Colony algorithm and the Ant Colony Optimization algorithm, the efficiency of which are ex amined and compared

10

Optimum heating of cylindrical pressure components weakened by holes

Dzierwa P., Taler J.

Archives of Thermodynamics

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2012

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Vol. 33, no. 3

111-121

EN

A method for determining time-optimum medium temperature changes is presented. The heating of the pressure elements will be conducted so that the circumferential stress caused by pressure and fluid temperature variations at the edge of the opening at the point of stress concentration, do not exceed the allowable value. In contrast to present standards, two points at the edge of the opening are taken into consideration. The first point, P[1], is located at the cross section and the second, P[2], at the longitudinal section of the vessel. It will be shown that the optimum temperature courses should be determined with respect to the total circumferential stress at the point P[2], and not, as in the existing standards due to the stress at the point P[1]. Optimum fluid temperature changes are assumed in the form of simple time functions. For practical reasons the optimum temperature in the ramp form is preferred. It is possible to increase the fluid temperature stepwise at the beginning of the heating process and then increase the fluid temperature with the constant rate. Allowing stepwise fluid temperature increase at the beginning of heating ensures that the heating time of a thick-walled component is shorter than heating time resulting from the calculations according to EN 12952-3 European Standard. @eng

11

Wyznaczanie przewodności cieplnej materiałów tekstylnych przy użyciu termowizji

Felczak M., Michalak M., Więcek B.

Pomiary Automatyka Kontrola

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2011

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R. 57, nr 10

1223-1226

PL

W pracy przedstawiono nową metodę wyznaczania parametrów termicznych materiałów włókienniczych, w tym także anizotropowych. Do próbek włókienniczych dostarczana jest energia cieplna i mierzona jest wartość temperatury po obu stronach materiału. Praca jest kontynuacją badań właściwości ciepłoizolacyjnych materiałów włókienniczych w dynamicznych warunkach za pomocą metody termograficznej w wykorzystaniem luster [1-6]. W stanowisku pomiarowym, którego schemat przedstawiono w cytowanych pracach zostało zastosowane źródło energii cieplnej umożliwiające szybkie nagrzewanie badanej próbki. Wykonano pomiary termowizyjne rozkładu temperatury i na podstawie uzyskanych wyników oraz modelowania termicznego wyznaczono przewodność cieplną badanych włóknin.

EN

A new method for evaluation of homogenous anisotropic textiles thermal parameters is presented in this paper. The research is a continuation of investigating the thermal properties of textile materials [1-6]. The thermal energy was supplied to textile materials and the temperature distribution on both surfaces of the textile waas recorded using an infrared camera. The setup enabled fast textile heating. A thermal energy impulse was supplied to nonwovens. Using the obtained results and the finite element model of heat conduction, the thermal conductivity of a textile is evaluated. In order to obtain the thermal conductivity, it is necessary to solve an inversed heat conduction problem. The parameterized direct heat conduction model is used to calculate it. The research included both isotropic and anisotropic textile materials. The work was performed as a part of the Research Project 3 T08E 050 28 financed by KBN, entitled "3688/B/T02/2009/36 "The elaboration of the method of evaluation of temperature dependent thermal parameters of smart textile materials".

12

An idea of a measurement system for determining thermal parameters of heat insulation materials

Chudzik S., Minkina W.

Metrology and Measurement Systems

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2011

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Vol. 18, nr 2

261-273

EN

The article presents the prototype of a measurement system with a hot probe, designed for testing thermal parameters of heat insulation materials. The idea is to determine parameters of thermal insulation materials using a hot probe with an auxiliary thermometer and a trained artificial neural network. The network is trained on data extracted from a nonstationary two-dimensional model of heat conduction inside a sample of material with the hot probe and the auxiliary thermometer. The significant heat capacity of the probe handle is taken into account in the model. The finite element method (FEM) is applied to solve the system of partial differential equations describing the model. An artificial neural network (ANN) is used to estimate coefficients of the inverse heat conduction problem for a solid. The network determines values of the effective thermal conductivity and effective thermal diffusivity on the basis of temperature responses of the hot probe and the auxiliary thermometer. All calculations, like FEM, training and testing processes, were conducted in the MATLAB environment. Experimental results are also presented. The proposed measurement system for parameter testing is suitable for temporary measurements in a building site or factory.

13

Reconstruction of the thermal conductivity coefficient by using the harmony search algorithm

Grzymkowski R., Hetmaniok E., Słota D., Zielonka A.

Journal of Achievements in Materials and Manufacturing Engineering

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2011

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Vol. 49, nr 2

299--304

EN

Purpose: of this paper: Aim of this paper is a presentation of the respectively new tool for solving the optimization problems, which is the Harmony Search algorithm in version slightly modified by the authors, used for identifying the thermal conductivity coefficient. Proposed approach is illustrated with an example confirming its usefulness for solving such kinds of problems. Design/methodology/approach: For solving the considered parametric inverse heat conduction problem the approach is applied in which the essential part consists in minimization of the functional representing the differences between the measurement values of temperature and approximate values calculated with the aid of finite difference method. For minimizing the functional the Harmony Search algorithm is used. Findings: The elaboration shows that approaches involving the algorithms of artificial intelligence for solving the inverse heat conduction problems of that kind are efficient and they ensure to receive satisfying results in shorter time in comparison with the classical procedures. Research limitations/implications: Specific properties of the heuristic algorithms require to execute the procedure several times and to average the obtained results because each running of the algorithm can give slightly different results. Each execution of the procedure means the solution of the direct problem associated with the considered inverse problem by using the finite difference method. Practical implications: In spite of the problem described above the approaches involving the heuristic algorithms of artificial intelligence are successful because they are respectively simple and easy to use and they give satisfying results after short time of working. Another advantage of using optimization algorithms of that kind is the fact that they do not need to satisfy any assumptions about the solved problem, oppositely to the classical optimization algorithms. Originality/value: Proposal of the original approach involving the heuristic optimization algorithm for solving the parametric inverse heat conduction problem is discussed in the paper.

14

New technique of the local heat flux measurement in combustion chambers of steam boilers

Taler J., Taler D., Sobota T., Dzierwa P.

Archives of Thermodynamics

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2011

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Vol. 32, no. 3

103-116

EN

A new method for measurement of local heat flux to waterwalls of steam boilers was developed. A flux meter tube was made from an eccentric tube of short length to which two longitudinal fins were attached. These two fins prevent the boiler setting from heating by a thermal radiation from the combustion chamber. The fins are not welded to the adjacent water-wall tubes, so that the temperature distribution in the heat flux meter is not influenced by neighbouring water-wall tubes. The thickness of the heat flux tube wall is larger on the fireside to obtain a greater distance between the thermocouples located inside the wall which increases the accuracy of heat flux determination. Based on the temperature measurements at selected points inside the heat flux meter, the heat flux absorbed by the water-wall, heat transfer coefficient on the inner tube surface and temperature of the water-steam mixture was determined.

15

Measurements of absorbed heat flux and water-side heat transfer coefficient in water wall tubes

Taler D., Taler J., Kowal A.

Archives of Thermodynamics

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2011

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Vol. 32, no. 1

77-88

EN

The tubular type instrument (flux tube) was developed to identify boundary conditions in water wall tubes of steam boilers. The meter is constructed from a short length of eccentric tube containing four thermocouples on the fire side below the inner and outer surface of the tube. The fifth thermocouple is located at the rear of the tube on the casing side of the water-wall tube. The boundary conditions on the outer and inner surfaces of the water flux-tube are determined based on temperature measurements at the interior locations. Four K-type sheathed thermocouples of 1 mm in diameter, are inserted into holes, which are parallel to the tube axis. The non-linear least squares problem is solved numerically using the Levenberg-Marquardt method. The heat transfer conditions in adjacent boiler tubes have no impact on the temperature distribution in the flux tubes.

16

A new method of drum heating determination during start-up of steam boilers

Taler D., Dzierwa P.

Archives of Thermodynamics

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2009

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Vol. 30, no. 4

81-95

EN

A method for determining time-optimum medium temperature changes is presented. Heating and cooling of pressure exposed elements will be conducted in such way, that the circumferential stresses caused by pressure and fluid temperature variations at the edge of the opening and at the point of stress concentration, do not exceed the allowable values. How-ever, the calculated optimum temperature changes are difficult to follow in practice in the initial stage of heating. It is however possible to in-crease the fluid temperature stepwise to the minimum value and then heat the pressure component according to the determined optimum temperature changes. Allowing stepwise fluid temperature increase at the beginning of heating ensures that the heating time of a thick-walled component is shorter, than heating time resulting from the calculations according to EN 12952-3 European Standard or TRD 301 regulations.

17

Identyfikacja zależnych od temperatury parametrów cieplnych ciał ortotropowych z wykorzystaniem rozwiązania zagadnienia odwrotnego przewodzenia ciepła

Kucypera S.

Modelowanie Inżynierskie

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2007

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T. 3, nr 34

79-84

PL

W zagadnieniach identyfikacji procesów termofizycznych istnieje często konieczność wyznaczenia charakterystyk temperaturowych dla współczynnika przewodzenia ciepła i ciepła właściwego materiałów ortotropowych. Dlatego celem niniejszej pracy jest identyfikacja charakterystyk temperaturowych parametrów termofizycznych materiałów ortotropowych za pomocą rozwiązania odwrotnego zagadnienia przewodzenia ciepła oraz danych pomiarowych. Do rozwiązania zagadnienia odwrotnego wykorzystano iteracyjną metodę dynamicznej estymacji sekwencyjnej. Przedstawiono przykładowe wyniki analizy.

EN

In the identification of the thermophysical processes often it is necessary to determine temperature characteristics for the thermal conductivity and specific heat of the ortotropic materials. Therefore the aim of this paper is identification temperature characteristics of the thermophysical parameters of the ortotropic materials by means of solving the inverse heat conduction problem and measurements data.. To solve the inverse problem the iterative sequential dynamic estimation method has been used. Selected results of the analysis have been presented.

18

Identification of source function using the numerical methods

Metelski A., Lara S., Pawlak E.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2006

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Vol. 5, nr 1

148-153

EN

In the paper the inverse heat conduction problem is discussed. The energy equation contains the term determining the capacity of volumetric internal heat sources q(x) (x is a geometrical coordinate) and this parameter is identified. The solution of inverse problem bases on the least square criterion in which the sensitivity coefficients are introduced. In the final part of paper the examples concerning 1D and 2D problems are shown.

19

Inverse analysis of the heat conduction process induced by impinging jet

Woelke M., Bogusławski L.

Archives of Mechanics

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2002

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Vol. 54, nr 4

299-317

EN

This paper presents an analysis of the cooling process of a solid, induced by the impingement of an air jet. Solutions of the inverse heat conduction problem were obtained by applying the heat functions to formulate the base functions of the Finite Element Method. The applied heat functions identically satisfy the heat conduction equation in dimensionless co-ordinates. The minimisation of the functional, presented in this paper, leads to the solutions of the analysed problem. The temperature distribution of the analysed solid was determined by solving the inverse heat conduction problem by means of the temperature measurements taken inside the solid. Properties of the heat function were applied to reconstruct the distribution of the Bi number on the heat exchange surface; this in turn enables to determine the heat transfer coefficient on the analysed surface. The results of the analysis were compared with the data found in the literature.