Inverse Estimation of Temperature-Dependent Thermal Conductivity and Heat Capacity Per Unit Volume With the Direct Integration Approach

Kim, Sin; Chung, Bum-Jin; Kim, Min Chan; Kim, Kyung Youn

doi:10.1080/713838252

Cited by 22 publications

(12 citation statements)

References 9 publications

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“…IHCPs can also be classified by the kinds of unknown to be determined. Such unknowns can be the material property [7,8], boundary conditions [1,9], and geometry [10,11]. Other unknowns are the heat sources [12,13] and interface conductance [14], which are not considered in this study.…”

Section: Introductionmentioning

confidence: 98%

Object-Oriented Development of Inverse Heat Conduction Code Adaptable to Various Configurations

Kim¹

2006

Numerical Heat Transfer, Part B: Fundamentals

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This article suggests a method for developing computer code that can solve inverse heat conduction problems (IHCPs). The concept of object-oriented development is employed to implement the computer code in an efficient and flexible fashion. The software design is conducted based on the unified modeling language. Furthermore, this article also explains how to implement the deliverable computer code using existing software development tools. The flexibility and reusability of the developed code is emphasized and verified through two examples, which are adaptable regularization and the modification of existing IHCP code for another IHCP.

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Section: Introductionmentioning

confidence: 98%

Object-Oriented Development of Inverse Heat Conduction Code Adaptable to Various Configurations

Kim¹

2006

Numerical Heat Transfer, Part B: Fundamentals

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“…Yang [4] estimated the temperature-dependent thermal conductivity and heat capacity, simultaneously, from two temperature responses measured at the system boundaries. Kim et al [5] proposed an integration approach to estimate the temperature-dependent thermal conductivity and heat capacity, simultaneously, in a one-dimensional non-linear heat conduction medium. The thermal properties were assumed to vary the time linearly with respect to temperature, and then were modelled as linear mathematical functions of temperature with unknown coefficients obtained by Levenberg-Marquardt method.…”

Section: Introductionmentioning

confidence: 99%

“…Unlike the conventional techniques, the resolution of the IHTP permits the determination of more than one thermo-physical property and the understanding of complex materials. Different optimization techniques, such as conjugate gradient and Levenberg-Marquardt methods were employed to estimate the thermo-physical properties in recent literature [1][2][3][4][5][6][7]. Modern optimization methodologies are being used to solve inverse problems, particularly stochastic methods, which usually supply potential solutions, but the computational time required by stochastic methods generally exceeds that of deterministic optimization methods [8,9].…”

Section: Introductionmentioning

confidence: 99%

Global optimization of thermal conductivity using stochastic algorithms

Mariani

Coelho

2009

Inverse Problems in Science and Engineering

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In this article, the performance of a self-organizing migration algorithm (SOMA), a new stochastic optimization algorithm, has been compared with a genetic algorithm with floating-point representation (GAF) and differential evolution (DE) for an engineering application. This application is the estimation of the apparent thermal conductivity of foods at freezing temperature using an inverse method. Assuming two piecewise functions for apparent thermal conductivity in function of the temperature data, the heat diffusion equation was solved to estimate the unknown variables of inverse problem. The thermal conductivity is continuously adjusted by three approaches of stochastic optimization algorithms, used to minimize a performance criterion based on error information for the inverse problem. The variables that provide the best fitness between the experimental and predicted time-temperature curves at centre of the food under freezing conditions were obtained. Moreover, a statistical analysis showed the agreement between reported and estimated curves. In this application domain, the SOMA and DE approaches outperform the GAF.Nomenclature c random value in GAF c p specific heat (J kg À1 C À1 ) CR crossover or recombination rate in DE DE differential evolutionf objective function f m mutation factor in DE g parameter in SOMA GAF genetic algorithm with floating-point representation h heat transfer coefficient (W m À2 C À1 )H volumetric specific enthalpy (J m À3 ) IHTP inverse heat transfer problem k thermal conductivity (W m À1 C À1 ) L half length in x direction (m) m difference between leader and start position of individual in SOMA N size population (individuals); number of samples N (0,1) random number with Gaussian distribution, zero mean and variance one PRT parameter in range [0,1] in SOMA PRT ! perturbation vector in SOMA rnd random number generation r vector candidate solution in SOMA R 2 Pearson multiple correlation coefficient index SOMA self-organizing migration algorithm t coordinate in freezing time (s) T theoretical temperature ( C) experimental temperature ( C) u trial vector in DE x vector solution z mutant vector in DE Greek symbols step length used in BFGS evaluated by Armijo or index for indicates vectors in DE recombination mechanism in DE " tolerance value density (kg m À3 ) index that indicates the method for selecting of the parent chromosome in DE Át temporal mesh step (s) Áx spatial mesh step (m) Subscripts i index represents mesh interval or individuals for optimization algorithms j index represents time interval or dimensions problem space l leader in SOMA max maximum n dimension of the vector solution n pop size population r 1 , r 2 , r 3 integers used in DE 0 initial 1 ambient 512 V.C. Mariani and L. dos Santos Coelho Superscripts ct generations counter L lower boundary tt time indicator U upper boundary * reference which corresponds to null enthalpy

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“…Huang and Yeh [12] employed the conjugate gradient method to solve the inverse problem in estimating the temperature-dependent thermal conductivity of the homogeneous and non-homogeneous solid material based on 12 temperatures measured at different positions. Kim et al [15] proposed an integration approach to estimate the temperature-dependent thermal conductivity and heat capacity per unit volume simultaneously in a onedimensional non-linear heat conduction medium. The thermal properties were assumed to vary linearly with respect to temperature, and then were modelled as linear mathematical functions of temperature with unknown coefficients obtained by Levenberg-Marquardt method.…”

Section: Introductionmentioning

confidence: 99%

“…Different techniques such as: the conjugate gradient method [8][9][10][11] and the Levenberg-Marquardt method [8,12] were performed in the literature and were used to estimate the thermophysical properties [13][14][15][16][17]. New methodologies are being used to solve inverse problems, particularly stochastic methods, which usually supply potential solutions, but the computational time required by stochastic methods generally exceeds that of deterministic optimization methods [18][19].…”

Section: Introductionmentioning

confidence: 99%

Estimation of the apparent thermal diffusivity coefficient using an inverse technique

Mariani

Coelho

2009

Inverse Problems in Science and Engineering

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In this work, an inverse heat conduction problem is solved and optimization methods are used to estimate the variable apparent thermal diffusivity coefficient of bananas during the drying process. Thermal diffusivity is the transport property that controls conduction heat transfer in a transient regime. During banana drying, the thermal diffusivity modifies with the drying time, i.e. with the temperature and moisture content. The estimation is based on transient temperature measurements taken by a thermocouple on the inner part of the banana on which the heat flow occurs. The inverse problem is solved as an optimization problem where the objective function is minimised by two optimization methods: quasi-Newton (Broyden-Fletcher-Goldfarb-Shanno algorithm) and differential evolution. Numerical experiments are used to test the proposed mathematical model of the measurement of thermal diffusivity coefficient. Specifically, statistical analysis showed no significant differences between reported and estimated curves using the differential evolution method, unfortunately the quasi-Newton method performs poorly.Nomenclature A 1 , A 4 ¼ optimization variables in Equation (12) x ¼ vector solution (optimization variables) in DE and BFGS X ¼ moisture content (kg w kg dm À1 ) X ¼ average moisture content (kg w kg dm À1 ) z ¼ mutant vector in DEGreek symbols ¼ thermal diffusivity (m 2 s À1 ) ¼ index for indicates vectors in DE ¼ step length used in BFGS ¼ recombination mechanism " ¼ tolerance value ¼ thermal conductivity (W m À1 C À1 ) ¼ density (kg m À3 ) r ¼ gradient vector Ár ¼ spatial mesh step (m) Át ¼ time step (s) ¼ viscosity (Pa s) ! ¼ method for selecting of the parent individual in DE 570

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Inverse Estimation of Temperature-Dependent Thermal Conductivity and Heat Capacity Per Unit Volume With the Direct Integration Approach

Cited by 22 publications

References 9 publications

Object-Oriented Development of Inverse Heat Conduction Code Adaptable to Various Configurations

Object-Oriented Development of Inverse Heat Conduction Code Adaptable to Various Configurations

Global optimization of thermal conductivity using stochastic algorithms

Estimation of the apparent thermal diffusivity coefficient using an inverse technique

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