Inverse problem in a porous medium: estimation of effective thermal properties

Znaidia, Sami; Mzali, Foued; Sassi, L.; Mhimid, Abdallah; Jemni, Abdelmajid; Nasrallah, Sassi Ben; Petit, Daniel

doi:10.1080/17415970500098337

Cited by 15 publications

(8 citation statements)

References 17 publications

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“…In the area of heat transfer, inverse problems have been investigated by many researchers [5][6][7][8][9][10][11][12][13][14][15][16]. Erturk et al [5] estimated boundary conditions in a transient radiative enclosure.…”

Section: Introductionmentioning

confidence: 99%

“…They estimated heat input to a heater located at the top of a three-dimensional enclosure that can satisfy a prescribed time-dependent temperature curve on a surface located at the base of the enclosure. 455 Downloaded by [University of California Santa Cruz] at 01: 37 20 November 2014 An inverse analysis to simultaneously estimate the effective thermal conductivity, the effective volumetric heat capacity, and the heat transfer coefficient between a porous medium and a hot wire was performed by Znaidia et al [11]. They used the Levenberg-Marquardt method to solve the inverse problem.…”

Section: Introductionmentioning

confidence: 99%

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An Inverse Analysis for Parameter Estimation Applied to a Non-Fourier Conduction–Radiation Problem

Das

Mishra

Kumar

et al. 2011

Heat Transfer Engineering

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Retrieval of parameters in a non-Fourier conduction and radiation heat transfer problem is reported. The direct problem is formulated using the lattice Boltzmann method (LBM) and the finite-volume method (FVM). The divergence of radiative heat flux is computed using the FVM, and the LBM formulation is employed to obtain the temperature field. In the inverse method, this temperature field is taken as exact. Simultaneous estimation of parameters, namely, the extinction coefficient and the conduction-radiation parameter, is done by minimizing the objective function. The genetic algorithm (GA) is used for this purpose. The accuracies of the estimated parameters are studied for the effects of measurement errors and genetic parameters such as the crossover and mutation probabilities, the population size, and the number of generations. The LBM-FVM in combination with GA has been found to provide a correct estimate of parameters.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Inverse Analysis for Parameter Estimation Applied to a Non-Fourier Conduction–Radiation Problem

Das

Mishra

Kumar

et al. 2011

Heat Transfer Engineering

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“…Znaidia et al [6] estimated the effective thermal conductivity, the effective volumetric heat capacity as well as the heat transfer coefficient between a porous medium and a hot wire by a numerical inverse analysis. An iterative procedure, based on minimizing a sum of squares function with the Levenberg-Marquardt method was used to solve an inverse problem.…”

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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“…The determination of these parameters by transient electro-thermal methods is the subject of many researches [1][2][3][4][5][6]. Some authors [2][3][4] proposed an estimation of effective thermal properties by using the hot wire method associated with a direct or an inverse method. Yi He [5] used the hot disk method for measuring the effective thermal conductivity.…”

Section: Introductionmentioning

confidence: 99%

Identification of thermophysical characteristics of materials using heating probe

Nasr

Alghamdi

Alsoufi

2016

IJET

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This paper investigates the numerical analysis to determine the thermo-physical characteristics of materials. This method is based on a heating probe kept at a constant temperature and maintained in contact with a cylindrical sample. The heat power dissipated in the sample is measured by the probe. The results address to identify simultaneously the thermal conductivity, the volumetric heat capacity and the heat transfer coefficient using the inverse problem.

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Inverse problem in a porous medium: estimation of effective thermal properties

Cited by 15 publications

References 17 publications

An Inverse Analysis for Parameter Estimation Applied to a Non-Fourier Conduction–Radiation Problem

An Inverse Analysis for Parameter Estimation Applied to a Non-Fourier Conduction–Radiation Problem

Global optimization of thermal conductivity using stochastic algorithms

Identification of thermophysical characteristics of materials using heating probe

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