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Research Papers: SPECIAL SECTION PAPERS

Identification of the Thermophysical Properties of the Soil by Inverse Problem

[+] Author and Article Information
Salwa Mansour

INRIA,
Campus de Beaulieu,
Rennes 35000, France
e-mail: salwa.mansour@inria.fr

Édouard Canot

IRISA,
Campus de Beaulieu,
Rennes 35000, France
e-mail: edouard.canot@irisa.fr

Mohamad Muhieddine

Assistant Professor
Lebanese University,
Nabatieh Campus Section V (Lb),
Nabatieh, Lebanon
e-mail: mohamad.muhieddine@liu.edu.lb

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 5, 2014; final manuscript received October 21, 2015; published online June 1, 2016. Assoc. Editor: Dennis A. Siginer.

J. Heat Transfer 138(9), 091010 (Jun 01, 2016) (8 pages) Paper No: HT-14-1585; doi: 10.1115/1.4032947 History: Received September 05, 2014; Revised October 21, 2015

This paper introduces a numerical strategy to estimate the thermophysical properties of a saturated porous medium (volumetric heat capacity (ρC)s, thermal conductivity λs, and porosity ϕ), where a phase change problem (liquid/vapor) appears due to strong heating. The estimation of these properties is done by inverse problem knowing the heating curves at selected points of the medium. To solve the inverse problem, we use both the damped Gauss Newton (DGN) and the Levenberg Marquardt methods to deal with high nonlinearity of the system and to tackle the problem with large residuals. We use the method of lines where time and space discretizations are considered separately. Special attention has been paid to the choice of the regularization parameter of the apparent heat capacity (AHC) method which may prevent the convergence of the inverse problem.

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References

Oladunjoye, M. A. , Sanuade, O. A. , and Olaojo, A. A. , 2013, “ Variability of Soil Thermal Properties of a Seasonally Cultivated Agricultural Teaching and Research Farm,” Global J. Sci. Front. Res. Agric. Vet., 13, pp. 40–64.
Muhieddine, M. , Canot, É. , and March, R. , 2012, “ Heat Transfer Modeling in Saturated Porous Media and Identification of the Thermophysical Properties of the Soil by Inverse Problem,” J. Appl. Numer. Math., 62(9), pp. 1026–1040. [CrossRef]
Engl, H. W. , and Kugler, P. , 2005, “ Nonlinear Inverse Problems: Theoretical Aspects and Some Industrial Applications,” Multidisciplinary Methods for Analysis, Optimization and Control of Complex Systems, Vol. 6, Springer, Berlin, pp. 3–47.
Dennis, J. E. , and Schnabel, R. B. , 1983, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, NJ.
Björck, A. , 1990, Numerical Methods for Least Squares Problems, Siam, Stockholm, Sweden.
Majchrzak, E. , Mochnacki, B. , and Suchy, J. , 2008, “ Identification of Substitute Thermal Capacity of Solidifying Alloy,” J. Theor. Appl. Mech., 46(2), pp. 257–268.
Muhieddine, M. , Canot, É. , and March, R. , 2009, “ Various Approaches for Solving Problems in Heat Conduction With Phase Change,” Int. J. Finite Vol., 6(1), pp. 1–20.
Bonacina, C. , and Comini, G. , 1973, “ Numerical Solution of Phase-Change Problems,” Int. J. Heat Mass Transfer, 16(10), pp. 1825–1832. [CrossRef]
Civan, F. , and Sliepcevich, C. M. , 1987, “ Limitation in the Apparent Heat Capacity Formulation for Heat Transfer With Phase Change,” Proc. Okla. Acad. Sci., 67, pp. 83–88.
Canot, É. , “ Muesli Reference Manual-Fortran 95 Implementation,” http://people.irisa.fr/Edouard.Canot/muesli
Özişik, M. N. , and Orlande, H. R. B. , 2000, Inverse Heat Transfer, Taylor and Francis, New York.
Moré, J. J. , 1978, “ The Levenberg–Marquardt Algorithm: Implementation and Theory,” Numerical Analysis (Lecture Notes in Mathematics), Springer, Berlin.
Pope, S. R. , Ellwein, L. M. , Zapata, C. L. , Novak, V. , Kelley, C. T. , and Olufsen, M. S. , 2009, “ Estimation and Identification of Parameters in a Lumped Cerebrovascular Model,” Math. Biosci. Eng., 6(1), pp. 93–115. [CrossRef] [PubMed]

Figures

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Fig. 1

Temperature history for ΔT=ΔToptimum and for 160 mesh cells. Comparison between numerical (continuous line) and reference (dotted line) solutions.

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Fig. 2

The enlarged view of temperature history near the phase change recorded at a depth x=1cm for three different values of ΔT

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Fig. 3

Variation of λs as function of iteration number (using scaling and approximation (Eq. (20))). The dotted line represents the exact value of λs.

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Fig. 8

Variation of the conductivity as function of iteration number using LMA (same number of mesh cells in both the forward and inverse problems). The dotted line represents the exact value of λs.

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Fig. 9

Variation of the residue as function of iteration number using LMA (same number of mesh cells in both the forward and inverse problems)

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Fig. 4

Variation of residue as function of number of mesh cells. The method is consistent (the error decreases as number of mesh cells increase).

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Fig. 5

Variation of the conductivity as function of iteration number. The dotted line represents the exact value of λs.

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Fig. 6

Variation of the volumetric heat capacity as function of iteration number using LMA (same number of mesh cells in both the forward and inverse problems). The dotted line represents the exact value of (ρC)s.

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Fig. 7

Variation of the porosity as function of iteration number using LMA (same number of mesh cells in both the forward and inverse problems). The dotted line represents the exact value ofϕ.

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