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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

Assistant Professor
Lebanese University,
Nabatieh Campus Section V (Lb),
Nabatieh, Lebanon

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

## Abstract

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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## Figures

Fig. 1

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

Fig. 2

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

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.

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).

Fig. 5

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

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.

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.

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.

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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