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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