Simultaneously estimate solid- and liquid-phase thermal conductivities

Abstract

This paper proposes a method for simultaneously estimating solid- and liquid-phase thermal conductivities of phase-change materials (PCMs). This parameter-estimation method is built on a phase-change line-source solution. Several theoretical issues of parameter estimation were discussed, including sensitivity, identifiability, and uncertainty. The analysis reveals that the liquid- and solid-phase thermal diffusivities (αl and αs) are insensitive to temperature responses and are difficult to estimate. Although the solid-phase conductivity ks have large sensitivity coefficients, they are linearly dependent on the sensitivity coefficients of αl and αs. This paper proposes estimating solid- and liquid-phase thermal conductivities simultaneously by a fitting and a non-fitting algorithms because they have large, uncorrelated sensitivity coefficients. The non-fitting algorithm differs the fitting one in that it produces a set of estimates, which can be considered as a set of samples involving experimental errors and can be used to estimate the uncertainty of the estimated parameters by variances, confidence limits, etc.