Effect of Heat Source and Imperfect Contact on Simultaneous Estimation of Thermal Properties of High-Conductivity Materials

Giampaolo D’Alessandro,Donald E Amos,Filippo De Monte

doi:10.1155/2019/5945413

Giampaolo D’Alessandro, Donald E Amos + Show 1 more

Open Access

https://doi.org/10.1155/2019/5945413

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Abstract

In the current paper a novel methodology accounting for both the heater heat capacity and the imperfect thermal contact between a thin heater and a specimen is proposed. In particular, the volumetric heat capacity of the heater is considered by modelling it as a lumped capacitance body, while the imperfect thermal contact is considered by means of a contact resistance. Thus, the experimental apparatus consisting of three layers (specimen-heater-specimen) is reduced to a single finite layer (sample) subject to a “nonclassical” boundary condition at the heated surface, known as sixth kind. Once the temperature solution is derived analytically using the Laplace transform method, the scaled sensitivity coefficients are computed analytically at the interface between the heater and the sample (heater side and sample side) and at the sample backside. By applying the proposed methodology to a lab-controlled experiment available in the specialized literature, a reduction of the thermal properties values of about 1.4% is observed for a high-conductivity material (Armco iron).

Highlights

Sensitivity coefficients are used in parameter estimation [1], optimal experimental design [2], and uncertainty analysis [3]
In an experimental apparatus for which sensitivity coefficients had not been studied adequately it is possible that additional materials used in the experimental set-up may affect the temperature more than the material under investigation; the temperature sensor location might not be the optimal one
The analysis shows that for estimating the thermal conductivity k, in the event that the heat capacity ratio (P) is unknown, the temperature sensor should be placed at x = 1, where the influence of this parameter is lower

Summary

Introduction

Sensitivity coefficients are used in parameter estimation [1], optimal experimental design [2], and uncertainty analysis [3]. The focus of the current paper is to develop a new procedure accounting for both the heater heat capacity and the imperfect thermal contact between the thin heater and the specimen For this reason, the dependence of the thermal properties on temperature is not considered here. By comparing measured and calculated temperatures through the ordinary least squares norm and, minimizing this by the well-established Gauss method, a reduction of about 1.4% was observed for the thermal properties values of the sample considered (Armco iron). This slight reduction is in accordance with the very thin heater and the very low contact resistance of the experimental apparatus considered

Mathematical Formulation

Temperature Solution

Sensitivity Coefficients

Experimental Results

Conclusions