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New Methodology for Measuring the Thermal Conductivity of Small Samples Using the Boxes Method with Reduced Sensors

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Abstract

The reduction of device components is of a major interest for the conception of low-cost devices with a simple design. Generally, the boxes method measures the effective thermal conductivity of relatively large-sized samples due to its industrial purposes. However, to determine the thermal conductivity of small samples, additional sensors are required. In this work, a new experimental procedure is developed to characterize the thermal conductivity of small samples without any additional sensor. A detailed uncertainty analysis in the thermal conductivity measurements is conducted. The improvement of the instrument uncertainty was also considered. Three different scenarios were examined, from ideal to worst-case, in order to assess the performance of the proposed methodology. The values of the measured thermal conductivity were compared with those obtained by a reference method (hot disk). The comparison shows a good agreement and proves the effectiveness of the used technique. The overall study of the propagation of measurement uncertainties shows that the instrument’s uncertainty was found to be less than 6.1 %.

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Abbreviations

C:

Thermal loss coefficient through the box (W·m−2·K−1)

es :

Thickness of the small sample (m)

eXPS :

Thickness of the insulating frame (m)

Pi :

ith permutation [one]

R:

Resistance of the heater element (Ω)

Ss :

Surface of the small sample (m2)

SXPS :

Surface of the insulating frame (m2)

Tbox_upper :

Temperature of the box (°C)

Tbox_lower :

Temperature of the isothermal capacity (°C)

Tlower :

Temperature of the lower face (°C)

Troom :

Temperature of the room (°C)

Tupper :

Temperature of the higher face (°C)

U:

Voltage (V)

Uxi :

Relative uncertainty in the xi variable (%)

UMFxi :

Uncertainty magnification factor of the xi variable

ΔTloss :

Box/room temperature difference (°C)

ΔTs :

Higher/lower temperature difference of the small sample (°C)

ΔTXPS :

Higher/lower temperature difference of the insulating frame (°C)

\(\delta_{xi}\) :

Absolute uncertainty in the xi variable

\(\uplambda\) :

Thermal conductivity (W·m−1·K−1)

\(\emptyset_{loss}\) :

Heat loss through the box (W)

\(\emptyset_{in}\) :

Heat flow produced by the heating element (W)

\(\emptyset_{sample}\) :

Heat flow through the small sample (W)

\(\emptyset_{XPS}\) :

Heat flow through the insulating frame (W)

EI702:

Boxes method cell

DRE:

Data reduction equation

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Acknowledgments

The authors would like to thank the “National Center for Scientific and Technical Research” for funding this work through the PPR project “Promotion of solar energy and energy efficiency in the oriental region of Morocco”.

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Authors and Affiliations

  1. Mechanics and Energy Laboratory, Mohammed First University, BV Mohammed VI BP 717, 60000, Oujda, Morocco

    Mouatassim Charai, Haitham Sghiouri & Ahmed Mezrhab

  2. CERTES, Université Paris-Est, 61 Avenue du Général de Gaulle, 94010, Créteil Cedex, France

    Mouatassim Charai & Mustapha Karkri

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  1. Mouatassim Charai
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Charai, M., Sghiouri, H., Mezrhab, A. et al. New Methodology for Measuring the Thermal Conductivity of Small Samples Using the Boxes Method with Reduced Sensors. Int J Thermophys 41, 72 (2020). https://doi.org/10.1007/s10765-020-02649-0

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