Abstract
A technique for determining thermophysical properties is proposed and applied to a sample of concrete by taking advantage of pseudo-random signals. Data are treated in the frequency domain. A new approach is developed for estimating the thermal impedance based on the formalism of non-integer order models. An experimental setup consisting of a heat flux and temperature sensor arranged in contact with a material assuming a semi-infinite boundary condition is studied. The theoretical expression for such a thermal impedance takes into account the thermal capacity of the sensor and the contact resistance and emphasizes fractional orders in the behavior model.
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Abbreviations
- a :
-
Thermal diffusivity (m2 · s−1)
- b :
-
Thermal effusivity (J · m−2 · s−1/2 · K−1)
- \({\bar{{b}}}\) :
-
Average value of the thermal effusivity
- c :
-
Specific heat capacity (J · kg−1 · K−1)
- C :
-
Thermal capacity of the system (J · m−2 · K−1)
- C f :
-
Fluxmeter capacity (J · m−2 · K−1)
- C v :
-
Coefficient of variation
- D:
-
Differentiation operator
- f :
-
Frequency (Hz)
- h :
-
Sampling period (s)
- j :
-
Complex variable
- ℓ :
-
Thickness of material (M)
- \({n_{\alpha _I} ,n_{\beta _J}}\) :
-
Derivative orders
- p :
-
Laplace variable
- p i :
-
Theoretical impedance parameter
- \({{S}_{p_{i}}}\) :
-
Impedance sensitivity function to parameter p i
- R :
-
Thermal resistance of the system (K · m2 · W−1)
- R c :
-
Contact resistance (K · m2 · W−1)
- R f :
-
Fluxmeter resistance (K · m2 · W−1)
- t :
-
Time (s)
- T :
-
Temperature (K)
- Z e :
-
Thermal input impedance (K · m2 · W−1)
- Z c :
-
Characteristic thermal impedance (K · m2 · W−1)
- Z th :
-
Theoretical Impedance (K · m2 · W−1)
- λ:
-
Thermal conductivity (W · m−1 · K−1)
- θ :
-
Temperature (°C)
- ρ :
-
Density (kg · m−3)
- ρc :
-
Volumetric heat capacity (J · m−3 · K−1)
- \({\phi}\) :
-
Heat flux (W · m−2)
- σ :
-
Standard deviation
- α i , β j :
-
Differential model parameters
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Defer, D., Chauchois, A., Antczak, E. et al. Determination of Thermal Properties in the Frequency Domain Based on a Non-integer Model: Application to a Sample of Concrete. Int J Thermophys 30, 1025–1039 (2009). https://doi.org/10.1007/s10765-009-0598-y
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DOI: https://doi.org/10.1007/s10765-009-0598-y