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International Journal of Thermophysics

, Volume 11, Issue 5, pp 923–935 | Cite as

On the analysis of the thermal diffusivity measurement method with modulated heat input

  • R. De Coninck
Article

Abstract

The present paper proposes a simplified way to analyze thermal diffusivity experiments in which the phase shift is measured between the modulations of the temperatures on either face of a disk-shaped sample. The direct application of complex numbers mathematics avoids the use of the cumbersome formulae which hitherto have hampered a wider confirmation of the method and which restricted the range of the phase lag to an angle of 180°. The algorithm exposed makes it more practical to refine the analysis, which may lead to a higher accuracy and a wider use of the method. The origins of some possible errors in the calculated results are briefly reviewed.

Key words

Complex numbers analysis modulated heat input phase shift measurement thermal conductivity thermal diffusivity 

Nomenclature

a

Thermal diffusivity, m2 · s−1

c

Index denoting a constant part, dimensionless

cl, c0

Inverse extrapolation length, m−1

Cp

Specific heat, J · kg−1 · K−1

f

Modulation frequency, Hz

l

Thickness of disk-shaped sample, m

Qc

Equilibrium energy per unit surface deposited on surface x=l, W · m−2

Qm(t)

Energy of modulation per unit surface deposited on surface x=l, W · m−2

Q(t)

Total energy per unit surface deposited on surface x=l, W · m−2

q

Complex energy modulation amplitude, W · m−2

Tl

Equilibrium temperature of heated surface, K

t0

Equilibrium temperature of nonheated surface, K

T(x, t)

Total temperature of any plane at distance x and at time t, K

Tm(x, t)

Modulation temperature at any distance x and at time t, K

t

Time, s

x

Distance perpendicular to the specimen's surface and with the nonheated surface as the reference, m

α

Thermal linear expansion coefficient, dimensionless

β

Intermediary parameter, m−2

Δ

Phase difference between heated and nonheated specimen face, radian

δ0

Phase difference between energy modulation and nonheated face, radian

δl

Phase difference between energy modulation and heated face, radian

ɛ

Total emissivity, dimensionless

ɛs

Spectral emissivity, dimensionless

θ

Temperature, amplitude of modulated part argument, K

λ

Thermal conductivity, W · m−1 · K−1

ρ

Density, kg · m−3

σ

Stefan-Boltzmann constant, 5.66961×10−8W · m−2 · K−4

ω

Angular frequency=2πf, s−1

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References

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Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • R. De Coninck
    • 1
  1. 1.Materials Development DepartmentSCK/CENMolBelgium

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