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

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.Nomenclature a Thermal diffusivity, m² · s^–1 - c Index denoting a constant part, dimensionless - c _l, c ₀ Inverse extrapolation length, m^–1 - C _p Specific heat, J · kg^–1 · K^–1 - f Modulation frequency, Hz - l Thickness of disk-shaped sample, m - Q _c Equilibrium energy per unit surface deposited on surface x=l, W · m^–2 - Q _m(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 - T _l Equilibrium temperature of heated surface, K - t ₀ Equilibrium temperature of nonheated surface, K - T(x, t) Total temperature of any plane at distance x and at time t, K - T _m(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 - Thermal linear expansion coefficient, dimensionless - Intermediary parameter, m^–2 - Phase difference between heated and nonheated specimen face, radian - ₀ Phase difference between energy modulation and nonheated face, radian - _l Phase difference between energy modulation and heated face, radian - Total emissivity, dimensionless - _s Spectral emissivity, dimensionless - Temperature, amplitude of modulated part argument, K - Thermal conductivity, W · m^–1 · K^–1 - Density, kg · m^–3 - Stefan-Boltzmann constant, 5.66961×10^–8W · m^–2 · K^–4 - Angular frequency=2f, s^–1