Conference, Proceedings

- from numeric solution of Eqs (9) and (10) expressed as [12]
256
2 ⎛ π f ⎞ ⎛ π f ⎞
= cosh⎜
⎟ + ⎜ ⎟
⎜
2 ⋅ l
⎟
cos
⎜
2 ⋅ l
ψ
⎟
⎝ a ⎠ ⎝ a ⎠
⎛ π f ⎞ ⎛ π f ⎞
tg ϕ = tg⎜
⎟ ⎜ ⎟
⎜
⋅ l
⎟
tanh
⎜
⋅ l
⎟
(21)
⎝ a ⎠ ⎝ a ⎠
4. Numerical modelling
Because of a complex character of the thermal diffusivity identification problem direct analyses
of any negative effects on the measurement procedure are difficult. For this reason a procedure
of numerical validation of the measurement procedure has been started. The numerical analysis
discussed here is of a preliminary character. It refers to real experiments performed while the
temperature oscillation procedure has been validated [12]. This is why certain thermophysical
parameters have been assumed for the modelled media (Table 1). Despite the fact that the
analysis has been focussed mostly on the effect of a scanning mode procedure it was started
from consideration of the heat loses and finite specimen lateral dimension on the identification
result (Fig. 2). The analysis has been performed applying finite element modelling (FEM)
software Comsol. Prior to main calculations all the numerical modelling procedures have been
tested and optimal parameter values for the time step, finite element type and dimension etc.
have been established. The numerical details have not been discussed here as we will rather
focus on the obtained results.
At first effects of convective heat transfer loses and a thermocouple (TC) location on the thermal
diffusivity identification have been studied. The calculations have been performed applying
thermal properties of the ice‐type solid with the temperature oscillation applied to the bottom
specimen surface (Fig. 3; z=0 mm) while the upper and the side surfaces have been exposed to
convection into the ambient of a certain temperature. Direct effects of the heat loses on the
temperature recordings are shown in Fig. 4. Results of the thermal diffusivity identification
listed in Table 2 prove that these effects are of a minor importance regarding thermal insulation
applied in real experiment [12]. It should be underlined that the expected real value of the heat
transfer coefficient is close to 4 W⋅m‐ 2 ⋅K ‐1 . The observed effects of TC location are non
significant.
Material
Table 1: Thermal properties of the modelled media
Density Heat capacity Thermal conductivity
kg⋅m 3 J⋅kg ‐1 ⋅K W⋅m ‐1 ⋅K ‐1
model ice‐like solid 925 2200 2
model H2O
(Comsol Script notation)
925+75*flc2hs(T‐
273,4)+(273‐T)
2200+83250*(flc2hs(T‐
271,2)‐flc2hs(T‐
275,2))+2000*flc2hs(T‐
273,4)
2.2‐1.7*flc1hs(273,10)
(20)