Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. 5, N. 2 Special Issue on Heat Transfer
232 power increases, and only a lower decrease with
increasing flow rate is detected. The experimental analysis suggests that in the LCM 2524 chip, a non-
linearity exists, produced by the dissipated power in the heater. The measurements used battery power supply,
completely isolated from the output, but eventually parasitic cross-talk effects between heater and thermopile
could not be completely avoided. The behavior of the sensitivity against power dissipation for an incidence
angle of roughly 45º is similar than for normal incidence.
We repeated the same experiment with the Xensor NCM 9924 chip 40
µm thick. It has a diffused p-type silicon resistor heater integrated in the membrane in the
same way than in the LCM 2524 chip, and two aluminum resistances, galvanically isolated from the
thermopiles, on the rear part of the surface. One of them is a square torus of 3.8 x 3.8 mm
2
, and about 50 µm
wide, underneath the chip heater, and the other is of 2.6 x 2.65 mm
2
square shape, nearly centred [2].
Fig. 8. Chip heater sensitivity of the LCM 2524 XENSOR against the dissipated power for constant gas flow rates. A and B are the linear fit
for both series of experimental points
The use of the central aluminum resistance for power dissipation means that the heat appears in a more
extended and uniform part of the surface 6.89 mm
2
in comparison with 0.7 mm
2
. By the other hand, the heat transfer acts on a higher silicon thickness 40
µm, compared to the case of the LCM 2524 25
µm. Increased surface and thickness works in the appropriate
direction. This fact implies a more realistic approach to the energetic dissipation that would take place in a
reaction between an incident gas over a deposited substance on the surface. On the other hand, it is still not
equivalent to a real situation because the reactive substance would be placed on the upper part of the chip
surface when the aluminum resistance is placed on the rear part of it.
We have measured the signal using on one hand the heater resistor, and on the other hand the aluminum
resistance placed in the centre, following the same procedure as with the former chip. Fig. 9 shows the
power dependence for the NCM 9924. It is possible to appreciate the disappearance of the previous non-
constancy. The experimental analysis established relevant
differences when the location of the heat dissipation is altered, related to a poor heat flux integration. Improved
accuracy needs supplementary hypotheses and experimental determinations. For gas-solid
measurements the relatively relevant non-constancy, related to the power concentration in the LCM 2524 chip
heater, induces an increase of the uncertainties in comparison with chip NCM 9924. The introduction of
the Al-heater increases the reliability of the device.
Fig. 9. Sensitivity against the dissipated power for constant gas flow rates. A and B are the linear fit for both series of experimental points.
Power is dissipated in the central aluminum resistance of the NCM
9924 XENSOR chip
V. Difficulties on Calorimetric Evaluation
The evaluation of the results is clearly associated to the effective model of the calorimeter and to the
thermodynamical image of the studied process. Two relevant wrong interpretations are related to the
martensitic transformations in Shape Memory Alloys. The phase transition in these materials can be induced
between meta-stable phases, from the austenite beta bcc or high temperature phase to martensite. The latter
is a monoclinic structure, and the transformation is completely reversible. The transition can also be induced
by stress. By increasing the stress, the austenite transforms to martensite and on decreasing the stress, the
beta-phase is recovered. This transformation show hysteresis.
In general,
m m
β β
σ σ
→ →
and
m m
T T
β β
→ →
. From the stress-strain cycles, it can be determined at
constant temperature by
ext
f dx
∫
, which is a frictional term. The f
ext
is the external force applied on doing the hysteresis cycle. Friction terms in temperature induced
cycles does not exist, because the force f
ext
reduces progressively to zero as the temperature decreases to
allow the stress free temperature induced cycles. This has not been done in references [30], [31], [32], relating
irreversible processes as hysteresis.
Temperature induced cycles have also hysteresis. The transformation on cooling are lower than those on
heating, in the absence of frictional terms or other
Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. 5, N. 2 Special Issue on Heat Transfer
233 “elastic” effects. In fact, the cooling-heating cycles
produce entropy, which is related to the difference between the terms
M s M f
p m
Q T
→ →
and
A s A f
m p
Q T
→ →
. The balance is a net increase of entropy
∆S
Universe
0 due to
p m
m p
Q Q
→ →
= and
A m s
m f A s
f
T T
→ →
. Another aspect of the interpretation difficulties ca be
found in the paper of Benke et al. in 2008 [7]. They present a method to determine the transformation
temperatures. The suggested idea is to determine the finishing
temperatures of the transition at the inflexion point of the DSC curves, instead of at the endpoint of the peaks.
They argue that after the inflexion point, no heat is absorbed nor released, and the rest of the signal
corresponds to the still existing temperature difference between the sample and the reference.
In [8] the authors explain the origin of this misunderstanding. When the input to a system is a unit
pulse, the response is obtained by applying a low pass filter and making an adjacent averaging, according to its
cut off frequency. In an ideal case the inflexion point falls exactly at the position where the source presents a
step in dissipation or the end of dissipation. In the real case of a calorimetric signal, the response cannot happen
before the variation of the source takes place, and therefore the response will present a delay which is
dependent on the several steps involved in the heat flow inside the calorimeter and also on the temperature
variation rate.
In [8] it is shown that the transformation actually occurs in a wider temperature range than that determined
from the DSC peak end points at low scanning rates. The inflexion points induce wrong results and are of no
interest. More confident results would be obtained by extrapolating the transition temperatures to zero scanning
rate, and even better using electrical resistance because this technique with 4 or 5 significant figures has a higher
sensitivity than calorimetry to detect the martensitic transition.
VI. Conclusion
