PULSE TRANSIENT METHOD
A heat pulse is generated inside the specimen and the following temperature response is measured.
The heat pulse is produced due to Joule heating from the electrical resistance of the planar source.
The thermocouple measures the temperature response to the heat pulse.
REAL EXPERIMENTAL SET-UP
Half of the third part is omitted to see
the structure of the heat source.
The thermophysical parameters are determined according used model. Ideal model is used that
- nonlimited specimen
- planar heat source of the negligible thickness
- ideal thermal contacts
- heat pulse in a form of Dirac's pulse.
Such model is characterized by formulas that describe the temperature response:
Representation in a and cp
Representation in a and l
is density and and
and R is electrical resistance of the planar heat source.
EVALUATION PROCEDURE :
Two procedures can be used for calculation of the thermophysical parameters:
One-point procedure using maximum of the temperature response
Fitting procedure within the time window
|thermal diffusivity a:
specific heat cp:
thermal conductivity l:
|Fitting of the function (1) or (2) over the
measured temperature response gives
- thermal diffusivity
- specific heat or thermal conductivity
The time window can be found by
The third parameter is given by relation
Ideal time window is limited by sensitivity coefficients and its linear dependency. Experimental
realization of the method causes deviations from the ideal model that limits the time window. Time
window is indicated in figures by box (difference
analysis). Several interfering effects distort the ideal temperature response:
Heat source and the heat loss effects.
The heat source and the heat loss effects deform the temperature response at the short times and
the heat loss effects at the long times. For heat loss effect, instead of ideal function (1) or (2), the function (6) is used for fitting.
where J0(x) and J1(x) are Bessel functions sß = H /
and αn are the roots of the equation:
The red line indicates the recommended value,
the box indicates time window
|The red line indicates the
recommended value, the box indicates time window
Heat pulse width effect.
The real heat pulse width deforms the temperature response. Instead of ideal function (1) or (2),
the function (7) is used for fitting.
where Q*(x) is error function
Heat source capacity effect.
The real heat source capacity effect deforms the temperature
response. Instead of ideal function (1) or (2), the function (8) is used for fitting.