Staff of the Department of Thermophysics is involved in the development of new innovative class of the testing methods – transient methods for measuring of the thermophysical properties of materials. Principle of this class of methods is based on generation of a small heat disturbance inside a specimen and the measuring of the following temperature response. Methods are included into this class where measuring probes are embedded into the material thus surface interfering effects are suppressed. Table 1 gives an overview of the basic experimental arrangement of the transient methods.

Table 1.: Transient methods and the corresponding parameters that can be determined by particular method.

Theory and the methodology of the following transient methods were worked out in our department:

Pulse transient method:

Principle: 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.

Principle

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 assumes:

  •  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

        (1)

            (2)

where r is density 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:

                                           (3)

 specific heat cp:

                             (4)

 thermal conductivity :

  (5)

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 difference analysis.

  

The third parameter is given by relation

       

 

Interfering effects:

 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. 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 at the long times. Instead of ideal function (1) or (2), the function (6) is used for fitting (case of heat loss effects).

     (6)

where J0(x) and J1(x) are Bessel functions s=H / λ  and an 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.

                    (7)

where Q*(x) is error function

Heat source capacity effect.

The real heat source capacity effect shifts in a way shown in upper figure the temperature response. Instead of ideal function (1) or (2), the function (8) is used for fitting.

   (8)   

where            

and B = c2ρ2/2bc1 ρ1

- XX