Step-Wise Transient method

Theory

The principle of the pulse transient method is shown in Fig. 1. The method can be described as follows. The temperature of the specimen is stabilized and uniform. Then a small disturbance in the form of a heat flux is applied to the specimen. From the temperature response the termophysical parameters can be calculated according to the model used. 

Fig 1 Experimental set up for step-wise transient method

The model of the method is characterized by the temperature function. 

          (1)

where q=RI2 is a heat flux supplied by heat source in the unit area, R is electrical resistance of heat source, I is supplied current, r is density and a, c are unknown thermophysical parameters (thermal diffusivity and specific heat). The temperature function (1) is the solution of the heat equation considering appropriate boundary and initial conditions.

Third termophysical parameter, l - thermal conductivity, is defined by well-known data consistency relation 

l=acr

(2)

The thermophysical parameters can be found by superimposing the temperature function (1) on the temperature response by an appropriate fitting technique. The sensitivity coefficients and their cross-correlation in Fig. 2 give us an overview on the time window in which the fitting technique should be used. There should be a balance between the sensitivity of measured parameters (better for longer time) and their cross-correlation (better for shorter time). 

(3)

where p is a parameter to be analysed and Ti(t) is the temperature function (1). The cross-correlation of the sensitivity coefficients b a and bc of parameters: thermal diffusivity a and specific heat c, is simply defined as   

Fig 2. Ideal temperature function T(t), sensitivity coefficients b a(t) and bc(t) of parameters: thermal diffusivity and specific heat, and their cross-correlation g(t).

Ideal model versus real experiment

Therefore analysis of differences between ideal model and real experiments has to be performed that enables to predict disturbing effects in the measuring process.
    The ideal model supposes:

  • geometrically non-limited specimen

  • infinitesimal thickness of the heat source with the same thermophysical properties as 
    the specimen

  • ideal thermal contact between the heat source, thermometer and the specimen

  • negligible mass of thermometer.

On the contrary, the real experiment has the following:

  • limited specimen

  • actual thickness of the heat source that induces its plumbless heat capacity

  • possible thermal contact resistance

  • negligible mass and heat capacity of thermometer

Considering some differences stated above, the assumed effects that influence the 
measurements are:

  • heat capacity and constriction of the heat source

  • heat loss from the free specimen surface

The effects are depicted in Fig. 3 as exemplary. The deviations between ideal function 
and real response are assigned to mentioned effects. One can notice the assumed ranges 
of effects in time.


Fig 3 The effects influencing experimental response