Thermocouple time delay measuring system

The aim of this measurement is to examine the dynamic behavior of thermocouples with different constructions and emissivity exposing them to the same amount of heat radiation or temperature change.

The equipment has four different thermocouples (I). These are:
  1. (ø 1,5 mm) thin, reflecting shielded thermocouple
  2. (ø 1,5 mm) thin, reflecting thermocouple
  3. (ø 3 mm) thick, ((bmelab_6_04.png≈1) black thermocouple,
  4. (ø 3 mm) thick, ((bmelab_6_04.png≈0,2) reflecting thermocouple,

The four thermocouples are in the channel within the equipment. The thermocouples are 10 mm far from each other. The bottom of the system is equipped with a ventilator and an electro-heating unit (III). These devices can be controlled by three switches:
  • The first switch turns on the ventilator which causes a continuous air movement in the channel and creates a relatively isothermal environment.
  • The second switch turns on half of the electro-heating unit and with the third switch the whole heating unit can be turned on. It is important to know that the temperature change is dependent on time.

The heating does not switch on up until the ventilator is not in use!

The left side of the system is equipped with an infra-lamp (II) which can be turned on and off separately from the heating unit or ventilator. With the help of the infra-lamp all thermocouples can be radiated with the same amount of heat.


  Important definitions:

Time delay TB

The time needed for the output signal to approach the final signal within the tolerance range at the unit offset of the input signal.
Time delay depends on:

  • the physical properties and the installation method of the transducer;
  • and the tolerance.

Half-life period Tf

The time period between a unit offset of the input signal and the time the output signal reaches 50% of the final output signal.

Time constant T (Indication time, Build-up time)

The time constant is calculated using the equation below:



m is mass;
c is the coefficient of specific heat
A is the area;
α is the heat transfer coefficient.

This physical phenomenon can be simulated as a single-capacity element:


Remarks: This equation is thru, when the heat transfer is convective and the single mass model is acceptable !

When the infra lamp turn on, the main part of heat transfer is radiative, so this solution is not acceptable, this calculated time constant is not true !

When the heating turn on the three mass model would be better, becasue the heater has a mass (one time constant), the heated air has a mass (an other time constant) too and the thermocouple has a mass, but the one mass results give good approximations!

The graphical determination of the time constant (T)


The time constant is the time period when the temperature difference between the test piece and the environment becomes ‘e’ times smaller than it was at the beginning.


  • Determine the time constants of the four thermocouples heating and cooling when the electro-heating unit on full and half load!
  • Evaluate the results of the measurement!
  • Determine the measurement errors of the four thermocouples when the infra-lamp is heating !  Explain the results!

You can download an excel xls file from here to help to find the timeconstant.

Please attach this feedback to your measurement's report.


B. Sarnesa and E. Schrüferb: Determination of the time behaviourof thermocouples for sensor speedup andmedium supervision, Proc. Estonian Acad. Sci. Eng., 2007, 13, 4, 295–309