Thermal Analysis



Transformer Theory

Test Circuit


Thermal Analysis



When testing is performed on the transformer, the short-circuit currents could reach as high as thousands of amps. Although the circuit will only be complete for a few milliseconds, we still want to make sure the wire will not melt.

Dissipation was ignored, and the worst-case scenario was analyzed--as if all the heat will remain in the wire.

Note: Although the melting point of metal is much higher, the temperature must be kept below 170° Celcius--since this is where insulation breaks down.

The analysis was done in MathCad, and the highest temperature calculated for copper wire was 48.226° Celcius. Aluminum has a higher temperature, but is still below 170° Celcius.

Equations used for temperature and thermal mass were as follows:
Temperature of Metal
Temperature of copper is the initial temperature plus the inverse of the thermal mass times the derivative of the power over time.
Thermal Mass
Thermal mass is the volume of copper times the density of copper times the specific heat of copper.
Temp equation

At room temperature To=20° Celcius.
Time of 1 second is 60 cycles and we want only 5 or 6 cycles.

Note: Even at 8000A, 1/10 second will not be enough to increase the temperature by too much. We remain well below 170° Celcius.
Below is a graph of temperature when current and time changes. The temperature is in Kelvin. 321 Kelvin is about 42° Celcius.
Temperature Graph

To see the MathCad document of thermal analysis, click here: Thermal

Actual Testing
While testing with some hand-fabricated fuses, the insulation on the wire in the fuses did start to smoke, but the insulation on the size 2 welding wire has remained intact.

We did attempt to measure temperature while testing with a digital thermometer and a thermocouple. The temperature never exceeded 34° Celcius. This was not entirely accurate, because the thermometer took a long time to actually reach a temperature--and the actual temperature could have dropped before this. Since the shorting circuit is only on for a brief period--less than a second--we do not think we will have problems with our testing.

Additional Thermal Consideration
Since the resistivity coefficient increases with temperature, here is a brief analysis of a possible new scenario with Temperature of copper being 50 degrees Celcius or 322 Kelvin which is a change of about 30 degrees.
temperature coefficient
Resistance changes with temperature as shown below.
resistance changing with temperature
R(To) is the resistance of copper. The change in temperature is listed below.
change in temperature
This causes the final temperature to increase by only a few degrees from 50 to 51.5 which is not significant enough to be taken into consideration.
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Last updated: 4/26/07.

University of Idaho, Moscow, Idaho.