Temperature dependent electrical resistance

QuickField simulation example

Electric current flows in the aluminum bus pipe. As a result of the thermal action of a current, the conductor heats up and its electrical conductivity changes.

Problem type
Axisymmetric multiphysics problem of DC Conduction coupled to Heat transfer.

Geometry

Given
Resistivity of aluminum ρ_20° = 2.65e-8 Ohm*m, temperature coefficient of resistivity α = 0.00429 1/°C.
Current I = 1 kA;
Convection coefficient 5 W/K-m², ambient air temperature +20°C.

Task
Calculate the conductor temperature.

Solution
The conductor resistance depends on the temperature as:
ρ = ρ_20° · ( 1 + α·( T - 20° ) ).
DC Conduction problem allows us to specify the electrical conductivity vs. temperature dependency and the temperature of the conductor. The problem solving is an iterative process:

1. Set up the initial temperature of the conductor +20°C.
2. Simulate DC conduction problem and calculate the Joule heat.
3. Simulate the coupled heat transfer problem and calculate the conductor temperature.

Then correct the conductor temperature in DC conduction problem and repeat the steps 2 and 3 till the temperature value converges.

Results
The steady state temperature of the aluminum conductor is 66°C.

• Video: Temperature dependent electrical resistance of the busbar. Watch on YouTube.
  
• Download simulation files (files may be viewed using any QuickField Edition).