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# Thermal relay

The thermal relay is attached to the tank with a hot liquid. Relay winding conductivity depends on temperature. With temperature raise the conductivity, current and electromagnetic force fall down.
The tank is cooling down. Calculate the relay switching temperature and time.

Problem Type:
An axisymmetric problem of nonlinear transient magnetics.

Geometry:

Given:
Magnetic permeability of core μ = 400;
Conductivity of copper σ - depends on temperature;
Voltage U = 12 V;
Spring force F = 0.8 H
Initial temperature T1 = 200 °C;
Ambient temperature T0 = 20 °C;
Time constant ts = 10 hrs;

Solution:
The temperature falls down as
T(t) = T0 + (T1-T0)·exp( -t / ts).
The integration time was chosen to be 3ts, integration step ts/5.
To calculate the electromagnetic force as a function of time transient magnetic problem is simulated. The temperature function T(t) was added to the material properties of 'winding' block.

Results:
After 16 hours the temperature falls down to 56°C and relay switches off.

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