In induction pump the travelling electromagnetic field induces eddy currents in the liquid metal, and interaction between the field and currents generate the force which moves the metal. The eddy currents value depends on the metal conductivity, which depends on temperature. Calculate the pump force and pressure as functions of temperature.

**Problem Type:**

An axisymmetric problem of nonlinear AC magnetics.

**Geometry:**

Due to the axial symmetry only the upper half is presented in the model.

**Given:**

Magnetic permeability of the steel core *μ* = 200;

Conductivity of the liquid metal *σ* - *depends on temperature, as shown on the plot below*;

Winding current density *j* = 6 A/mm²;

Frequency *f* = 50 Hz.

**Task:**

Calculate the pump force and pressure as functions of temperature.

**Solution:**

As the induced current rapidly fades outside the inductor it is possible to limit the model *z*-length by 400 mm.

Conductivity vs. temperature dependency was specified for the 'liquid metal' block.

The series of problems was solved for temperature range 600-900°C. The mechanical force acting on the liquid metal was calculated at each step.

**Results:**

Temperature, °C |
Force, H |
Pressure, Pa |

100 | 41 | 14 500 |

200 | 30 | 10 500 |

600 | 23 | 8 100 |

900 | 18 | 6 500 |