Moving slab heating in the inductor

QuickField simulation example

Steel slab is moving through the inline induction heater with 6 m/min speed. Find the temperature distribution in the slab.
We are grateful to Selit S.R.L. for providing us with the idea of this model.

Problem Type
Plane-parallel problem of Transient heat transfer.

Geometry

Given
Inductor length is 0.6 m, slab speed is 6 m/min (0.1 m/s).
Power density in the slab layers was calculated in the related AC magnetic example: Q0 = 34.0 MW/m³, Q1 = 27.3 MW/m³, Q2 = 19.4 MW/m³ Q3 = 11.4 MW/m³ Q4 = 5.8 MW/m³ Q5 = 2.1 MW/m³ Q6 = 0.29 MW/m³.
Slab initial temperature is +900°C. Slab surface emissivity coefficient ε = 0.8, ambient temperature is +20°C.
Density of steel ρ = 7880 kg/m³.

Task
Calculate the temperature distribution in the steel slab.

Solution
We analyze the temperature distribution in one slab cross-section which moves inside the inductor.
We neglect the heat redistribution along the slab and consider the heating of a cross-section due to the internal heat sources and cooling by the radiation from the surface only.

The heating time is t = Inductor length / slab speed = 0.6/0.1 = 6 seconds. We specify time-dependent power sources in transient thermal problem: Q * impulse(t,0,6). The solution time is set to be 10 seconds, so that we can simulate the heating and the subsequent cooling in the same problem.

Results

• Video: Moving slab heating in the inductor. Watch on YouTube
  
• Download simulation files (files may be viewed using any QuickField Edition).