# INDUCTO 2D

**INDUCTO 2D** program provides coupled electromagnetic and thermal analysis in the 2D/RS domain. The eddy current simulation capabilities of OERSTED are linked to the thermal analysis capabilities of KELVIN to provide a complete solution for induction heating problems.

INDUCTO 2D can perform both transient and steady-state simulations. In addition, the OERSTED and KELVIN modules can be used separately when coupled simulations are not required.

Using INDUCTO 2D designers can:

- Determine temperature distribution at all points within a model
- Calculate effective resistance and reactance of induction coils
- Calculate total power requirements for induction heating systems
- Custom design coils to accommodate specific induction heating applications
- Design flux concentrators, magnetic shunts and electromagnetic shields
- Investigate effects of transient heating and cooling regimes

FARADAY Overview Part 1

FARADAY Overview Part 2

FARADAY Overview Part 3

### Applications

**INDUCTO 2D** utilizes the eddy current field solver to compute the current distribution induced in a work-piece. It provides the choice of both Boundary Element Method (BEM) and Finite Element Method (FEM) field solvers.The current density distribution produced by induction heating are highly dependent on source frequency. Skin effects increase with frequency and result in high current densities near the surface.
The resulting Joule Loss heating will display a greater concentration since it is proportional to the square of the current.

The electromagnetic solution typically has a much smaller time constant than the thermal solution. As such the steady state electromagnetic solution can be used as a distributed power source for either the steady-state or transient thermal analysis.

The thermal analysis module imports the spatial power loss computed as a constant non-uniform distributed heat source. The resulting heat source can be modified to simulate virtually any type of time dependence. In the simplest case, an on/off pulsing of the source can be used to simulate a heating and cooling transient.

The heat flux distribution in the work-piece will be determined by both the eddy current and thermal field solutions.

Though the Joule Loss is heavily concentrated near the surface because of skin effect, conduction within the work-piece may result in the highest temperatures occurring at some distance from the surface. The temperature variation within the work-piece will be highly dependent on its thermal conductivity. A comparison of steady-state Joule Loss distribution (left) computed from electromagnetic solution and the resulting steady-state temperature distribution (right) computed from coupled thermal analysis is presented.

Rotationally symmetric model of a sphere surrounded by a toroidal coil. Color contours show power density produced by induced eddy currents. Color contours show steady-state temperature distribution produced by eddy current heating.

### Electromagnetic Eddy Current Field Solvers

Accurate calculation of induced eddy currents is the foundation of coupled electromagnetic/thermal simulations. Eddy current field simulations can be performed using either Self-Adaptive Boundary Element Method (BEM) or Finite Element Method (FEM) solvers. BEM is particularly well suited to open region problems (encountered in air core inductors) while FEM can easily accommodate transient problems.

The resulting heat source can be used for several types simulations:

- As a constant source for a static analysis to obtain the steady-state temperature distribution
- As a step source to study time and spatial dependent transients
- As a completely general time varying source to simulate alternate heating and cooling regimes

of a copper tube induction coil

a rotationally symmetric model

### Tools for Induction Heating System Design

Using INDUCTO, designers can:- Simulate temperature distribution at all points within a work-piece
- Calculate effective resistance and reactance of induction coils
- Calculate total power requirements for induction heating systems
- Custom design coils to accommodate specific induction heating applications
- Design flux concentrators, magnetic shunts and electromagnetic shields
- Calculate hoop forces in induction coils and forces acting on work-pieces
- Investigate effects of transient heating and cooling regimes

Having obtained the eddy current solution using the electromagnetic solver, the resulting Joule heating power is automatically transferred into a distributed heat source for the thermal solution. Magnetic field lines and temperature contour plots for an aluminum slab inside a solenoidal induction coil

turn induction coil with magnetic flux concentrator