# Thin conducting regions

## Introduction

For the modeling of a conducting (magnetic or not) region where the eddy currents are not negligible ( ) the user uses a Solid conductor type region .

He uses:

• a solid region if the part is solid
• a thin region, if the part is thin (thin thickness)

A certain amount of additional information about the utilization of thin regions is presented below. These blocks try to answer the following questions:

• What are the Flux hypotheses for the computation of the current density in the thin regions?
• What are the limitations and the conditions required to use thin regions?

## Thin regions: reminder

The utilization of thin regions is briefly summarized in the table below.

A thin region allows replacing…
2D application

… a face (of small thickness)

… by a line

3D application

… a volume

(of small thickness)

… by a face

## Current density in the thickness?

Concerning the current density in a thin region, a certain number of hypotheses are assumed in Flux. These hypotheses are presented below for 2D and 3D applications.

For a line (in 2D) of the thin region type …
2D application

Thin conducting region

… the current density is assumed to be constant* throughout the thickness

Note: * the variation of the current density throughout the thickness of a thin region can be modeled, if a user subroutine is used.
For a surface (in 3D) of thin region type …
3D application Thin conducting region (hyperbolic variation of current density on thickness) … the current density is hyperbolic* through the thickness
Note: * the variation of the current density through the thickness of a thin region can be constant if non automatic formulations are used.

## Specificity in 3D: problem of connectivity

The electric connectivity problem that can occur with volume solid conducting regions can exist in the same manner with the thin conducting regions.

In the presence of holes, the user must create the necessary electric cuts and assign them to the appropriate lines.

Attention: magnetic/electric cuts should not touch the thin regions.

## Specificity in 3D: mechanical coupling / circuit coupling

• Mechanical coupling: If the thin region belongs to a mechanical assembly, its faces must not touch the boundaries of other mechanical assemblies.
• Circuit coupling: If the thin region is circuit coupled, it will be necessary to use a component of the type 2 terminal solid conductor, or N terminal solid conductor, depending on the case.

The faces of the electrical terminals must form a connected surface (namely adjoining faces).

The faces of the electrical terminals are:

• either at the boundary of the study domain
• or in contact with the extremity of a non-meshed coil

## Specificity in 3D: current density

Local quantities available in thin conducting regions are presented in the table below.

Instantaneous local quantity (complex vector) PyFlux Unit
Current density : J A/m2
Surface current density : K A/m

The surface density of the current corresponds to the density of the current integrated over the thickness of the thin region

## Complete information

Detailed information about thin conducting regions (with hyperbolic current density) is given in the “Time-harmonic magnetodynamics” chapter in volume 5 (see § 2.3.5).