Current Conservation
The Current Conservation node adds the continuity equation for the electrical potential and provides an interface for defining the electric conductivity as well as the constitutive relation and the relative permittivity for the displacement current.
Material Type
The Material type setting decides how materials behave and how material properties are interpreted when the mesh is deformed. Select Solid for materials whose properties change as functions of material strain, material orientation, and other variables evaluated in a material reference configuration (material frame). Select Non-solid for materials whose properties are defined only as functions of the current local state at each point in the spatial frame, and for which no unique material reference configuration can be defined. Select From material to pick up the corresponding setting from the domain material on each domain.
Conduction Current
By default, the Electrical conductivity σ (SI unit: S/m) for the media is defined From material. Or select User defined or Linearized resistivity.
User Defined
For User defined select Isotropic, Diagonal, Symmetric, or Anisotropic depending on the characteristics of the electrical conductivity, and then enter values or expressions for the electrical conductivity σ in the field or matrix. The default is 0 S/m. If type of temperature dependence is used other than a linear temperature relation, enter any expression for the conductivity as a function of temperature.
Linearized Resistivity
Select Linearized resistivity for a temperature-dependent conductivity (this occurs in, for example, Joule heating, and is also called resistive heating). The equation describing the conductivity:
where ρ0 is the resistivity at the reference temperature Tref, and α is the temperature coefficient of resistance, which describes how the resistivity varies with temperature.
The default Reference resistivity ρ0 (SI unit: Ω⋅m), Reference temperature Tref (SI unit: K), and Resistivity temperature coefficient α (SI unit: 1/K) are taken From material, which means that the values are taken from the domain (or boundary) material. T is the current temperature, which can be a value that is specified as a model input or the temperature from a heat transfer interface. The definition of the temperature field is in the Model Inputs section.
To specify other values for any of these properties, select User defined from the list and then enter a value or expression for each. The default values are:
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1 Ω⋅m for the Reference resistivity
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273.15 K for the Reference temperature, and
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0 1/K for the Resistivity temperature coefficient
Electric Field
Select a Constitutive relation to describe the macroscopic properties of the medium (relating the electric displacement D with the electric field E) and the applicable material properties, such as the relative permittivity. For a description of the constitutive relations Relative permittivity, Polarization, and Remanent electric displacement, see Electric Field as described for the Charge Conservation node for the Electrostatics interface. The constitutive relations specific to Electric Currents are:
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Dielectric losses: uses the constitutive relation D = ε0(ε'+ε")E. Specify that the Relative permittivity (real part) ε' (dimensionless) and the Relative permittivity (imaginary part) ε" (dimensionless) must be taken From material or be User defined. For User defined, select Isotropic, Diagonal, Symmetric, or Anisotropic and enter values or expressions in the field or matrix. The default is 1.
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Loss tangent, loss angle: uses the constitutive relation D = ε0ε'(1+jtanδ)E. Specify the Relative permittivity (real part) ε' (dimensionless) and Loss angle δ (SI unit: rad).
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Loss tangent, dissipation factor: uses the constitutive relation D = ε0ε'(1+jtanδ)E. Specify the Relative permittivity (real part) ε' (dimensionless) and the Dissipation factor tanδ (dimensionless).