MagneticFluxDensityValue

MagneticFluxDensityValue[pred,vars,pars]

represents a magnetic flux density boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.

MagneticFluxDensityValue[pred,vars,pars,lkey]

represents a magnetic flux density boundary condition with local parameters specified in pars[lkey].

Details

MagneticFluxDensityValue specifies a Neumann boundary value for the MagnetostaticPDEComponent.
MagneticFluxDensityValue specifies a boundary condition for the MagnetostaticPDEComponent and is used as part of the modeling equation:

MagneticFluxDensityValue is typically used to model a magnetic flux density field in units of [ $TemplateBox[{InterpretationBox[, 1], {"Wb", , "/", , {"m", ^, 2}}, webers per meter squared, {{(, "Webers", )}, /, {(, {"Meters", ^, 2}, )}}}, QuantityTF]$ ] that enters or leaves a boundary.
A positive value denotes the inward magnetic flux, and a negative value denotes an outward flux.
MagneticFluxDensityValue models a magnetic flux density , normal to the boundary with dependent variable in volts [] and independent variables in [].
Stationary variables vars are vars={V_m[x₁,…,x_n],{x₁,…,x_n}}.
The linear form of MagnetostaticPDEComponent with vacuum permeability in units of [] and relative permeability is given by:

MagneticFluxDensityValue with a specified scalar magnetic flux density , normal to the boundary, models:

MagneticFluxDensityValue models a specified magnetic flux density vector [ $TemplateBox[{InterpretationBox[, 1], {"Wb", , "/", , {"m", ^, 2}}, webers per meter squared, {{(, "Webers", )}, /, {(, {"Meters", ^, 2}, )}}}, QuantityTF]$ ] with unit normal :

Model parameters pars are specified as for MagnetostaticPDEComponent.
The following additional model parameters pars can be given:

parameter	default	symbol
"BoundaryUnitNormal"	Automatic
"MagneticFluxDensity"	{0,...}	, magnetic flux density in [ $TemplateBox[{InterpretationBox[, 1], {"Wb", , "/", , {"m", ^, 2}}, webers per meter squared, {{(, "Webers", )}, /, {(, {"Meters", ^, 2}, )}}}, QuantityTF]$ ]
"NormalMagneticFluxDensity"		, normal magnetic flux density in [ $TemplateBox[{InterpretationBox[, 1], {"Wb", , "/", , {"m", ^, 2}}, webers per meter squared, {{(, "Webers", )}, /, {(, {"Meters", ^, 2}, )}}}, QuantityTF]$ ]
"Thickness"		, thickness in []

All model parameters may depend on the spatial variables .
In two dimensions, the parameter "Thickness" is taken into account.
To localize model parameters, a key lkey can be specified, and values from association pars[lkey] are used for model parameters.
MagneticFluxDensityValue evaluates to a NeumannValue.
The boundary predicate pred can be specified as in NeumannValue.
If the MagneticFluxDensityValue depends on parameters that are specified in the association pars as …,keyp_i…,p_iv_i,…], the parameters are replaced with .

Examples

open allclose all

Basic Examples (3)

Set up a magnetic flux density boundary condition:

Set up a normal magnetic flux density at the boundary:

Set up a normal magnetic flux density at a boundary for a 2D magnetostatic model that has a thickness :

Scope (2)

Create a magnetic flux density boundary condition with a boundary unit normal :

Create a normal magnetic flux density boundary condition:

Applications (1)

Model an iron cube embedded inside air and emerged in a homogeneous magnetic field of [] directed along the axis. The domain is composed of an iron cube of length []. Due to symmetry, only 1/8 of the whole domain is simulated. The air boundary surrounding the iron cube is modeled as a second cube of length [].