MassOutflowValue
MassOutflowValue[pred,vars,pars]
represents a mass outflow boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.
MassOutflowValue[pred,vars,pars,lkey]
represents a mass outflow boundary condition with local parameters specified in pars[lkey].
Details
- MassOutflowValue specifies a boundary condition for MassTransportPDEComponent and is used as part of the modeling equation:
- MassOutflowValue is typically used to model a mass outlet for a convective mass transport where mass is transferred out of the domain by fluid flow.
- Typically, the mass convection outweighs the mass diffusion, and a MassOutflowValue needs to be present.
- MassOutflowValue models the rate of mass species flowing through some part of the boundary with dependent variable
in [![TemplateBox[{InterpretationBox[, 1], {"mol", , "/", , {"m", ^, 3}}, moles per meter cubed, {{(, "Moles", )}, /, {(, {"Meters", ^, 3}, )}}}, QuantityTF]](Files/MassOutflowValue.en/4.png "TemplateBox[{InterpretationBox[, 1], {\"mol\", , \"/\", , {\"m\", ^, 3}}, moles per meter cubed, {{(, \"Moles\", )}, /, {(, {\"Meters\", ^, 3}, )}}}, QuantityTF]")
], independent variables 
in [![TemplateBox[{InterpretationBox[, 1], "m", meters, "Meters"}, QuantityTF]](Files/MassOutflowValue.en/6.png "TemplateBox[{InterpretationBox[, 1], \"m\", meters, \"Meters\"}, QuantityTF]")
] and time variable 
in [![TemplateBox[{InterpretationBox[, 1], "s", seconds, "Seconds"}, QuantityTF]](Files/MassOutflowValue.en/8.png "TemplateBox[{InterpretationBox[, 1], \"s\", seconds, \"Seconds\"}, QuantityTF]")
]. - Stationary variables vars are vars={c[x1,…,xn],{x1,…,xn}}.
- Time-dependent variables vars are vars={c[t,x1,…,xn],t,{x1,…,xn}}.
- The non-conservative time-dependent mass transport model MassTransportPDEComponent is based on a convection-diffusion model with mass diffusivity
, mass convection velocity vector 
, mass reaction rate 
and mass source term 
: - The conservative time-dependent mass transport model MassTransportPDEComponent is based on a conservative convection-diffusion model given by:
- In the non-conservative form, MassOutflowValue with boundary unit normal
models: - A MassOutflowValue is the implicit default boundary condition for the non-conservative model form.
- In the conservative form, MassOutflowValue models:
- MassOutflowValue only has an effect when the flow velocity
is normal to the boundary. - Model parameters pars as specified for MassTransportPDEComponent.
- The following additional model parameters pars can be given:
-
parameter default symbol "BoundaryUnitNormal" Automatic 
"ModelForm" "NonConservative" 
- MassOutflowValue evaluates to a NeumannValue.
- The boundary predicate pred can be specified as in NeumannValue.
- If the MassOutflowValue depends on parameters
that are specified in the association pars as …,keypi…,pivi,…, the parameters 
are replaced with 
.
Examples
open all close allBasic Examples (4)
Set up a mass outflow boundary condition in non-conservative form:
MassOutflowValue[x ≥ 0, {c[t, x], t, {x}}, <|"ModelForm" -> "NonConservative", "MassConvectionVelocity" -> {v}|>]Set up a mass outflow boundary condition in conservative form:
MassOutflowValue[x ≥ 0, {c[t, x], t, {x}}, <|"ModelForm" -> "Conservative", "MassConvectionVelocity" -> {v}|>]Set up a system of mass outflow boundary conditions in non-conservative form:
MassOutflowValue[x ≥ 0, {{Subscript[c, 1][x], Subscript[c, 2][x]}, {x}}, <|"ModelForm" -> "NonConservative", "MassConvectionVelocity" -> {{Subscript[v, 11], Subscript[v, 12]}, {Subscript[v, 21], Subscript[v, 22]}}|>]Set up a system of mass outflow boundary conditions in conservative form:
MassOutflowValue[x ≥ 0, {{Subscript[c, 1][x], Subscript[c, 2][x]}, {x}}, <|"ModelForm" -> "Conservative", "MassConvectionVelocity" -> {{Subscript[v, 11], Subscript[v, 12]}, {Subscript[v, 21], Subscript[v, 22]}}|>]Scope (2)
Define model variables vars for a transient acoustic pressure field with model parameters pars and a specific boundary condition parameter:
vars = {c[t, x, y], t, {x, y}};
pars = <|"DiffusionCoefficient" -> 0.026, "MassConvectionVelocity" -> {0.1}, "BoundaryCondition1" -> <||>|>;
MassOutflowValue[x == 1, vars, pars, "BoundaryCondition1"]Define model variables vars for a transient acoustic pressure field with model parameters pars and multiple specific parameter boundary conditions:
vars = {c[t, x, y], t, {x, y}};
pars = <|"DiffusionCoefficient" -> 0.026, "MassConvectionVelocity" -> {0.1}, "BoundaryCondition1" -> <||>, "BoundaryCondition2" -> <||>|>;MassOutflowValue[x == 0, vars, pars, "BoundaryCondition1"]MassOutflowValue[x == 1, vars, pars, "BoundaryCondition2"]Text
Wolfram Research (2020), MassOutflowValue, Wolfram Language function, https://reference.wolfram.com/language/ref/MassOutflowValue.html.
CMS
Wolfram Language. 2020. "MassOutflowValue." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MassOutflowValue.html.
APA
Wolfram Language. (2020). MassOutflowValue. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MassOutflowValue.html