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HeatOutflowValue[pred,vars,pars]

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

HeatOutflowValue[pred,vars,pars,lkey]

represents a thermal outflow boundary condition with local parameters specified in pars[lkey].

Details
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Examples  
Basic Examples  
Scope  
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HeatOutflowValue

HeatOutflowValue[pred,vars,pars]

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

HeatOutflowValue[pred,vars,pars,lkey]

represents a thermal outflow boundary condition with local parameters specified in pars[lkey].

Details

  • HeatOutflowValue specifies a boundary condition for HeatTransferPDEComponent and is used as part of the modeling equation:
  • HeatOutflowValue is typically used to model a heat outlet for a convective heat transfer where heat is transferred out of the domain by fluid flow.
  • Typically, the thermal convection outweighs the thermal diffusion and a HeatOutflowValue needs to be present.
  • HeatOutflowValue models fluid flowing out of a domain with dependent variable [TemplateBox[{InterpretationBox[, 1], "K", kelvins, "Kelvins"}, QuantityTF]], independent variables in [TemplateBox[{InterpretationBox[, 1], "m", meters, "Meters"}, QuantityTF]] and time variable in [TemplateBox[{InterpretationBox[, 1], "s", seconds, "Seconds"}, QuantityTF]].
  • Stationary variables vars are vars={Θ[x1,…,xn],{x1,…,xn}}.
  • Time-dependent variables vars are vars={Θ[t,x1,…,xn],t,{x1,…,xn}}.
  • The non-conservative time-dependent heat transfer model HeatTransferPDEComponent is based on a convection-diffusion model with mass density , specific heat capacity , thermal conductivity , convection velocity vector and heat source :
  • In the non-conservative form, HeatOutflowValue with boundary unit normal models:
  • A HeatOutflowValue is the implicit default boundary condition for the non-conservative model form.
  • HeatOutflowValue only has an effect when the flow velocity is normal to the boundary.
  • Model parameters pars as specified for HeatTransferPDEComponent.
  • The following additional model parameters pars can be given:
  • parameterdefaultsymbol
    "BoundaryUnitNormal"Automatic
    "ModelForm""NonConservative"-
  • HeatOutflowValue evaluates to a NeumannValue.
  • The boundary predicate pred can be specified as in NeumannValue.
  • If the HeatOutflowValue depends on parameters that are specified in the association pars as …,keypi…,pivi,…, the parameters are replaced with .

Examples

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Basic Examples  (2)

Set up a thermal outflow boundary condition:

Wolfram Language code: HeatOutflowValue[x ≥ 0, {Θ[t, x, y], t, {x, y}}, <||>]

Compute the temperature field with model variables vars and parameters pars:

Wolfram Language code: vars = {Θ[t, x], t, {x}}; pars = <|"MassDensity" -> 1.2, "SpecificHeatCapacity" -> 1006.14, "ThermalConductivity" -> 0.026, "HeatConvectionVelocity" -> {0.01}|>;

Set up the equation with a thermal outflow boundary at the right end:

Wolfram Language code: eqn = HeatTransferPDEComponent[vars, pars] == HeatOutflowValue[x == 1 / 5, vars, pars];

Define the initial temperature field:

Wolfram Language code: ics = Θ[0, x] == D[0.2 Erf[(x - 0.1) / 0.025], x];

Solve the PDE:

Wolfram Language code: Tfun = NDSolveValue[{eqn, ics}, Θ, {t, 0, 15}, x∈Line[{{0}, {1 / 5}}]];

Visualize the solution and note how the energy leaves the domain through the thermal outflow boundary on the right:

Wolfram Language code: Manipulate[Plot[Tfun[t, x], {x, 0, 1 / 5}, ...], {{t, 8}, 0, 15, 1 / 2}, Rule[...]]

Scope  (2)

Basic Uses  (2)

Define model variables vars for a transient acoustic pressure field with model parameters pars and a specific boundary condition parameter:

Wolfram Language code: vars = {Θ[t, x, y], t, {x, y}}; pars = <|"MassDensity" -> 1.2, "SpecificHeatCapacity" -> 1006.14, "ThermalConductivity" -> 0.026, "BoundaryCondition1" -> <||>|>; HeatOutflowValue[x == 1, vars, pars, "BoundaryCondition1"]

Define model variables vars for a transient acoustic pressure field with model parameters pars and multiple specific parameters boundary conditions:

Wolfram Language code: vars = {Θ[t, x, y], t, {x, y}}; pars = <|"MassDensity" -> 1.2, "SpecificHeatCapacity" -> 1006.14, "ThermalConductivity" -> 0.026, "BoundaryCondition1" -> <||>, "BoundaryCondition2" -> <||>|>;
Wolfram Language code: HeatOutflowValue[x == 0, vars, pars, "BoundaryCondition1"]
Wolfram Language code: HeatOutflowValue[x == 1, vars, pars, "BoundaryCondition2"]
Wolfram Research (2020), HeatOutflowValue, Wolfram Language function, https://reference.wolfram.com/language/ref/HeatOutflowValue.html.

Text

Wolfram Research (2020), HeatOutflowValue, Wolfram Language function, https://reference.wolfram.com/language/ref/HeatOutflowValue.html.

CMS

Wolfram Language. 2020. "HeatOutflowValue." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/HeatOutflowValue.html.

APA

Wolfram Language. (2020). HeatOutflowValue. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HeatOutflowValue.html

BibTeX

@misc{reference.wolfram_2026_heatoutflowvalue, author="Wolfram Research", title="{HeatOutflowValue}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/HeatOutflowValue.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_heatoutflowvalue, organization={Wolfram Research}, title={HeatOutflowValue}, year={2020}, url={https://reference.wolfram.com/language/ref/HeatOutflowValue.html}, note=[Accessed: 13-June-2026]}