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HeatSymmetryValue[pred,vars,pars]

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

HeatSymmetryValue[pred,vars,pars,lkey]

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

Details
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Basic Examples  
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HeatSymmetryValue

HeatSymmetryValue[pred,vars,pars]

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

HeatSymmetryValue[pred,vars,pars,lkey]

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

Details

  • HeatSymmetryValue specifies a boundary condition for HeatTransferPDEComponent and is used as part of the modeling equation:
  • HeatSymmetryValue is typically used to model a boundary with mirror symmetry along an axis.
  • HeatSymmetryValue models a boundary with mirror symmetry with dependent variable in [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 :
  • The normal flow velocity on the symmetry boundary will remain at zero at all times.
  • HeatSymmetryValue with boundary unit normal models:
  • Model parameters pars as specified for HeatTransferPDEComponent.
  • The following additional model parameters pars can be given:
  • parameterdefaultsymbol
    "ModelForm""NonConservative"-
  • HeatSymmetryValue is effectively the same as HeatFluxValue with a heat flux of 0.
  • The boundary predicate pred can be specified as in NeumannValue.
  • If the HeatSymmetryValue 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 symmetry boundary condition:

Wolfram Language code: HeatSymmetryValue[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, "HeatFlux" -> 3|>;

Set up the equation with a symmetry axis at and a constant heat flux of applied on the left end:

Wolfram Language code: eqn = HeatTransferPDEComponent[vars, pars] == HeatFluxValue[x == 0, vars, pars] + HeatSymmetryValue[x == 1 / 5, vars, pars];

Solve the PDE:

Wolfram Language code: Tfun = NDSolveValue[{eqn, Θ[0, x] == 0}, Θ, {t, 0, 600}, x∈Line[{{0}, {1 / 5}}]];

Visualize the solution computed in the reduced domain over the full domain:

Wolfram Language code: Manipulate[Show[Plot[Tfun[t, x], {x, 0, 2 / 5}, ...], Graphics[...], Plot[Tfun[t, 2 / 5 - x], {x, 1 / 5, 2 / 5}, Rule[...]]], {{t, 300}, 0, 600, 20}, Rule[...]]

Scope  (1)

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

Wolfram Language code: vars = {Θ[t, x], t, {x}}; pars = <|"MassDensity" -> 1.2, "SpecificHeatCapacity" -> 1006.14, "ThermalConductivity" -> 0.026, "HeatFlux" -> 3, "BoundaryCondition1" -> <||>|>;

Evaluate the boundary condition:

Wolfram Language code: HeatSymmetryValue[x == 1 / 5, vars, pars, "BoundaryCondition1"]
Wolfram Research (2020), HeatSymmetryValue, Wolfram Language function, https://reference.wolfram.com/language/ref/HeatSymmetryValue.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_heatsymmetryvalue, author="Wolfram Research", title="{HeatSymmetryValue}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/HeatSymmetryValue.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_heatsymmetryvalue, organization={Wolfram Research}, title={HeatSymmetryValue}, year={2020}, url={https://reference.wolfram.com/language/ref/HeatSymmetryValue.html}, note=[Accessed: 12-June-2026]}