HeatInsulationValue
HeatInsulationValue[pred,vars,pars]
represents a thermal insulation boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.
HeatInsulationValue[pred,vars,pars,lkey]
represents a thermal insulation boundary condition with local parameters specified in pars[lkey].
Details
- HeatInsulationValue specifies a boundary condition for HeatTransferPDEComponent and is used as part of the modeling equation:
- HeatInsulationValue is typically used to model insulation and is also called adiabatic boundary condition.
- HeatInsulationValue models a boundary where there is no heat flux across it with dependent variable
in [![TemplateBox[{InterpretationBox[, 1], "K", kelvins, "Kelvins"}, QuantityTF]](Files/HeatInsulationValue.en/4.png "TemplateBox[{InterpretationBox[, 1], \"K\", kelvins, \"Kelvins\"}, QuantityTF]")
], independent variables 
in [![TemplateBox[{InterpretationBox[, 1], "m", meters, "Meters"}, QuantityTF]](Files/HeatInsulationValue.en/6.png "TemplateBox[{InterpretationBox[, 1], \"m\", meters, \"Meters\"}, QuantityTF]")
] and time variable 
in [![TemplateBox[{InterpretationBox[, 1], "s", seconds, "Seconds"}, QuantityTF]](Files/HeatInsulationValue.en/8.png "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, HeatInsulationValue with the boundary unit normal
models: - Model parameters pars as specified for HeatTransferPDEComponent.
- The following additional model parameters pars can be given:
-
parameter default symbol "BoundaryUnitNormal" Automatic 
"ModelForm" "NonConservative" - - HeatInsulationValue is a special case of HeatFluxValue where the heat flux coefficient is 0.
- HeatInsulationValue evaluates to a NeumannValue.
- The boundary predicate pred can be specified as in NeumannValue.
- If the HeatInsulationValue depends on parameters
that are specified in the association pars as …,keypi…,pivi,…, the parameters 
are replaced with 
.
Examples
open all close allBasic Examples (2)
Set up a thermal insulation boundary condition:
HeatInsulationValue[x ≥ 0, {Θ[t, x, y], t, {x, y}}, <||>]Model a temperature field and a thermal insulation and a thermal heat flux boundary with:
Set up the heat transfer model variables 
:
vars = {Θ[t, x], t, {x}};
Ω = Line[{{0}, {1 / 5}}];Specify heat transfer model parameters mass density 
, specific heat capacity 
and thermal conductivity 
:
pars = <|"MassDensity" -> 1.2, "SpecificHeatCapacity" -> 1006.14, "ThermalConductivity" -> 0.026|>;Specify boundary condition parameters for a heat flux 
of 
:
pars["BC1"] = <|"HeatFlux" -> 3|>;eqn = HeatTransferPDEComponent[vars, pars] ==
HeatInsulationValue[x == 0, vars, pars] + HeatFluxValue[x == 1 / 5, vars, pars, "BC1"]ics = Θ[0, x] == 0;Tfun = NDSolveValue[{eqn, ics}, Θ, {t, 0, 600}, x∈Ω];Manipulate[Plot[Tfun[t, x], {x}∈Ω, ...], {{t, 140}, 0, 600, 20}, Rule[...]]Scope (2)
Define model variables vars for a transient acoustic pressure field with model parameters pars and a specific boundary condition parameter:
vars = {Θ[t, x, y], t, {x, y}};
pars = <|"MassDensity" -> 1.2, "SpecificHeatCapacity" -> 1006.14, "ThermalConductivity" -> 0.026, "BoundaryCondition1" -> <||>|>;
HeatInsulationValue[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 = {Θ[t, x, y], t, {x, y}};
pars = <|"MassDensity" -> 1.2, "SpecificHeatCapacity" -> 1006.14, "ThermalConductivity" -> 0.026, "BoundaryCondition1" -> <||>, "BoundaryCondition2" -> <||>|>;HeatInsulationValue[x == 0, vars, pars, "BoundaryCondition1"]HeatInsulationValue[x == 1, vars, pars, "BoundaryCondition2"]Text
Wolfram Research (2020), HeatInsulationValue, Wolfram Language function, https://reference.wolfram.com/language/ref/HeatInsulationValue.html.
CMS
Wolfram Language. 2020. "HeatInsulationValue." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/HeatInsulationValue.html.
APA
Wolfram Language. (2020). HeatInsulationValue. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HeatInsulationValue.html