HeatTransferValue [pred,vars,pars]
represents a thermal transfer boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.
HeatTransferValue [pred,vars,pars,lkey]
represents a thermal transfer boundary condition with local parameters specified in pars[lkey].
HeatTransferValue
HeatTransferValue [pred,vars,pars]
represents a thermal transfer boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.
HeatTransferValue [pred,vars,pars,lkey]
represents a thermal transfer boundary condition with local parameters specified in pars[lkey].
Details
- HeatTransferValue specifies a boundary condition for HeatTransferPDEComponent and is used as part of the modeling equation:
- HeatTransferValue is typically used to model the effect of a cooling or heating flow outside the simulation domain. Common examples include a heat sink.
- HeatTransferValue models thermal energy transferred across a boundary with dependent variable temperature [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 heat transfer value HeatTransferValue with heat transfer coefficient in units of [TemplateBox[{InterpretationBox[, 1], {"W", , "/(", , {"m", ^, 2}, , "K", , ")"}, watts per meter squared kelvin, {{(, "Watts", )}, /, {(, {{"Meters", ^, 2}, , "Kelvins"}, )}}}, QuantityTF]] and external temperature [TemplateBox[{InterpretationBox[, 1], "K", kelvins, "Kelvins"}, QuantityTF]] and boundary unit normal models:
- Model parameters pars as specified for HeatTransferPDEComponent .
- The following additional model parameters pars can be given:
-
parameter default symbol"AmbientTemperature"
- 0
, ambient temperature [TemplateBox[{InterpretationBox[, 1], "K", kelvins, "Kelvins"}, QuantityTF]]"HeatTransferCoefficient" , heat transfer coefficient [TemplateBox[{InterpretationBox[, 1], {"W", , "/(", , {"m", ^, 2}, , "K", , ")"}, watts per meter squared kelvin, {{(, "Watts", )}, /, {(, {{"Meters", ^, 2}, , "Kelvins"}, )}}}, QuantityTF]] - To localize model parameters, a key lkey can be specified, and values from association pars[lkey] are used for model parameters.
- All model parameters may depend on any of , and , as well as other dependent variables.
- HeatTransferValue is a special case of HeatFluxValue .
- HeatTransferValue evaluates to a generalized NeumannValue .
- The boundary predicate pred can be specified as in NeumannValue .
- If the HeatTransferValue 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 convection boundary condition:
Model a temperature field with heat transfer boundary:
Set up the heat transfer model variables vars:
Set up a region :
Specify heat transfer model parameters mass density , specific heat capacity and thermal conductivity :
Specify boundary condition parameters with an external flow temperature of 10 °C and a heat transfer coefficient of :
Specify the equation:
Set up initial conditions:
Solve the PDE:
Visualize the solution:
Scope (4)
Basic Examples (2)
Define model variables vars for a transient acoustic pressure field with model parameters pars and a specific boundary condition parameter:
Define model variables vars for a transient acoustic pressure field with model parameters pars and multiple specific parameter boundary conditions:
Make use of "BoundaryCondition1":
Make use of "BoundaryCondition2":
2D (1)
Model a ceramic strip that is embedded in a high-thermal-conductive material. The side boundaries of the strip are maintained at a constant temperature . The top surface of the strip is losing heat via both heat convection and heat radiation to the ambient environment at . The bottom boundary, however, is assumed to be thermally insulated:
Model a temperature field and the thermal radiation and thermal transfer with:
Set up the heat transfer model variables vars:
Set up a rectangular domain with a width of and a height of :
Specify thermal conductivity :
Set up temperature surface boundary conditions at the left and right boundaries:
Set up a heat transfer boundary condition on the top surface:
Also set up a thermal radiation boundary condition on the top surface:
Set up the equation:
Solve the PDE:
Visualize the solution:
Coupled Equations (1)
Solve a coupled heat transfer and mass transport model with a thermal transfer value and a mass flux value on the boundary:
Set up the heat transfer mass transport model variables vars:
Set up a region :
Specify heat transfer and mass transport model parameters, heat source , thermal conductivity , mass diffusivity and mass source :
Specify boundary condition parameters for a thermal convection value with an external flow temperature of 1000 K and a heat transfer coefficient of :
Specify the equation:
Set up initial conditions:
Solve the model:
Visualize the solution:
Tech Notes
Related Guides
History
Text
Wolfram Research (2020), HeatTransferValue, Wolfram Language function, https://reference.wolfram.com/language/ref/HeatTransferValue.html.
CMS
Wolfram Language. 2020. "HeatTransferValue." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/HeatTransferValue.html.
APA
Wolfram Language. (2020). HeatTransferValue. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HeatTransferValue.html
BibTeX
@misc{reference.wolfram_2025_heattransfervalue, author="Wolfram Research", title="{HeatTransferValue}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/HeatTransferValue.html}", note=[Accessed: 08-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_heattransfervalue, organization={Wolfram Research}, title={HeatTransferValue}, year={2020}, url={https://reference.wolfram.com/language/ref/HeatTransferValue.html}, note=[Accessed: 08-January-2026]}