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 [], independent variables in [] and time variable in [].
Stationary variables vars are vars={Θ[x₁,…,x_n],{x₁,…,x_n}}.
Time-dependent variables vars are vars={Θ[t,x₁,…,x_n],t,{x₁,…,x_n}}.
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 [] 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 []
"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 …,keyp_i…,p_iv_i,…], the parameters are replaced with .

Examples

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Basic Examples (2)

Set up a thermal convection boundary condition:

Model a temperature field with heat transfer boundary:

Set up the heat transfer model variables :

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 :

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:

(partialTheta(t, x))/(partialt)+del .(-k del Theta(t,x))-Q^(︷^( heat transfer model )) = |_(Gamma_(x=1))h (Theta_(ext)(t,x)-Theta(t,x))^(︷^( heat transfer boundary )); (partialc(t,x))/(partialt)+del .(-d del c(t,x))-R^(︷^( mass transport model )) = |_(Gamma_(x=0||x=1))q (t,x)^(︷^( mass flux boundary ))