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 in , independent variables in and time variable in .
  • 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 and external temperature in and boundary unit normal models:
  • Model parameters pars as specified for HeatTransferPDEComponent.
  • The following additional model parameters pars can be given:
  • parameterdefaultsymbol
    "AmbientTemperature"
  • 0
  • , ambient temperature in
    "HeatTransferCoefficient", heat transfer coefficient in
  • 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 allclose all

Basic Examples  (2)

Set up a thermal convection boundary condition:

Model a temperature field with heat transfer boundary:

 rho C_p(partialTheta(t, x))/(partialt)+del .(-k del Theta(t,x))^(︷^(                        heat transfer model                       )) =|_(Gamma_(x=0))h (Theta_(ext)(t,x)-Theta(t,x))^(︷^(    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)

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:

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:

 del .(-k del Theta(x,y))^(︷^( heat transfer model      )) =|_(Gamma_(x=0))epsilon k_B ((Theta_(amb)-Theta_(ref))^4-(Theta(x,y)-Theta_(ref))^( 4))^(︷^(                         heat radiation boundary                     ))+|_(Gamma_(x=0))h (Theta_(ext)(x,y)-Theta(x,y))^(︷^(    heat transfer boundary      ))

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:

(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 ))

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:

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

Text

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

BibTeX

@misc{reference.wolfram_2021_heattransfervalue, author="Wolfram Research", title="{HeatTransferValue}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/HeatTransferValue.html}", note=[Accessed: 22-September-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_heattransfervalue, organization={Wolfram Research}, title={HeatTransferValue}, year={2020}, url={https://reference.wolfram.com/language/ref/HeatTransferValue.html}, note=[Accessed: 22-September-2021 ]}

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