HeatFluxValue

HeatFluxValue[pred,vars,pars]

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

HeatFluxValue[pred,vars,pars,lkey]

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

Details

  • HeatFluxValue specifies a boundary condition for HeatTransferPDEComponent and is used as part of the modeling equation:
  • HeatFluxValue is typically used to model heat flow through a boundary caused by a heat source or sink outside of the domain.
  • A flow rate is the flow of a quantity like energy or mass per time. Flux is the flow rate through the boundary and measured in the units of the quantity per area per time.
  • HeatFluxValue models the rate of thermal energy flowing through some part of the 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 :
  • In the non-conservative form, HeatFluxValue with heat flux in or and boundary unit normal models:
  • Model parameters pars as specified for HeatTransferPDEComponent.
  • The following additional model parameters pars can be given:
  • parameterdefaultsymbol
    "BoundaryUnitNormal"Automatic
    "HeatFlux"
  • 0
  • , heat flux in
    "ModelForm""NonConservative"-
  • All model parameters may depend on any of , and , as well as other dependent variables.
  • To localize model parameters, a key lkey can be specified and values from association pars[lkey] are used for model parameters.
  • HeatFluxValue evaluates to a NeumannValue.
  • The boundary predicate pred can be specified as in NeumannValue.
  • If the HeatFluxValue 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 heat flux boundary condition:

Model a temperature field and a thermal insulation and a thermal heat flux boundary with:

 rho C_p(partialTheta(t, x))/(partialt)+del .(-k del Theta(t,x))^(︷^(                        heat transfer model                       )) =|_(Gamma_(x=0))0^(︷^( heat insulation ))+|_(Gamma_(x=1/5))q(t,x)^(︷^(         heat flux       ))

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 for a heat flux of :

Specify the equation:

Set up initial conditions:

Solve the PDE:

Visualize the solution:

Scope  (5)

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 heat field with model parameters pars and multiple specific parameter boundary conditions:

Model a temperature field and a thermal insulation and a thermal heat flux boundary with:

 rho C_p(partialTheta(t, x))/(partialt)+del .(-k del Theta(t,x))^(︷^(                        heat transfer model                       )) =|_(Gamma_(x=0))0^(︷^( heat insulation ))+|_(Gamma_(x=1/5))q(t,x)^(︷^(       heat flux       ))

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 for a heat flux of :

Specify the equation:

Set up initial conditions:

Solve the PDE:

Visualize the solution:

Time Dependent  (1)

Model a temperature field and a thermal heat flux through part of the boundary with:

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

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 a thermal heat flux of applied at the left end for the first 300 seconds:

Set up initial conditions:

Set up the equation with a thermal heat flux of applied at the left end for the first 300 seconds:

Solve the PDE:

Visualize the solution:

Time-Dependent Nonlinear  (1)

Model a temperature field with a nonlinear heat conductivity term with:

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

Set up the heat transfer model variables vars:

Set up a region :

Specify heat transfer model parameters mass density , specific heat capacity and a nonlinear thermal conductivity :

Specify a thermal heat flux of applied at the left end for the first 300 seconds:

Set up initial conditions:

Set up the equation with a thermal heat flux of applied at the left end for the first 300 seconds:

Solve the PDE:

Solve a linear version of the PDE:

Visualize the solutions:

Applications  (2)

Time Dependent  (1)

Model a temperature field and a thermal heat flux through part of the boundary with:

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

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 a thermal heat flux of applied at the left end for the first 300 seconds:

Set up initial conditions:

Set up the equation with a thermal heat flux of applied at the left end for the first 300 seconds:

Solve the PDE:

Visualize the solution:

Time-Dependent Nonlinear  (1)

Model a temperature field with a nonlinear heat conductivity term with:

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

Set up the heat transfer model variables vars:

Set up a region :

Specify heat transfer model parameters mass density , specific heat capacity and a nonlinear thermal conductivity :

Specify a thermal heat flux of applied at the left end for the first 300 seconds:

Set up initial conditions:

Set up the equation with a thermal heat flux of applied at the left end for the first 300 seconds:

Solve the PDE:

Solve a linear version of the PDE:

Visualize the solutions:

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

Text

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

BibTeX

@misc{reference.wolfram_2020_heatfluxvalue, author="Wolfram Research", title="{HeatFluxValue}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/HeatFluxValue.html}", note=[Accessed: 18-April-2021 ]}

BibLaTeX

@online{reference.wolfram_2020_heatfluxvalue, organization={Wolfram Research}, title={HeatFluxValue}, year={2020}, url={https://reference.wolfram.com/language/ref/HeatFluxValue.html}, note=[Accessed: 18-April-2021 ]}

CMS

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

APA

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