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 is 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 [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 :
  • In the non-conservative form, HeatFluxValue with heat flux in [TemplateBox[{InterpretationBox[, 1], {"W", , "/", , {"m", ^, 2}}, watts per meter squared, {{(, "Watts", )}, /, {(, {"Meters", ^, 2}, )}}}, QuantityTF]] or [TemplateBox[{InterpretationBox[, 1], {"J", , "/(", , {"m", ^, 2}, , "s", , ")"}, joules per meter squared second, {{(, "Joules", )}, /, {(, {{"Meters", ^, 2}, , "Seconds"}, )}}}, QuantityTF]] 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 [TemplateBox[{InterpretationBox[, 1], {"W", , "/", , {"m", ^, 2}}, watts per meter squared, {{(, "Watts", )}, /, {(, {"Meters", ^, 2}, )}}}, QuantityTF]]
  • 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

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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.

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

BibTeX

@misc{reference.wolfram_2023_heatfluxvalue, author="Wolfram Research", title="{HeatFluxValue}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/HeatFluxValue.html}", note=[Accessed: 20-April-2024 ]}

BibLaTeX

@online{reference.wolfram_2023_heatfluxvalue, organization={Wolfram Research}, title={HeatFluxValue}, year={2020}, url={https://reference.wolfram.com/language/ref/HeatFluxValue.html}, note=[Accessed: 20-April-2024 ]}