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HeatFluxValue
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HeatFluxValue

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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.

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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)Summary of the most common use cases

Set up a thermal heat flux boundary condition:

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In[1]:=1
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https://wolfram.com/xid/0bni4boi2fj8q-vw7olo
Direct link to example
Out[1]=1

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:

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In[1]:=1
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https://wolfram.com/xid/0bni4boi2fj8q-l31rgn
Direct link to example

Set up a region :

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In[2]:=2
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https://wolfram.com/xid/0bni4boi2fj8q-mb3sl1
Direct link to example

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

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In[3]:=3
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https://wolfram.com/xid/0bni4boi2fj8q-twb86
Direct link to example

Specify boundary condition parameters for a heat flux of :

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In[4]:=4
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https://wolfram.com/xid/0bni4boi2fj8q-uhib7k
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Specify the equation:

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In[5]:=5
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https://wolfram.com/xid/0bni4boi2fj8q-hk3stc
Direct link to example
Out[5]=5
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In[6]:=6
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https://wolfram.com/xid/0bni4boi2fj8q-ubindq
Direct link to example
Out[6]=6

Set up initial conditions:

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In[7]:=7
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https://wolfram.com/xid/0bni4boi2fj8q-kb731w
Direct link to example

Solve the PDE:

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In[8]:=8
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https://wolfram.com/xid/0bni4boi2fj8q-vxinx8
Direct link to example

Visualize the solution:

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In[9]:=9
✖
https://wolfram.com/xid/0bni4boi2fj8q-82p6y4
Direct link to example
Out[9]=9

Scope  (5)Survey of the scope of standard use cases

Basic Examples  (3)

Define model variables vars for a transient acoustic pressure field with model parameters pars and a specific boundary condition parameter:

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In[1]:=1
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https://wolfram.com/xid/0bni4boi2fj8q-glqeii
Direct link to example
Out[3]=3

Define model variables vars for a transient heat field with model parameters pars and multiple specific parameter boundary conditions:

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In[1]:=1
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https://wolfram.com/xid/0bni4boi2fj8q-uwpzeb
Direct link to example
Copy to clipboard.
In[2]:=2
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https://wolfram.com/xid/0bni4boi2fj8q-hwq3hg
Direct link to example
Out[2]=2
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In[3]:=3
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https://wolfram.com/xid/0bni4boi2fj8q-zk0k6a
Direct link to example
Out[3]=3

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:

Copy to clipboard.
In[1]:=1
✖
https://wolfram.com/xid/0bni4boi2fj8q-58b0vw
Direct link to example

Set up a region :

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In[2]:=2
✖
https://wolfram.com/xid/0bni4boi2fj8q-pxkjuo
Direct link to example

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

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In[3]:=3
✖
https://wolfram.com/xid/0bni4boi2fj8q-hxcnyd
Direct link to example

Specify boundary condition parameters for a heat flux of :

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In[4]:=4
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https://wolfram.com/xid/0bni4boi2fj8q-ml9b8u
Direct link to example

Specify the equation:

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In[5]:=5
✖
https://wolfram.com/xid/0bni4boi2fj8q-8fooqp
Direct link to example
Out[5]=5

Set up initial conditions:

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In[6]:=6
✖
https://wolfram.com/xid/0bni4boi2fj8q-rmaw60
Direct link to example

Solve the PDE:

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In[7]:=7
✖
https://wolfram.com/xid/0bni4boi2fj8q-nnhj0f
Direct link to example

Visualize the solution:

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In[8]:=8
✖
https://wolfram.com/xid/0bni4boi2fj8q-31aqe5
Direct link to example
Out[8]=8

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:

Copy to clipboard.
In[1]:=1
✖
https://wolfram.com/xid/0bni4boi2fj8q-7ny7iw
Direct link to example

Set up a region :

Copy to clipboard.
In[2]:=2
✖
https://wolfram.com/xid/0bni4boi2fj8q-gwy6jj
Direct link to example

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

Copy to clipboard.
In[3]:=3
✖
https://wolfram.com/xid/0bni4boi2fj8q-5shujp
Direct link to example

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

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In[4]:=4
✖
https://wolfram.com/xid/0bni4boi2fj8q-qij550
Direct link to example

Set up initial conditions:

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In[5]:=5
✖
https://wolfram.com/xid/0bni4boi2fj8q-hp017j
Direct link to example

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

Copy to clipboard.
In[6]:=6
✖
https://wolfram.com/xid/0bni4boi2fj8q-s8azb
Direct link to example
Out[6]=6

Solve the PDE:

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In[7]:=7
✖
https://wolfram.com/xid/0bni4boi2fj8q-m1n2xb
Direct link to example

Visualize the solution:

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In[8]:=8
✖
https://wolfram.com/xid/0bni4boi2fj8q-4d7cd1
Direct link to example
Out[8]=8

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:

Copy to clipboard.
In[1]:=1
✖
https://wolfram.com/xid/0bni4boi2fj8q-u5cci5
Direct link to example

Set up a region :

Copy to clipboard.
In[2]:=2
✖
https://wolfram.com/xid/0bni4boi2fj8q-uo2l5e
Direct link to example

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

Copy to clipboard.
In[3]:=3
✖
https://wolfram.com/xid/0bni4boi2fj8q-3t4q7p
Direct link to example

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

Copy to clipboard.
In[4]:=4
✖
https://wolfram.com/xid/0bni4boi2fj8q-j6ntf
Direct link to example

Set up initial conditions:

Copy to clipboard.
In[5]:=5
✖
https://wolfram.com/xid/0bni4boi2fj8q-k5ayvo
Direct link to example

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

Copy to clipboard.
In[6]:=6
✖
https://wolfram.com/xid/0bni4boi2fj8q-dtflit
Direct link to example
Out[6]=6

Solve the PDE:

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In[7]:=7
✖
https://wolfram.com/xid/0bni4boi2fj8q-kf4hr2
Direct link to example

Solve a linear version of the PDE:

Copy to clipboard.
In[8]:=8
✖
https://wolfram.com/xid/0bni4boi2fj8q-c8kfxe
Direct link to example

Visualize the solutions:

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In[11]:=11
✖
https://wolfram.com/xid/0bni4boi2fj8q-c1eliu
Direct link to example
Out[11]=11

Applications  (2)Sample problems that can be solved with this function

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:

Copy to clipboard.
In[1]:=1
✖
https://wolfram.com/xid/0bni4boi2fj8q-34j9jk
Direct link to example

Set up a region :

Copy to clipboard.
In[2]:=2
✖
https://wolfram.com/xid/0bni4boi2fj8q-r7tzll
Direct link to example

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

Copy to clipboard.
In[3]:=3
✖
https://wolfram.com/xid/0bni4boi2fj8q-nh5hwt
Direct link to example

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

Copy to clipboard.
In[4]:=4
✖
https://wolfram.com/xid/0bni4boi2fj8q-qhujyr
Direct link to example

Set up initial conditions:

Copy to clipboard.
In[5]:=5
✖
https://wolfram.com/xid/0bni4boi2fj8q-mo5420
Direct link to example

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

Copy to clipboard.
In[6]:=6
✖
https://wolfram.com/xid/0bni4boi2fj8q-q9buq4
Direct link to example
Out[6]=6

Solve the PDE:

Copy to clipboard.
In[7]:=7
✖
https://wolfram.com/xid/0bni4boi2fj8q-hdh9t
Direct link to example

Visualize the solution:

Copy to clipboard.
In[8]:=8
✖
https://wolfram.com/xid/0bni4boi2fj8q-9rw1lg
Direct link to example
Out[8]=8

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:

Copy to clipboard.
In[1]:=1
✖
https://wolfram.com/xid/0bni4boi2fj8q-89v7o3
Direct link to example

Set up a region :

Copy to clipboard.
In[2]:=2
✖
https://wolfram.com/xid/0bni4boi2fj8q-pwm7no
Direct link to example

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

Copy to clipboard.
In[3]:=3
✖
https://wolfram.com/xid/0bni4boi2fj8q-52zc5m
Direct link to example

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

Copy to clipboard.
In[4]:=4
✖
https://wolfram.com/xid/0bni4boi2fj8q-olua29
Direct link to example

Set up initial conditions:

Copy to clipboard.
In[5]:=5
✖
https://wolfram.com/xid/0bni4boi2fj8q-07dtcx
Direct link to example

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

Copy to clipboard.
In[7]:=7
✖
https://wolfram.com/xid/0bni4boi2fj8q-q79fer
Direct link to example
Out[7]=7

Solve the PDE:

Copy to clipboard.
In[8]:=8
✖
https://wolfram.com/xid/0bni4boi2fj8q-ba1s25
Direct link to example

Solve a linear version of the PDE:

Copy to clipboard.
In[9]:=9
✖
https://wolfram.com/xid/0bni4boi2fj8q-vk4bd5
Direct link to example

Visualize the solutions:

Copy to clipboard.
In[13]:=13
✖
https://wolfram.com/xid/0bni4boi2fj8q-q1rikc
Direct link to example
Out[13]=13
Wolfram Research (2020), HeatFluxValue, Wolfram Language function, https://reference.wolfram.com/language/ref/HeatFluxValue.html.
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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.

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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.

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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

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

BibTeX

@misc{reference.wolfram_2025_heatfluxvalue, author="Wolfram Research", title="{HeatFluxValue}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/HeatFluxValue.html}", note=[Accessed: 26-March-2025 ]}

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@misc{reference.wolfram_2025_heatfluxvalue, author="Wolfram Research", title="{HeatFluxValue}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/HeatFluxValue.html}", note=[Accessed: 26-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_heatfluxvalue, organization={Wolfram Research}, title={HeatFluxValue}, year={2020}, url={https://reference.wolfram.com/language/ref/HeatFluxValue.html}, note=[Accessed: 26-March-2025 ]}

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@online{reference.wolfram_2025_heatfluxvalue, organization={Wolfram Research}, title={HeatFluxValue}, year={2020}, url={https://reference.wolfram.com/language/ref/HeatFluxValue.html}, note=[Accessed: 26-March-2025 ]}