HeatSourceFromTotalPower

This component is a heat structure heat source from a total power $var element = document.getElementById("moose-equation-5e1df068-b6a8-492f-8616-fec99548cb72");katex.render("Q", element, {displayMode:false,throwOnError:false});$ , provided by a power component. A fraction $var element = document.getElementById("moose-equation-50fb26d5-10b1-4911-afc0-6b3703a88a27");katex.render("f", element, {displayMode:false,throwOnError:false});$ of this total power may be specified, as well as a shape function $var element = document.getElementById("moose-equation-5789b6c1-b226-4f38-8090-ae26af6ef505");katex.render("a(\\mathbf{x})", element, {displayMode:false,throwOnError:false});$ if a non-uniform distribution is desired.

Usage

The user must supply the name of the heat structure via the parameter /Components/HeatSourceFromTotalPower/hs and then the applicable regions of the heat structure using the /Components/HeatSourceFromTotalPower/regions parameter. For a 2D heat structure, /Components/HeatSourceFromTotalPower/regions may include any set of the heat structure's names parameter. For HeatStructureFromFile3D, /Components/HeatSourceFromTotalPower/regions may include any set of blocks existing in the mesh file.

The user is required to specify the name of a power component via the /Components/HeatSourceFromTotalPower/power parameter. This power can be scaled with the parameter /Components/HeatSourceFromTotalPower/power_fraction. If a non-uniform power distribution is desired, the parameter /Components/HeatSourceFromTotalPower/power_shape_function may be used to specify a spatial shape function, which gets normalized internally.

Input Parameters

hsHeat structure in which to apply heat source
C++ Type:std::string
Controllable:No
Description:Heat structure in which to apply heat source
powerComponent that provides total power
C++ Type:std::string
Controllable:No
Description:Component that provides total power
regionsHeat structure regions where heat generation is to be applied
C++ Type:std::vector<std::string>
Controllable:No
Description:Heat structure regions where heat generation is to be applied

Required Parameters

power_fraction1Fraction of the total power that goes into the heat structure [-]
Default:1
C++ Type:Real
Unit:(no unit assumed)
Controllable:Yes
Description:Fraction of the total power that goes into the heat structure [-]
power_shape_functionAxial power shape [-]
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Axial power shape [-]

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:No
Description:Set the enabled status of the MooseObject.

Advanced Parameters

Formulation

The heat conduction equation is the following: $var element = document.getElementById("moose-equation-12815cd4-c973-4fd5-b22f-e5315865689e");katex.render(" \\rho c_p \\pd{T}{t} - \\nabla \\cdot (k \\nabla T) = q''' \\eqc", element, {displayMode:true,throwOnError:false});$ where

$var element = document.getElementById("moose-equation-fd111229-b18a-4273-87c9-662fc03eab5d");katex.render("\\rho", element, {displayMode:false,throwOnError:false});$ is density,
$var element = document.getElementById("moose-equation-c9babb18-a6cf-4ad0-805a-8f9235b7655a");katex.render("c_p", element, {displayMode:false,throwOnError:false});$ is specific heat capacity,
$var element = document.getElementById("moose-equation-5808a8ca-416a-4982-ad50-3b9d04c41c79");katex.render("k", element, {displayMode:false,throwOnError:false});$ is thermal conductivity,
$var element = document.getElementById("moose-equation-e6a1b79f-5d20-4661-ba4b-ab46e0d23f9e");katex.render("T", element, {displayMode:false,throwOnError:false});$ is temperature, and
$var element = document.getElementById("moose-equation-03c3c54a-93fb-4d0f-ba80-70bf9d962cad");katex.render("q'''", element, {displayMode:false,throwOnError:false});$ is a volumetric heat source.

Multiplying by a test function $var element = document.getElementById("moose-equation-60b2f750-6e7c-4cdf-813e-72991d542338");katex.render("\\phi_i", element, {displayMode:false,throwOnError:false});$ and integrating by parts over the domain $var element = document.getElementById("moose-equation-dc5c7b04-7ae2-42f2-93fc-c314d5c19b88");katex.render("\\Omega", element, {displayMode:false,throwOnError:false});$ gives $var element = document.getElementById("moose-equation-0ab8883f-cb6d-480a-9c29-013636e675e9");katex.render(" \\pr{\\rho c_p \\pd{T}{t}, \\phi_i}_\\Omega + \\pr{k \\nabla T, \\nabla\\phi_i}_\\Omega - \\left\\langle k \\nabla T, \\phi_i\\mathbf{n}\\right\\rangle_{\\partial\\Omega} = \\pr{q''', \\phi_i}_\\Omega \\eqc", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-a9d55dc5-2860-4224-b371-03c6799c0964");katex.render("\\partial\\Omega", element, {displayMode:false,throwOnError:false});$ is the boundary of the domain $var element = document.getElementById("moose-equation-e4777bf3-31e2-4c14-8d05-50dafd1da3df");katex.render("\\Omega", element, {displayMode:false,throwOnError:false});$ .

The power density from this component is the following:

var element = document.getElementById("moose-equation-c627692e-480c-447d-b77b-17576ed08ee8");katex.render("q'''(\\mathbf{x}) = f Q \\frac{a(\\mathbf{x})}{\\tilde{A}} \\eqc", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-d7595e32-cd58-4fdf-aff9-0b1c43062c4a");katex.render("\\tilde{A}", element, {displayMode:false,throwOnError:false});$ denotes the discrete approximation to

var element = document.getElementById("moose-equation-025c3015-89e6-47c9-8c7c-7f17c19a1be6");katex.render("A \\equiv \\int\\limits_\\Omega a(\\mathbf{x}) d\\Omega \\eqc", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-bb889ce4-9f81-4346-9132-da0cf53a60a4");katex.render("\\Omega", element, {displayMode:false,throwOnError:false});$ is the heat source domain. Note that the discrete integral of the power density over $var element = document.getElementById("moose-equation-cb5ed8eb-0b87-4a77-bba7-349b3e1eefa7");katex.render("\\Omega", element, {displayMode:false,throwOnError:false});$ is exactly equal to $var element = document.getElementById("moose-equation-0afe1938-5048-40d8-a2bc-a992d8fbe525");katex.render("f Q", element, {displayMode:false,throwOnError:false});$ .

Usage
Input Parameters
Formulation