internalHeatSource
Specify internal heat source for a thermal model
Domain-specific heat transfer workflow is not recommended. New features might not be compatible with this workflow. For help migrating your existing code to the unified finite element workflow, see Migration from Domain-Specific to Unified Workflow.
Syntax
Description
internalHeatSource(
specifies an internal heat source for the thermal model. This syntax declares that
the entire geometry is a heat source.thermalmodel
,heatSourceValue
)
Note
Use internalHeatSource
for specifying internal heat generators, that is, for specifying
heat sources that belong to the geometry of the model. To specify a heat
influx from an external source, use the thermalBC
function with the
HeatFlux
parameter.
internalHeatSource(
specifies geometry regions of type thermalmodel
,heatSourceValue
,RegionType
,RegionID
)RegionType
with ID numbers
in RegionID
as heat sources. Always specify
heatSourceValue
first, then specify
RegionType
and RegionID
.
internalHeatSource(___,"Label",
adds a label for the internal heat source to be used by the labeltext
)linearizeInput
function. This function lets you pass internal heat
sources to the linearize
function that extracts sparse linear models for use with Control System Toolbox™.
returns the heat source object.heatSource
= internalHeatSource(___)
Examples
Specify Internal Heat Generation on Entire Geometry
Create a transient thermal model.
thermalmodel = createpde("thermal","transient");
Import the geometry.
gm = importGeometry(thermalmodel,"SquareBeam.stl");
Set thermal conductivity to 0.2
, mass density to 2700e-9
, and specific heat to 920
.
thermalProperties(thermalmodel,"ThermalConductivity",0.2, ... "MassDensity",2700e-9, ... "SpecificHeat",920)
ans = ThermalMaterialAssignment with properties: RegionType: 'cell' RegionID: 1 ThermalConductivity: 0.2000 MassDensity: 2.7000e-06 SpecificHeat: 920
Specify that the entire geometry generates heat at the rate 2e-4
.
internalHeatSource(thermalmodel,2e-4)
ans = HeatSourceAssignment with properties: RegionType: 'cell' RegionID: 1 HeatSource: 2.0000e-04 Label: []
Specify a Face of a 2-D Geometry as a Heat Source
Create a steady-state thermal model.
thermalModel = createpde("thermal","transient");
Create the geometry.
SQ1 = [3; 4; 0; 3; 3; 0; 0; 0; 3; 3]; D1 = [2; 4; 0.5; 1.5; 2.5; 1.5; 1.5; 0.5; 1.5; 2.5]; gd = [SQ1 D1]; sf = 'SQ1+D1'; ns = char('SQ1','D1'); ns = ns'; dl = decsg(gd,sf,ns); geometryFromEdges(thermalModel,dl);
Set thermal conductivity to 50, mass density to 2500, and specific heat to 600.
thermalProperties(thermalModel,"ThermalConductivity",50, ... "MassDensity",2500, ... "SpecificHeat",600);
Specify that face 1 generates heat at 25.
internalHeatSource(thermalModel,25,"Face",1)
ans = HeatSourceAssignment with properties: RegionType: 'face' RegionID: 1 HeatSource: 25 Label: []
Specify Nonconstant Internal Heat Source
Use a function handle to specify an internal heat source that depends on coordinates.
Create a thermal model for transient analysis and include the geometry. The geometry is a rod with a circular cross section. The 2-D model is a rectangular strip whose x-dimension extends from the axis of symmetry to the outer surface, and whose y-dimension extends over the actual length of the rod.
thermalmodel = createpde("thermal","transient"); g = decsg([3 4 0 0 .2 .2 -1.5 1.5 1.5 -1.5]'); geometryFromEdges(thermalmodel,g); pdegplot(thermalmodel.Geometry)
The heat is generated within the rod due to the radioactive decay. Therefore, the entire geometry is an internal nonlinear heat source and can be represented by a function of the x-coordinate, for example, .
q = @(location,state)2000*location.x;
Specify the internal heat source for the transient model.
internalHeatSource(thermalmodel,q)
ans = HeatSourceAssignment with properties: RegionType: 'face' RegionID: 1 HeatSource: @(location,state)2000*location.x Label: []
Specify Time-Dependent Internal Heat Source
Use a function handle to specify an internal heat source that depends on time.
Create a thermal model for transient analysis and include the geometry. The geometry is a rectangular strip.
thermalmodel = createpde("thermal","transient"); g = decsg([3 4 -1.5 1.5 1.5 -1.5 0 0 .2 .2]'); geometryFromEdges(thermalmodel,g);
Specify the thermal properties of the rod.
thermalProperties(thermalmodel,"ThermalConductivity",40,... "MassDensity",7800,... "SpecificHeat",500);
Specify the boundary conditions and initial temperature.
thermalBC(thermalmodel,"Edge",2,"Temperature",100); thermalBC(thermalmodel,"Edge",3,... "ConvectionCoefficient",50,... "AmbientTemperature",100); thermalIC(thermalmodel,0);
Specify that the entire geometry generates heat at the rate 20000t during the first 500 seconds, and then the heat source turns off. For details, see Time-Dependent Heat Source Function.
internalHeatSource(thermalmodel,@heatSource);
Generate the mesh, solve the model using the solution times from 0 to 50000 seconds, and plot the results.
generateMesh(thermalmodel); tfinal = 50000; tlist = 0:100:tfinal; result = solve(thermalmodel,tlist); T = result.Temperature; figure subplot(2,1,1) pdeplot(thermalmodel,"XYData",T(:,6),"Contour","on") axis equal title(sprintf("Temperature at %g s",tlist(6))) subplot(2,1,2) pdeplot(thermalmodel,"XYData",T(:,end),"Contour","on") axis equal title(sprintf("Temperature at %g s",tfinal))
Always ensure that your function returns a matrix of NaN
of the correct size when state.time
is NaN
. The solver properly recognizes a time-dependent problem by passing NaN
state values and looking for returned NaN
values. Without this condition, the solver might fail or return incorrect results.
internalHeatSource(thermalmodel,@heatSourceInvalid); result = solve(thermalmodel,tlist); T = result.Temperature; figure subplot(2,1,1) pdeplot(thermalmodel,"XYData",T(:,6),"Contour","on") axis equal title(sprintf("Temperature at %g s",tlist(6))) subplot(2,1,2) pdeplot(thermalmodel,"XYData",T(:,end),"Contour","on") axis equal title(sprintf("Temperature at %g s",tfinal))
Time-Dependent Heat Source Function
function Q = heatSource(location,state) Q = zeros(1,numel(location.x)); if(isnan(state.time)) % Returning a NaN when time=NaN tells % the solver that the heat source is a function of time. Q(1,:) = NaN; return end if state.time < 500 Q(1,:) = 20000*state.time; end end function Q = heatSourceInvalid(location,state) % No checks for NaN Q = zeros(1,numel(location.x)); if state.time < 500 Q(1,:) = 20000*state.time; end end
Input Arguments
thermalmodel
— Thermal model
ThermalModel
object
Thermal model, specified as a ThermalModel
object.
The model contains the geometry, mesh, thermal properties of the material,
internal heat source, boundary conditions, and initial conditions.
Example: thermalmodel = createpde("thermal","steadystate")
RegionType
— Geometric region type
"Face"
| "Cell"
Geometric region type, specified as "Face"
for a 2-D
model or "Cell"
for a 3-D model.
Example: internalHeatSource(thermalmodel,25,"Cell",1)
Data Types: char
| string
RegionID
— Geometric region ID
vector of positive integers
Geometric region ID, specified as a vector of positive integers. Find the
region IDs by using pdegplot
.
Example: internalHeatSource(thermalmodel,25,"Cell",1:3)
Data Types: double
heatSourceValue
— Heat source value
number | function handle
Heat source value, specified as a number or a function handle. Use a function handle to specify the internal heat source that depends on space, time, or temperature. For details, see More About.
Example: internalHeatSource(thermalmodel,25)
Data Types: double
| function_handle
labeltext
— Label for internal heat source
character vector | string
Label for the internal heat source, specified as a character vector or a string.
Data Types: char
| string
Output Arguments
heatSource
— Handle to heat source
HeatSourceAssignment
object
Handle to heat source, returned as a
HeatSourceAssignment
object. See HeatSourceAssignment Properties.
heatSourceValue
associates the heat source value with
the geometric region.
More About
Specifying Nonconstant Parameters of a Thermal Model
Use a function handle to specify these thermal parameters when they depend on space, temperature, and time:
Thermal conductivity of the material
Mass density of the material
Specific heat of the material
Internal heat source
Temperature on the boundary
Heat flux through the boundary
Convection coefficient on the boundary
Radiation emissivity coefficient on the boundary
Initial temperature (can depend on space only)
For example, use function handles to specify the thermal conductivity, internal heat source, convection coefficient, and initial temperature for this model.
thermalProperties(model,"ThermalConductivity", ... @myfunConductivity) internalHeatSource(model,"Face",2,@myfunHeatSource) thermalBC(model,"Edge",[3,4], ... "ConvectionCoefficient",@myfunBC, ... "AmbientTemperature",27) thermalIC(model,@myfunIC)
For all parameters, except the initial temperature, the function must be of the form:
function thermalVal = myfun(location,state)
For the initial temperature the function must be of the form:
function thermalVal = myfun(location)
The solver computes and populates the data in the location
and
state
structure arrays and passes this data to your function. You can
define your function so that its output depends on this data. You can use any names instead of
location
and state
, but the function must have exactly
two arguments (or one argument if the function specifies the initial temperature).
location
— A structure containing these fields:location.x
— The x-coordinate of the point or pointslocation.y
— The y-coordinate of the point or pointslocation.z
— For a 3-D or an axisymmetric geometry, the z-coordinate of the point or pointslocation.r
— For an axisymmetric geometry, the r-coordinate of the point or points
Furthermore, for boundary conditions, the solver passes these data in the
location
structure:location.nx
— x-component of the normal vector at the evaluation point or pointslocation.ny
— y-component of the normal vector at the evaluation point or pointslocation.nz
— For a 3-D or an axisymmetric geometry, z-component of the normal vector at the evaluation point or pointslocation.nr
— For an axisymmetric geometry, r-component of the normal vector at the evaluation point or points
state
— A structure containing these fields for transient or nonlinear problems:state.u
— Temperatures at the corresponding points of the location structurestate.ux
— Estimates of the x-component of temperature gradients at the corresponding points of the location structurestate.uy
— Estimates of the y-component of temperature gradients at the corresponding points of the location structurestate.uz
— For a 3-D or an axisymmetric geometry, estimates of the z-component of temperature gradients at the corresponding points of the location structurestate.ur
— For an axisymmetric geometry, estimates of the r-component of temperature gradients at the corresponding points of the location structurestate.time
— Time at evaluation points
Thermal material properties (thermal conductivity, mass density, and specific heat) and internal heat source get these data from the solver:
location.x
,location.y
,location.z
,location.r
Subdomain ID
state.u
,state.ux
,state.uy
,state.uz
,state.r
,state.time
Boundary conditions (temperature on the boundary, heat flux, convection coefficient, and radiation emissivity coefficient) get these data from the solver:
location.x
,location.y
,location.z
,location.r
location.nx
,location.ny
,location.nz
,location.nr
state.u
,state.time
Initial temperature gets the following data from the solver:
location.x
,location.y
,location.z
,location.r
Subdomain ID
For all thermal parameters, except for thermal conductivity, your function must return a row
vector thermalVal
with the number of columns
equal to the number of evaluation points, for example, M =
length(location.y)
.
For thermal conductivity, your function must return a matrix
thermalVal
with number of rows equal to 1, Ndim
,
Ndim*(Ndim+1)/2
, or Ndim*Ndim
, where
Ndim
is 2 for 2-D problems and 3 for 3-D problems. The number of columns
must equal the number of evaluation points, for example, M =
length(location.y)
. For details about dimensions of the matrix, see c Coefficient for specifyCoefficients.
If properties depend on the time or temperature, ensure that your function returns a matrix of
NaN
of the correct size when state.u
or
state.time
are NaN
. Solvers check whether a problem is
time dependent by passing NaN
state values and looking for returned
NaN
values.
Additional Arguments in Functions for Nonconstant Thermal Parameters
To use additional arguments in your function, wrap your function (that takes additional arguments) with an anonymous function that takes only the location
and state
arguments. For example:
thermalVal = ... @(location,state) myfunWithAdditionalArgs(location,state,arg1,arg2...) thermalBC(model,"Edge",3,"Temperature",thermalVal) thermalVal = @(location) myfunWithAdditionalArgs(location,arg1,arg2...) thermalIC(model,thermalVal)
Version History
Introduced in R2017aR2021b: Label to extract sparse linear models for use with Control System Toolbox
Now you can add a label for the internal heat source to be used by the linearizeInput
function. This function lets you pass internal heat
sources to the linearize
function that extracts sparse linear models for use with Control System Toolbox.
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