thermalBC
Specify boundary conditions 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
thermalBC(
adds a temperature boundary condition to thermalmodel
,RegionType
,RegionID
,"Temperature",Tval
)thermalmodel
. The
boundary condition applies to regions of type RegionType
with
ID numbers in RegionID
.
thermalBC(
adds a heat flux boundary condition to thermalmodel
,RegionType
,RegionID
,"HeatFlux",HFval
)thermalmodel
. The
boundary condition applies to regions of type RegionType
with
ID numbers in RegionID
.
Note
Use thermalBC
with the HeatFlux
parameter to specify a heat flux to or from an external source. To specify
internal heat generation, that is, heat sources that belong to the geometry
of the model, use internalHeatSource
.
thermalBC(
adds a convection boundary condition to thermalmodel
,RegionType
,RegionID
,"ConvectionCoefficient",CCval
,"AmbientTemperature",ATval
)thermalmodel
. The
boundary condition applies to regions of type RegionType
with
ID numbers in RegionID
.
thermalBC(
adds a radiation boundary condition to thermalmodel
,RegionType
,RegionID
,"Emissivity",REval
,"AmbientTemperature",ATval
)thermalmodel
. The
boundary condition applies to regions of type RegionType
with
ID numbers in RegionID
.
thermalBC(___,"Label",
adds a label for the thermal boundary condition to be used by the labeltext
)linearizeInput
function. This function lets you pass thermal
boundary conditions to the linearize
function that extracts sparse linear models for use with Control System Toolbox™.
returns the thermal boundary condition object.thermalBC
= thermalBC(___)
Examples
Specify Temperature on the Boundary
Apply temperature boundary condition on two edges of a square.
thermalmodel = createpde("thermal"); geometryFromEdges(thermalmodel,@squareg); thermalBC(thermalmodel,"Edge",[1,3],"Temperature",100)
ans = ThermalBC with properties: RegionType: 'Edge' RegionID: [1 3] Temperature: 100 HeatFlux: [] ConvectionCoefficient: [] Emissivity: [] AmbientTemperature: [] Vectorized: 'off' Label: []
Specify Heat Coming Through the Boundary
Apply heat flux boundary condition on two faces of a block.
thermalmodel = createpde("thermal","transient"); gm = importGeometry(thermalmodel,"Block.stl"); thermalBC(thermalmodel,"Face",[1,3],"HeatFlux",20)
ans = ThermalBC with properties: RegionType: 'Face' RegionID: [1 3] Temperature: [] HeatFlux: 20 ConvectionCoefficient: [] Emissivity: [] AmbientTemperature: [] Vectorized: 'off' Label: []
Specify Convection on the Boundary
Apply convection boundary condition on four faces of a block.
thermalModel = createpde("thermal","transient"); gm = importGeometry(thermalModel,"Block.stl"); thermalBC(thermalModel,"Face",[2 4 5 6], ... "ConvectionCoefficient",5, ... "AmbientTemperature",27)
ans = ThermalBC with properties: RegionType: 'Face' RegionID: [2 4 5 6] Temperature: [] HeatFlux: [] ConvectionCoefficient: 5 Emissivity: [] AmbientTemperature: 27 Vectorized: 'off' Label: []
Specify Radiation Through the Boundary
Apply radiation boundary condition on four faces of a block.
thermalmodel = createpde("thermal","transient"); gm = importGeometry(thermalmodel,"Block.stl"); thermalmodel.StefanBoltzmannConstant = 5.670373E-8; thermalBC(thermalmodel,"Face",[2,4,5,6],... "Emissivity",0.1,... "AmbientTemperature",300)
ans = ThermalBC with properties: RegionType: 'Face' RegionID: [2 4 5 6] Temperature: [] HeatFlux: [] ConvectionCoefficient: [] Emissivity: 0.1000 AmbientTemperature: 300 Vectorized: 'off' Label: []
Specify Nonconstant Thermal Boundary Conditions
Use function handles to specify thermal boundary conditions that depend 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 y-dimension extends from the axis of symmetry to the outer surface, and whose x-dimension extends over the actual length of the rod.
thermalmodel = createpde("thermal","transient"); g = decsg([3 4 -1.5 1.5 1.5 -1.5 0 0 .2 .2]'); geometryFromEdges(thermalmodel,g);
Plot the geometry.
figure pdegplot(thermalmodel,"EdgeLabels","on"); xlim([-2 2]); ylim([-2 2]); title 'Rod Section Geometry with Edge Labels'
Assume that there is a heat source at the left end of the rod and a fixed temperature at the right end. The outer surface of the rod exchanges heat with the environment due to convection.
Define the boundary conditions for the model. The edge at y = 0 (edge 1) is along the axis of symmetry. No heat is transferred in the direction normal to this edge. This boundary is modeled as an insulated boundary, by default.
The temperature at the right end of the rod (edge 2) is a fixed temperature, T = 100 C. Specify the boundary condition for edge 2 as follows.
thermalBC(thermalmodel,"Edge",2,"Temperature",100)
ans = ThermalBC with properties: RegionType: 'Edge' RegionID: 2 Temperature: 100 HeatFlux: [] ConvectionCoefficient: [] Emissivity: [] AmbientTemperature: [] Vectorized: 'off' Label: []
The convection coefficient for the outer surface of the rod (edge 3) depends on the y-coordinate, 50y. Specify the boundary condition for this edge as follows.
outerCC = @(location,~) 50*location.y; thermalBC(thermalmodel,"Edge",3,... "ConvectionCoefficient",outerCC,... "AmbientTemperature",100)
ans = ThermalBC with properties: RegionType: 'Edge' RegionID: 3 Temperature: [] HeatFlux: [] ConvectionCoefficient: @(location,~)50*location.y Emissivity: [] AmbientTemperature: 100 Vectorized: 'off' Label: []
The heat flux at the left end of the rod (edge 4) is also a function of the y-coordinate, 5000y. Specify the boundary condition for this edge as follows.
leftHF = @(location,~) 5000*location.y; thermalBC(thermalmodel,"Edge",4,"HeatFlux",leftHF)
ans = ThermalBC with properties: RegionType: 'Edge' RegionID: 4 Temperature: [] HeatFlux: @(location,~)5000*location.y ConvectionCoefficient: [] Emissivity: [] AmbientTemperature: [] Vectorized: 'off' Label: []
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
"Edge"
for a 2-D model | "Face"
for a 3-D model
Geometric region type, specified as "Edge"
or
"Face"
.
Example: thermalBC(thermalmodel,"Face",1,"Temperature",72)
Data Types: char
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
with the
"FaceLabels"
(3-D) or "EdgeLabels"
(2-D) value set to "on"
.
Example: thermalBC(thermalmodel,"Edge",2:5,"Temperature",72)
Data Types: double
Tval
— Temperature boundary condition
number | function handle
Temperature boundary condition, specified as a number or a function handle. Use a function handle to specify the temperature that depends on space and time. For details, see More About.
Example: thermalBC(thermalmodel,"Face",1,"Temperature",72)
Data Types: double
| function_handle
HFval
— Heat flux boundary condition
number | function handle
Heat flux boundary condition, specified as a number or a function handle. Use a function handle to specify the heat flux that depends on space and time. For details, see More About.
Example: thermalBC(thermalmodel,"Face",[1,3],"HeatFlux",20)
Data Types: double
| function_handle
CCval
— Coefficient for convection to ambient heat transfer condition
number | function handle
Convection to ambient boundary condition, specified as a number or a function handle. Use a function handle to specify the convection coefficient that depends on space and time. For details, see More About.
Specify ambient temperature using the
AmbientTemperature
argument. The value of
ConvectionCoefficient
is positive for heat convection
into the ambient environment.
Example: thermalBC(thermalmodel,"Edge",[2,4],"ConvectionCoefficient",5,"AmbientTemperature",60)
Data Types: double
| function_handle
REval
— Radiation emissivity coefficient
number in the range (0,1)
Radiation emissivity coefficient, specified as a number in the range (0,1). Use a function handle to specify the radiation emissivity that depends on space and time. For details, see More About.
Specify ambient temperature using the
AmbientTemperature
argument and the Stefan-Boltzmann
constant using the thermal model properties. The value of
Emissivity
is positive for heat radiation into the
ambient environment.
Example: thermalmodel.StefanBoltzmannConstant = 5.670373E-8;
thermalBC(thermalmodel,"Edge",[2,4,5,6],"Emissivity",0.1,"AmbientTemperature",300)
Data Types: double
| function_handle
ATval
— Ambient temperature
number
Ambient temperature, specified as a number. The ambient temperature value is required for specifying convection and radiation boundary conditions.
Example: thermalBC(thermalmodel,"Edge",[2,4],"ConvectionCoefficient",5,"AmbientTemperature",60)
Data Types: double
labeltext
— Label for thermal boundary condition
character vector | string
Label for the thermal boundary condition, specified as a character vector or a string.
Data Types: char
| string
Output Arguments
thermalBC
— Handle to thermal boundary condition
ThermalBC
object
Handle to thermal boundary condition, returned as a
ThermalBC
object. See ThermalBC Properties.
thermalBC
associates the thermal boundary condition
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 thermal boundary conditions to be used by the
linearizeInput
function. This function lets you pass thermal
boundary conditions to the linearize
function that extracts sparse linear models for use with Control System Toolbox.
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