Assign thermal properties of a material for a thermal model
thermalProperties(
assigns material properties, such as thermal conductivity, mass density, and
specific heat. For transient analysis, specify all three properties. For
steady-state analysis, specifying thermal conductivity is enough. This syntax sets
material properties for the entire geometry.thermalmodel
,'ThermalConductivity',TCval
,'MassDensity',MDval
,'SpecificHeat',SHval
)
For a nonconstant or nonlinear material, specify TCval
,
MDval
, and SHval
as function
handles.
thermalProperties(___,
assigns material properties for a specified geometry region.RegionType
,RegionID
)
returns the material properties object.mtl
= thermalProperties(___)
Assign material properties for a steady-state thermal model.
model = createpde('thermal','steadystate'); gm = importGeometry(model,'SquareBeam.STL'); thermalProperties(model,'ThermalConductivity',0.08)
ans = ThermalMaterialAssignment with properties: RegionType: 'cell' RegionID: 1 ThermalConductivity: 0.0800 MassDensity: [] SpecificHeat: []
Assign material properties for transient analysis.
thermalmodel = createpde('thermal','transient'); gm = importGeometry(thermalmodel,'SquareBeam.STL'); thermalProperties(thermalmodel,'ThermalConductivity',0.2,... 'MassDensity',2.7*10^(-6),... 'SpecificHeat',920)
ans = ThermalMaterialAssignment with properties: RegionType: 'cell' RegionID: 1 ThermalConductivity: 0.2000 MassDensity: 2.7000e-06 SpecificHeat: 920
Create a steady-state thermal model.
thermalModel = createpde('thermal');
Create nested cylinders to model a two-layered insulated pipe section, consisting of inner metal pipe surrounded by insulated material.
gm = multicylinder([20,25,35],20,'Void',[1,0,0]);
Assign geometry to the thermal model and plot the geometry.
thermalModel.Geometry = gm; pdegplot(thermalModel,'CellLabels','on','FaceAlpha',0.5)
Specify thermal conductivities for metal and insulation.
thermalProperties(thermalModel,'Cell',1,'ThermalConductivity',0.4)
ans = ThermalMaterialAssignment with properties: RegionType: 'cell' RegionID: 1 ThermalConductivity: 0.4000 MassDensity: [] SpecificHeat: []
thermalProperties(thermalModel,'Cell',2,'ThermalConductivity',0.0015)
ans = ThermalMaterialAssignment with properties: RegionType: 'cell' RegionID: 2 ThermalConductivity: 0.0015 MassDensity: [] SpecificHeat: []
Use function handles to specify a thermal conductivity that depends on temperature and specific heat 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 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);
Specify the thermal conductivity as a linear function of temperature, .
k = @(location,state)40 + 0.003*state.u;
Specify the specific heat as a linear function of the y-coordinate, .
cp = @(location,state)500*location.y;
Specify the thermal conductivity, mass density, and specific heat of the material.
thermalProperties(thermalmodel,'ThermalConductivity',k,... 'MassDensity',2.7*10^(-6),... 'SpecificHeat',cp)
ans = ThermalMaterialAssignment with properties: RegionType: 'face' RegionID: 1 ThermalConductivity: @(location,state)40+0.003*state.u MassDensity: 2.7000e-06 SpecificHeat: @(location,state)500*location.y
thermalmodel
— Thermal modelThermalModel
objectThermal 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'
for a 2-D model | 'Cell'
for a 3-D modelGeometric region type, specified as 'Face'
or
'Cell'
.
Example: thermalProperties(thermalmodel,'Cell',1,'ThermalConductivity',100)
Data Types: char
| string
RegionID
— Geometric region IDGeometric region ID, specified as a vector of positive integers. Find the
region IDs by using pdegplot
.
Example: thermalProperties(thermalmodel,'Cell',1:3,'ThermalConductivity',100)
Data Types: double
TCval
— Thermal conductivity of the materialThermal conductivity of the material, specified as a positive number, a matrix, or a function handle. You can specify thermal conductivity for a steady-state or transient model. In case of orthotropic thermal conductivity, use a thermal conductivity matrix.
Use a function handle to specify the thermal conductivity that depends on space, time, or temperature. The function must be of the form
TCval = TCfun(location,state)
The solver passes location
data as a structure array
with the fields location.x
,
location.y
, and, for 3-D problems,
location.z
. The state
data is a
structure array with the fields state.u
,
state.ux
, state.uy
,
state.uz
(for 3-D problems), and
state.time
(for transient problems). The
state.u
field contains the solution vector. The
state.ux
, state.uy
,
state.uz
fields are estimates of the solution’s
partial derivatives at the corresponding points of the location structure.
The state.time
field contains time at evaluation
points.
TCfun
must return a matrix TCval
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, M
= length(location.x)
. For details about dimensions of the
matrix, see c Coefficient for specifyCoefficients.
Example: thermalProperties(thermalmodel,'Cell',1,'ThermalConductivity',100)
or
thermalProperties(thermalmodel,'ThermalConductivity',[80;10;80])
for orthotropic thermal conductivity
Data Types: double
| function_handle
MDval
— Mass density of the materialMass density of the material, specified as a positive number or a function handle. Specify this property for a transient thermal conduction analysis model.
Use a function handle to specify the mass density that depends on space, time, or temperature. The function must be of the form
MDval = MDfun(location,state)
The solver passes location
data as a structure array
with the fields location.x
,
location.y
, and, for 3-D problems,
location.z
. The state
data is a
structure array with the fields state.u
,
state.ux
, state.uy
,
state.uz
(for 3-D problems), and
state.time
(for transient problems). The
state.u
field contains the solution vector. The
state.ux
, state.uy
,
state.uz
fields are estimates of the solution’s
partial derivatives at the corresponding points of the location structure.
The state.time
field contains time at evaluation
points.
MDfun
must return a row vector MDval
with the number of columns equal to the number of evaluation points,
M = length(location.x)
.
Example: thermalProperties(thermalmodel,'Cell',1,'ThermalConductivity',100,'MassDensity',2730e-9,'SpecificHeat',910)
Data Types: double
| function_handle
SHval
— Specific heat of the materialSpecific heat of the material, specified as a positive number or a function handle. Specify this property for a transient thermal conduction analysis model.
Use a function handle to specify the specific heat that depends on space, time, or temperature. The function must be of the form
SHval = SHfun(location,state)
The solver passes location
data as a structure array
with the fields location.x
,
location.y
, and, for 3-D problems,
location.z
. The state
data is a
structure array with the fields state.u
,
state.ux
, state.uy
,
state.uz
(for 3-D problems), and
state.time
(for transient problems). The
state.u
field contains the solution vector. The
state.ux
, state.uy
,
state.uz
fields are estimates of the solution’s
partial derivatives at the corresponding points of the location structure.
The state.time
field contains time at evaluation
points.
SHfun
must return a row vector SHval
with the number of columns equal to the number of evaluation points,
M = length(location.x)
.
Example: thermalProperties(thermalmodel,'Cell',1,'ThermalConductivity',100,'MassDensity',2730e-9,'SpecificHeat',910)
Data Types: double
| function_handle
mtl
— Handle to material propertiesHandle to material properties, returned as an object.
mtl
associates material properties with the
geometric region.
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