thermalProperties

Assign thermal properties of a material for a thermal model

Syntax

thermalProperties(thermalmodel,'ThermalConductivity',TCval,'MassDensity',MDval,'SpecificHeat',SHval)

thermalProperties(___,RegionType,RegionID)

mtl = thermalProperties(___)

Description

thermalProperties(thermalmodel,'ThermalConductivity',TCval,'MassDensity',MDval,'SpecificHeat',SHval) 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.

For a nonconstant or nonlinear material, specify TCval, MDval, and SHval as function handles.

thermalProperties(___,RegionType,RegionID) assigns material properties for a specified geometry region.

mtl = thermalProperties(___) returns the material properties object.

Examples

Assign Thermal Conductivity

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 Thermal Conductivity, Mass Density, and Specific Heat

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

Assign Thermal Conductivities for Each Geometric Region

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: []

Specify Nonconstant Thermal Properties

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, $\mathit{k}=40+0.003\mathit{T}$.

k = @(location,state)40 + 0.003*state.u;

Specify the specific heat as a linear function of the y-coordinate, $\mathit{cp}=500\mathit{y}$.

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

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' for a 2-D model | 'Cell' for a 3-D model

Geometric region type, specified as 'Face' or 'Cell'.

Example: thermalProperties(thermalmodel,'Cell',1,'ThermalConductivity',100)

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: thermalProperties(thermalmodel,'Cell',1:3,'ThermalConductivity',100)

Data Types: double

TCval — Thermal conductivity of the material

positive number | matrix | function handle

Thermal 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. For details, see More About.

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 material

positive number | function handle

Mass 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. For details, see More About.

Example: thermalProperties(thermalmodel,'Cell',1,'ThermalConductivity',100,'MassDensity',2730e-9,'SpecificHeat',910)

Data Types: double | function_handle

SHval — Specific heat of the material

positive number | function handle

Specific 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. For details, see More About.

Example: thermalProperties(thermalmodel,'Cell',1,'ThermalConductivity',100,'MassDensity',2730e-9,'SpecificHeat',910)

Data Types: double | function_handle

Output Arguments

mtl — Handle to material properties

ThermalMaterialAssignment object

Handle to material properties, returned as a ThermalMaterialAssignment object. See ThermalMaterialAssignment Properties.

mtl associates material properties 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). 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)

• location — A structure containing these fields:

  • location.x — The x-coordinate of the point or points

  • location.y — The y-coordinate of the point or points

  • location.z — For a 3-D or an axisymmetric geometry, the z-coordinate of the point or points

  • location.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 points

  • location.ny — y-component of the normal vector at the evaluation point or points

  • location.nz — For a 3-D or an axisymmetric geometry, z-component of the normal vector at the evaluation point or points

  • location.nz — For an axisymmetric geometry, z-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 structure

  • state.ux — Estimates of the x-component of temperature gradients at the corresponding points of the location structure

  • state.uy — Estimates of the y-component of temperature gradients at the corresponding points of the location structure

  • state.uz — For a 3-D or an axisymmetric geometry, estimates of the z-component of temperature gradients at the corresponding points of the location structure

  • state.ur — For an axisymmetric geometry, estimates of the r-component of temperature gradients at the corresponding points of the location structure

  • state.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.