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

For example, use function handles to specify the thermal conductivity, internal heat source, convection coefficient, and initial temperature for this model.

thermalProperties(model,'ThermalConductivity',@myfun)
internalHeatSource(model,'Face',2,@myfun)
thermalBC(model,'Edge',[3,4], ...
                'ConvectionCoefficient',@myfun, ...
                'AmbientTemperature',27)
thermalIC(model,@myfun)

The function must be of the form:

function thermalVal = myfun(location,state)

The solver passes the location and state data to your function:

• 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.