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. 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 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. 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 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. 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

Output Arguments

mtl — Handle to material properties

object

Handle to material properties, returned as an object. mtl associates material properties with the geometric region.