# thermalProperties

Assign thermal properties of a material for a thermal model

## Syntax

## Description

`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(___)

## 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).

`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.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 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.

### 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 R2017a**

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