ThermalModel

Thermal model object

Domain-specific heat transfer workflow is not recommended. New features might not be compatible with this workflow. For help migrating your existing code to the unified finite element workflow, see Migration from Domain-Specific to Unified Workflow.

Description

A ThermalModel object contains information about a heat transfer problem: the geometry, material properties, internal heat sources, temperature on the boundaries, heat fluxes through the boundaries, mesh, and initial conditions.

Creation

Create a ThermalModel object using createpde with the first argument "thermal".

Properties

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`AnalysisType` — Type of thermal analysis
`"steadystate"` | `"transient"` | `"modal"` | `"steadystate-axisymmetric"` | `"transient-axisymmetric"` | `"modal-axisymmetric"`

Type of thermal analysis, specified as "steadystate", "transient", "modal", "steadystate-axisymmetric", "transient-axisymmetric", or "modal-axisymmetric".

To change a thermal analysis type, assign a new type to model.AnalysisType. Ensure that all other properties of the model are consistent with the new analysis type.

`Geometry` — Geometry description
`AnalyticGeometry` | `DiscreteGeometry`

Geometry description, specified as AnalyticGeometry for a 2-D geometry or DiscreteGeometry for a 2-D or 3-D geometry.

`MaterialProperties` — Material properties within the domain
object containing material property assignments

Material properties within the domain, specified as an object containing the material property assignments.

`HeatSources` — Heat source within the domain or subdomain
object containing heat source assignments

Heat source within the domain or subdomain, specified as an object containing heat source assignments.

`BoundaryConditions` — Boundary conditions applied to the geometry
object containing boundary condition assignments

Boundary conditions applied to the geometry, specified as an object containing the boundary condition assignments.

`InitialConditions` — Initial temperature or initial guess
object containing the initial temperature assignments within the geometric domain

Initial temperature or initial guess, specified as an object containing the initial temperature assignments within the geometric domain.

`Mesh` — Finite element mesh
`FEMesh` object

Finite element mesh, specified as an FEMesh object. You create the mesh by using the generateMesh function.

`StefanBoltzmannConstant` — Constant of proportionality in Stefan-Boltzmann law governing radiation heat transfer
number

Constant of proportionality in Stefan-Boltzmann law governing radiation heat transfer, specified as a number. This value must be consistent with the units of the model. Values of the Stefan-Boltzmann constant in commonly used system of units are:

SI – 5.670367e-8 W/(m²·K⁴)
CGS – 5.6704e-5 erg/(cm²·s·K⁴)
US customary – 1.714e-9 BTU/(hr·ft²·R⁴)

`LinearizeInputs` — Inputs for linearized model
structure array

Inputs for a linearized model, specified as a structure array. The inputs are used by the linearize that extracts a sparss (Control System Toolbox) model from a thermal model.

`LinearizeOutputs` — Outputs for linearized model
structure array

Inputs for a linearized model, specified as a structure array. The outputs are used by the linearize that extracts a sparss (Control System Toolbox) model from a thermal model.

`SolverOptions` — Algorithm options for PDE solvers
`PDESolverOptions` object

Algorithm options for the PDE solvers, specified as a PDESolverOptions Properties object. The properties of PDESolverOptions include absolute and relative tolerances for internal ODE solvers, maximum solver iterations, and so on.

Object Functions

`geometryFromEdges`	Create 2-D geometry from decomposed geometry matrix
`geometryFromMesh`	Create 2-D or 3-D geometry from mesh
`importGeometry`	Import geometry from STL or STEP file
`thermalProperties`	Assign thermal properties of a material for a thermal model
`internalHeatSource`	Specify internal heat source for a thermal model
`thermalBC`	Specify boundary conditions for a thermal model
`thermalIC`	Set initial conditions or initial guess for a thermal model
`generateMesh`	Create triangular or tetrahedral mesh
`solve`	Solve structural analysis, heat transfer, or electromagnetic analysis problem
`reduce`	Reduce structural or thermal model
`linearize`	Linearize structural or thermal model
`linearizeInput`	Specify inputs to linearized model
`linearizeOutput`	Specify outputs of linearized model

Examples

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Create and Populate Thermal Model

Open Live Script

Create a transient thermal model container.

thermalmodel = createpde("thermal","transient")

thermalmodel = 
  ThermalModel with properties:

               AnalysisType: "transient"
                   Geometry: []
         MaterialProperties: []
                HeatSources: []
    StefanBoltzmannConstant: []
         BoundaryConditions: []
          InitialConditions: []
                       Mesh: []
              SolverOptions: [1x1 pde.PDESolverOptions]

Create the geometry and include it in the model.

g = @squareg;
geometryFromEdges(thermalmodel,g)

ans = 
  AnalyticGeometry with properties:

       NumCells: 0
       NumFaces: 1
       NumEdges: 4
    NumVertices: 4
       Vertices: [4x2 double]

Assign material properties.

thermalProperties(thermalmodel,"ThermalConductivity",79.5,...
                               "MassDensity",7850,...
                               "SpecificHeat",450,...
                               "Face",1)

ans = 
  ThermalMaterialAssignment with properties:

             RegionType: 'face'
               RegionID: 1
    ThermalConductivity: 79.5000
            MassDensity: 7850
           SpecificHeat: 450

Specify that the entire geometry generates heat at the rate of 25.

internalHeatSource(thermalmodel,25)

ans = 
  HeatSourceAssignment with properties:

    RegionType: 'face'
      RegionID: 1
    HeatSource: 25
         Label: []

Apply insulated boundary conditions on three edges and the free convection boundary condition on the right edge.

thermalBC(thermalmodel,"Edge",[1,3,4],"HeatFlux",0);
thermalBC(thermalmodel,"Edge",2,...
                       "ConvectionCoefficient",5000,...
                       "AmbientTemperature",25)

ans = 
  ThermalBC with properties:

               RegionType: 'Edge'
                 RegionID: 2
              Temperature: []
                 HeatFlux: []
    ConvectionCoefficient: 5000
               Emissivity: []
       AmbientTemperature: 25
               Vectorized: 'off'
                    Label: []

Set the initial conditions: uniform room temperature across domain and higher temperature on the left edge.

thermalIC(thermalmodel,25);
thermalIC(thermalmodel,100,"Edge",4)

ans = 
  GeometricThermalICs with properties:

            RegionType: 'edge'
              RegionID: 4
    InitialTemperature: 100

Specify the Stefan-Boltzmann constant.

thermalmodel.StefanBoltzmannConstant = 5.670367e-8;

Generate the mesh.

generateMesh(thermalmodel)

ans = 
  FEMesh with properties:

             Nodes: [2x1529 double]
          Elements: [6x728 double]
    MaxElementSize: 0.1131
    MinElementSize: 0.0566
     MeshGradation: 1.5000
    GeometricOrder: 'quadratic'

thermalmodel now contains the following properties.

thermalmodel

thermalmodel = 
  ThermalModel with properties:

               AnalysisType: "transient"
                   Geometry: [1x1 AnalyticGeometry]
         MaterialProperties: [1x1 MaterialAssignmentRecords]
                HeatSources: [1x1 HeatSourceAssignmentRecords]
    StefanBoltzmannConstant: 5.6704e-08
         BoundaryConditions: [1x1 ThermalBCRecords]
          InitialConditions: [1x1 ThermalICRecords]
                       Mesh: [1x1 FEMesh]
              SolverOptions: [1x1 pde.PDESolverOptions]

Version History

Introduced in R2017a

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R2022a: Reduced-order modeling for thermal analysis

You can now approximate the dynamics of the original system with a smaller system while retaining most of the dynamic characteristics. See reduce for details.

R2021b: Sparse linear models for use with Control System Toolbox

ThermalModel now has additional properties, LinearizeInputs and LinearizeOutputs containing inputs and outputs for linearized model. They are used by the linearize that extracts a sparss (Control System Toolbox) model from a thermal model.

R2020a: Axisymmetric analysis

You can now specify AnalysisType for axisymmetric models. Axisymmetric analysis simplifies 3-D thermal problems to 2-D using their symmetry around the axis of rotation.

ThermalModel

Description

Creation

Properties

AnalysisType — Type of thermal analysis "steadystate" | "transient" | "modal" | "steadystate-axisymmetric" | "transient-axisymmetric" | "modal-axisymmetric"

Geometry — Geometry description AnalyticGeometry | DiscreteGeometry

MaterialProperties — Material properties within the domain object containing material property assignments

HeatSources — Heat source within the domain or subdomain object containing heat source assignments

BoundaryConditions — Boundary conditions applied to the geometry object containing boundary condition assignments

InitialConditions — Initial temperature or initial guess object containing the initial temperature assignments within the geometric domain

Mesh — Finite element mesh FEMesh object

StefanBoltzmannConstant — Constant of proportionality in Stefan-Boltzmann law governing radiation heat transfer number

LinearizeInputs — Inputs for linearized model structure array

LinearizeOutputs — Outputs for linearized model structure array

SolverOptions — Algorithm options for PDE solvers PDESolverOptions object