ThermalModel

Thermal model object

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

AnalysisType — Type of thermal analysis

'steadystate' | 'transient'

Type of thermal analysis, returned as 'steadystate' or 'transient'.

Geometry — Geometry description

geometry object

Geometry description, returned as a geometry object.

• AnalyticGeometry Properties object for 2-D geometry. Create this geometry using the geometryFromEdges function.

• DiscreteGeometry Properties object for 3-D geometry. Create this geometry using the importGeometry function or the geometryFromMesh function.

MaterialProperties — Material properties within the domain

object containing material property assignments

Material properties within the domain, returned 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, returned 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, returned 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, returned as an object containing the initial temperature assignments within the geometric domain.

Mesh — Mesh for solution

FEMesh object

Mesh for solution, returned as a FEMesh Properties object. You create the mesh 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, returned 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)

SolverOptions — Algorithm options for PDE solvers

PDESolverOptions object

Algorithm options for the PDE solvers, returned 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 2-D or 3-D geometry from STL data
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 heat transfer or structural analysis problem

Examples

Create and Populate a Thermal Model

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

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 25 W/m^3.

internalHeatSource(thermalmodel,25)

ans = 
  HeatSourceAssignment with properties:

    RegionType: 'face'
      RegionID: 1
    HeatSource: 25

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'

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 mesh.

generateMesh(thermalmodel)

ans = 
  FEMesh with properties:

             Nodes: [2x1541 double]
          Elements: [6x734 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]