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Solve conduction-dominant heat transfer problems with convection and
radiation occurring at boundaries

Address challenges with thermal management by analyzing the temperature distributions of components based on material properties, external heat sources, and internal heat generation for steady-state and transient problems.

A typical programmatic workflow for solving a heat transfer problem includes the following steps:

Create a special thermal model container for a steady-state or transient thermal model.

Define 2-D or 3-D geometry and mesh it.

Assign thermal properties of the material, such as thermal conductivity

*k*, specific heat*c*, and mass density*ρ*.Specify internal heat sources

*Q*within the geometry.Specify temperatures on the boundaries or heat fluxes through the boundaries. For convective heat flux through the boundary $$htc\left(T-{T}_{\infty}\right)$$, specify the ambient temperature $${T}_{\infty}$$ and the convective heat transfer coefficient

*htc*. For radiative heat flux $$\epsilon \sigma \left({T}^{4}-{T}_{\infty}{}^{4}\right)$$, specify the ambient temperature $${T}_{\infty}$$, emissivity*ε*, and Stefan-Boltzmann constant*σ*.Set an initial temperature or initial guess.

Solve and plot results, such as the resulting temperatures, temperature gradients, heat fluxes, and heat rates.

`ThermalModel` | Thermal model object |

`SteadyStateThermalResults` | Steady-state thermal solution and derived quantities |

`TransientThermalResults` | Transient thermal solution and derived quantities |

ThermalMaterialAssignment Properties | Thermal material properties assignments |

HeatSourceAssignment Properties | Heat source assignments |

ThermalBC Properties | Boundary condition for thermal model |

NodalThermalICs Properties | Initial temperature at mesh nodes |

GeometricThermalICs Properties | Initial temperature over a region or region boundary |

PDESolverOptions Properties | Algorithm options for solvers |

PDEVisualization Properties | PDE visualization of mesh and nodal results |

**Heat Transfer in Block with Cavity**

Solve a heat equation that describes heat diffusion in a block with a rectangular cavity.

**Temperature Distribution in Heat Sink**

Perform a 3-D transient heat transfer analysis of a heat sink.

**Heat Distribution in Circular Cylindrical Rod**

Analyze a 3-D axisymmetric model by using a 2-D model.

**Heat Conduction in Multidomain Geometry with Nonuniform Heat Flux**

Perform a 3-D transient heat conduction analysis of a hollow sphere made of three different layers of material, subject to a nonuniform external heat flux.

**Inhomogeneous Heat Equation on Square Domain**

Solve the heat equation with a source term.

**Heat Transfer Problem with Temperature-Dependent Properties**

Solve the heat equation with a temperature-dependent thermal conductivity.

**Thermal Analysis of Disc Brake**

Use Partial Differential Equation Toolbox™ and Simscape™ Driveline™ to simulate a brake pad moving around a disc and analyze temperatures when braking.

**Axisymmetric Thermal and Structural Analysis of Disc Brake**

Simplify analysis of a disc brake by using an axisymmetric model for thermal and thermal stress computations.

**Nonlinear Heat Transfer in Thin Plate**

Perform a heat transfer analysis of a thin plate.