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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.

The heat transfer equation is a parabolic partial differential equation that describes the distribution of temperature in a particular region over given time:

$$\rho c\frac{\partial T}{\partial t}-\nabla \cdot \left(k\nabla T\right)=Q$$

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 |

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