# Heat Transfer

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. For details about partial differential equations for heat transfer, see Thermal Analysis Equations.

The solver returns one of the results objects containing the basic solution values, such as temperature and temperature gradient, at mesh nodes. After solving the problem, you can interpolate returned results to arbitrary spatial locations instead of mesh nodes and also evaluate other solution values, such as heat flux and heat rate.

## Functions

`filterByIndex` | Access transient results for specified time steps (Since R2023b) |

`interpolateTemperature` | Interpolate temperature in thermal result at arbitrary spatial locations |

`evaluateTemperatureGradient` | Evaluate temperature gradient of thermal solution at arbitrary spatial locations |

`evaluateHeatFlux` | Evaluate heat flux of thermal solution at nodal or arbitrary spatial locations |

`evaluateHeatRate` | Evaluate integrated heat flow rate normal to specified boundary |

## Objects

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

`TransientThermalResults` | Transient thermal solution and derived quantities |

`ModalThermalResults` | Modal thermal solution (Since R2022a) |

## Topics

**Heat Transfer in Block with Cavity**Find the heat distribution in a block with a cavity by using the unified workflow.

**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.

**Radiation Heat Transfer in Spherical Cavity**This example shows the effect of surface-to-surface radiation in thermal analysis of nested annular spheres.

**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.

**Heat Sink Finite Element Model and Data for State-Space Simulation**Convert a finite element model to a form that you can easily use in a Simulink® model for a closed-loop control system.

**Reduced-Order Model for Thermal Behavior of Battery**Generate a reduced-order model (ROM) to enable analysis of the spatial thermal behavior of a battery cell during a fast-charging scenario.

**Battery Module Cooling Analysis and Reduced-Order Thermal Model**Perform a battery cooling analysis to determine effect of a cooling system.

**Effect of Surface-to-Surface Radiation on Battery Module Under Thermal Runaway Condition**This example shows how to include surface-to-surface radiation effects in thermal analysis of a battery module.