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.
The heat transfer equation is a parabolic partial differential equation that describes the distribution of temperature in a particular region over given time:
A typical programmatic workflow for solving a heat transfer problem includes these 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 , specify the ambient temperature and the convective heat transfer coefficient htc. For radiative heat flux , specify the ambient temperature , 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.
Approximate dynamic characteristics of a thermal model by using reduced order modeling (ROM).
Functions
Live Editor Tasks
Visualize PDE Results | Create and explore visualizations of PDE results in the Live Editor (Since R2022b) |
Objects
ThermalModel | Thermal model object |
ReducedThermalModel | Reduced-order thermal model (Since R2022a) |
SteadyStateThermalResults | Steady-state thermal solution and derived quantities |
TransientThermalResults | Transient thermal solution and derived quantities |
ModalThermalResults | Modal thermal solution (Since R2022a) |
Properties
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 (Since R2021a) |
Topics
Thermal Analysis Workflow
- 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. - 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.
General PDE Workflow
- Nonlinear Heat Transfer in Thin Plate
Perform a heat transfer analysis of a thin plate.