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 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 , 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.
Thermal Model Setup
|Assign thermal properties of a material for a thermal model|
|Specify internal heat source for a thermal model|
|Specify boundary conditions for a thermal model|
|Set initial conditions or initial guess for a thermal model|
|Solve heat transfer, structural analysis, or electromagnetic analysis problem|
|Assemble finite element matrices|
|Linearize structural or thermal model|
|Specify inputs to linearized model|
|Specify outputs of linearized model|
Solutions at Nodal and Custom Locations
|Interpolate temperature in a thermal result at arbitrary spatial locations|
|Evaluate temperature gradient of a thermal solution at arbitrary spatial locations|
|Evaluate heat flux of a thermal solution at nodal or arbitrary spatial locations|
|Evaluate integrated heat flow rate normal to specified boundary|
Thermal Model 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|
Thermal Analysis Workflow
Solve a heat equation that describes heat diffusion in a block with a rectangular cavity.
Perform a 3-D transient heat transfer analysis of a heat sink.
Analyze a 3-D axisymmetric model by using a 2-D model.
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.
Solve the heat equation with a source term.
Solve the heat equation with a temperature-dependent thermal conductivity.
Use Partial Differential Equation Toolbox™ and Simscape™ Driveline™ to simulate a brake pad moving around a disc and analyze temperatures when braking.
Simplify analysis of a disc brake by using an axisymmetric model for thermal and thermal stress computations.
General PDE Workflow
Perform a heat transfer analysis of a thin plate.