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).
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 structural analysis, heat transfer, or electromagnetic analysis problem
|Assemble finite element matrices
|Reduce structural or thermal model (Since R2019b)
|Recover full-model transient solution from reduced-order model (ROM) (Since R2019b)
|Linearize structural or thermal model (Since R2021b)
|Specify inputs to linearized model (Since R2021b)
|Specify outputs of linearized model (Since R2021b)
Solutions at Nodal and Custom Locations
|Interpolate temperature in thermal result at arbitrary spatial locations
|Evaluate temperature gradient of thermal solution at arbitrary spatial locations
|Evaluate heat flux of thermal solution at nodal or arbitrary spatial locations
|Evaluate integrated heat flow rate normal to specified boundary
Thermal Model Properties
Live Editor Tasks
|Visualize PDE Results
|Create and explore visualizations of PDE results in the Live Editor (Since R2022b)
|Thermal material properties assignments
|Heat source assignments
|Boundary condition for thermal model
|Initial temperature at mesh nodes
|Initial temperature over a region or region boundary
|Algorithm options for solvers
|PDE visualization of mesh and nodal results (Since R2021a)
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.