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Heat Transfer

Solve conduction-dominant heat transfer problems with convection and radiation occurring at boundaries

In this workflow, you can only specify and store parameters belonging to thermal analysis. To store all physical parameters for structural, thermal, and electromagnetic analyses, and for ease of switching between analyses types, use Unified Modeling. For help migrating your existing code to the unified finite element workflow, see Migration from Domain-Specific to Unified Workflow.

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 htc(TT), specify the ambient temperature T and the convective heat transfer coefficient htc. For radiative heat flux εσ(T4T4), specify the ambient temperature T, 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).

Temperature distribution on a sphere


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createpdeCreate model
thermalPropertiesAssign thermal properties of a material for a thermal model
internalHeatSourceSpecify internal heat source for a thermal model
thermalBCSpecify boundary conditions for a thermal model
thermalICSet initial conditions or initial guess for a thermal model
solveSolve structural analysis, heat transfer, or electromagnetic analysis problem
assembleFEMatricesAssemble finite element matrices
reduceReduce structural or thermal model (Since R2019b)
reconstructSolutionRecover full-model transient solution from reduced-order model (ROM) (Since R2019b)
linearizeLinearize structural or thermal model (Since R2021b)
linearizeInputSpecify inputs to linearized model (Since R2021b)
linearizeOutputSpecify outputs of linearized model (Since R2021b)
interpolateTemperatureInterpolate temperature in thermal result at arbitrary spatial locations
evaluateTemperatureGradientEvaluate temperature gradient of thermal solution at arbitrary spatial locations
evaluateHeatFluxEvaluate heat flux of thermal solution at nodal or arbitrary spatial locations
evaluateHeatRateEvaluate integrated heat flow rate normal to specified boundary
pdeplotPlot solution or mesh for 2-D problem
pdeplot3DPlot solution or surface mesh for 3-D problem
pdegplotPlot PDE geometry
pdemeshPlot PDE mesh
pdevizCreate and plot PDE visualization object (Since R2021a)
findThermalPropertiesFind thermal material properties assigned to a geometric region
findHeatSourceFind heat source assigned to a geometric region
findThermalBCFind thermal boundary conditions assigned to a geometric region
findThermalICFind thermal initial conditions assigned to a geometric region

Live Editor Tasks

Visualize PDE ResultsCreate and explore visualizations of PDE results in the Live Editor (Since R2022b)


ThermalModelThermal model object
ReducedThermalModelReduced-order thermal model (Since R2022a)
SteadyStateThermalResultsSteady-state thermal solution and derived quantities
TransientThermalResultsTransient thermal solution and derived quantities
ModalThermalResults Modal thermal solution (Since R2022a)


ThermalMaterialAssignment PropertiesThermal material properties assignments
HeatSourceAssignment PropertiesHeat source assignments
ThermalBC PropertiesBoundary condition for thermal model
NodalThermalICs PropertiesInitial temperature at mesh nodes
GeometricThermalICs PropertiesInitial temperature over a region or region boundary
PDESolverOptions PropertiesAlgorithm options for solvers
PDEVisualization PropertiesPDE visualization of mesh and nodal results (Since R2021a)


Thermal Analysis Workflow

General PDE Workflow