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.
For 2-D geometry problems, you also can use the PDE Modeler app. The app includes geometry creation and preset modes for applications.
|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 or structural analysis problem|
|Assemble finite element matrices|
|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|
|Plot solution or mesh for 2-D geometry|
|Plot solution or surface mesh for 3-D geometry|
|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|
|PDE Modeler||Solve partial differential equations in 2-D regions|
Use command-line functions to solve a heat equation that describes heat diffusion in a metal block with a rectangular cavity.
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.
Perform a heat transfer analysis of a thin plate.
Use the PDE Modeler app to solve a heat equation that describes heat diffusion in a block with a rectangular cavity.
Solve a 3-D parabolic PDE problem by reducing it to 2-D using coordinate transformation.
Solve a heat transfer problem with different material parameters.