Heat Transfer in Solids (ht)
Heat transfer by conduction (and convection by a prescribed velocity). Elmer HeatSolver.
Category |
Heat Transfer |
Name (tag) |
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Space dimensions |
3D, 2D, 2D axisymmetric |
Studies |
Stationary, Time Dependent |
Dependent variables |
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Default features |
\(\rho C_p \frac{\partial T}{\partial t} + \rho C_p\mathbf{u}\cdot\nabla T + \nabla\cdot\mathbf{q} = Q,\quad \mathbf{q}=-k\nabla T\)
Material properties used: Thermal conductivity (k), Density (ρ), Heat capacity at constant pressure (Cₚ).
Interface settings
| Setting | Symbol | Unit | Default | Choices / type |
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Discretization |
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Element order |
Quadratic |
Linear, Quadratic |
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Elmer Solver |
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Additional Elmer solver keywords |
Text (multi-line) |
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Domain features
Solid
Selection: Domains (all by default) · Physics ribbon › Domains, or right-click the interface in the Model Builder
\(\rho C_p \frac{\partial T}{\partial t} + \nabla\cdot\mathbf{q} = Q,\quad \mathbf{q}=-k\nabla T\)
| Setting | Symbol | Unit | Default | Choices / type |
|---|---|---|---|---|
Heat Conduction, Solid |
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Thermal conductivity |
k |
From material |
From material, User defined |
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k |
k |
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Expression |
Density |
ρ |
From material |
From material, User defined |
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rho |
ρ |
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Expression |
Heat capacity at constant pressure |
Cₚ |
From material |
From material, User defined |
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Cp |
Cₚ |
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Expression |
Fluid
Selection: Domains · Physics ribbon › Domains, or right-click the interface in the Model Builder
\(\rho C_p \frac{\partial T}{\partial t} + \rho C_p\mathbf{u}\cdot\nabla T + \nabla\cdot\mathbf{q} = Q\)
| Setting | Symbol | Unit | Default | Choices / type |
|---|---|---|---|---|
Model Inputs |
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Velocity field |
User defined |
User defined, Velocity field (spf) |
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u x |
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Expression |
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u y |
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Expression |
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u z |
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Expression |
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Heat Convection |
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Thermal conductivity |
k |
From material |
From material, User defined |
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k |
k |
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Expression |
Density |
ρ |
From material |
From material, User defined |
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rho |
ρ |
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Expression |
Heat capacity at constant pressure |
Cₚ |
From material |
From material, User defined |
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Cp |
Cₚ |
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Expression |
Boundary features
Temperature
Selection: Boundaries · Physics ribbon › Boundaries, or right-click the interface in the Model Builder
\(T = T_0\)
| Setting | Symbol | Unit | Default | Choices / type |
|---|---|---|---|---|
Temperature |
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Temperature |
T₀ |
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Expression |
Heat Flux
Selection: Boundaries · Physics ribbon › Boundaries, or right-click the interface in the Model Builder
\(-\mathbf{n}\cdot\mathbf{q} = q_0 + h\,(T_{ext}-T)\)
| Setting | Symbol | Unit | Default | Choices / type |
|---|---|---|---|---|
Heat Flux |
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Flux type |
General inward heat flux |
General inward heat flux, Convective heat flux |
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Heat flux |
q₀ |
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Expression |
Heat transfer coefficient |
h |
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Expression |
External temperature |
Tₑₓₜ |
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Expression |
Surface-to-Ambient Radiation
Selection: Boundaries · Physics ribbon › Boundaries, or right-click the interface in the Model Builder
\(-\mathbf{n}\cdot\mathbf{q} = \varepsilon\sigma(T_{amb}^4 - T^4)\)
| Setting | Symbol | Unit | Default | Choices / type |
|---|---|---|---|---|
Surface Emissivity |
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Surface emissivity |
ε |
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Expression |
Ambient |
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Ambient temperature |
T_amb |
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Expression |