Docs: conductTemperature

Mon, 01 Jan 0001 00:00:00 +0000

Overview

conductTemperature models transient heat conduction in a solid. It solves a single energy equation for the temperature T, using density rho, specific heat cv and thermal conductivity kappa. There is no velocity field, no advection and no pressure-velocity coupling. It is meant to be the solid side of a conjugate heat transfer problem, coupled to a fluid region (usually pimpleFluid transportTemperature) through a heatTransferInterface. It can also be stacked with a solid mechanics region type (e.g. solidStVK) for thermo-FSI.

Governing Equations

Energy (heat conduction)

$$ \frac{\partial \left( \rho \, c_v \, T \right)}{\partial t} = \nabla \cdot \left( \kappa \, \nabla T \right) $$

Symbol	Description	Unit
$T$	Temperature	K
$\rho$	Density	kg/m³
$c_v$	Specific heat capacity	J/(kg K) = m²/(s² K)
$\kappa$	Thermal conductivity	W/(m K) = kg m/(s³ K)

The equation is assembled as

fvm::ddt(rho_*cv_, T()) == fvm::laplacian(kappa_(), T(), "laplacian(kappa,T)")

so fvSchemes must provide a laplacian(kappa,T) entry (or a default laplacian scheme). The equation has no source term.

Numerical Algorithm

conductTemperature does not run its own solve loop. usesPIMPLE() returns false. solveRegion(), prePredictor(), momentumPredictor(), pressureCorrector(), meshMotionCorrector() and postSolve() are all no-ops. The temperature is solved only when multiRegionSystem asks for it:

The region does not override selfCoupledFieldNames(), so the base default (an empty list) applies. T is therefore solved only when it appears as a partitioned-coupled field, i.e. when the case has a DNA { T { ... } } entry in multiRegionProperties and T is listed in coupledFields of an interface in regionInterfaceProperties.
Inside each DNA coupling iteration, multiRegionSystem::assembleAndSolveEqns<fvMatrix, scalar>("T") calls setCoupledEqns("T"). This assembles the equation above and stores it under the key T<regionName>MeshconductTemperatureTypeEqn. The equation is then relaxed (relaxationFactors in fvSolution) and solved. The region Picard corrector (maxCorr / relTol / tolerance per field in fvSolution) can re-assemble and re-solve it within one DNA iteration. setCoupledEqns ignores its fieldName argument and always assembles the T equation.
correct() only calls kappa.correctBoundaryConditions().
getMinDeltaT() returns GREAT, so this region never limits the global time step.

Sub-Models

None. The region does not read fvOptions, a thermophysical model or turbulence. All material properties come from transportProperties or from optional field files.

Required Fields

Field	Type	Read mode	Description	Unit
`T`	`volScalarField`	`MUST_READ`, `AUTO_WRITE`	Temperature	K
`kappa`	`volScalarField`	`READ_IF_PRESENT`, `AUTO_WRITE`	Thermal conductivity. If there is no file, a uniform field is created from `transportProperties` with `calculated` patches.	W/(m K)
`rho`	`volScalarField`	`READ_IF_PRESENT`, `NO_WRITE`	Density. If there is no file, it is uniform from `transportProperties`.	kg/m³
`cv`	`volScalarField`	`READ_IF_PRESENT`, `NO_WRITE`	Specific heat. If there is no file, it is uniform from `transportProperties`.	m²/(s² K)

T and kappa are created through lookupOrRead. If a sibling region type on the same mesh has already registered a field with that name, that field is reused. rho and cv are always constructed by this region.

Case Setup

Required dictionaries

constant/<region>/transportProperties – rho, cv, kappa (all required, dimensioned)
system/<region>/fvSolution – T solver, relaxationFactors
system/<region>/fvSchemes – ddt and laplacian(kappa,T) schemes
0/<region>/T – temperature with coupled BC on the interface patch

`multiRegionProperties` entry

regions
(
 ( fluid (pimpleFluid transportTemperature) )
 ( solid (conductTemperature) )
);

DNA
{
 T
 {
 maxCoupleIter 20;

 residualControl
 {
 maxJumpRes 1e-07;
 outputJumpResField no;
 maxFluxRes 1e-07;
 outputFluxResField no;
 }
 }
}

`transportProperties`

All three entries are looked up as dimensionedScalar and are required, even when a field file overrides them:

rho rho [1 -3 0 0 0 0 0] 1.0;
cv cv [0 2 -2 -1 0 0 0] 100.0;
kappa kappa [1 1 -3 -1 0 0 0] 100.0;

Key `fvSolution` settings

solvers
{
 T
 {
 solver PCG;
 preconditioner DIC;
 tolerance 1e-15;
 relTol 0;
 minIter 2;
 maxIter 250;
 }
}

relaxationFactors
{
 T 1.0;
}

Interface boundary condition on `T`

On the solid side of a partitioned heatTransferInterface (flux side; the fluid side then uses regionCoupledTemperatureJump):

top
{
 type regionCoupledHeatFlux;
 interfaceType (heatTransferInterface);
 secondOrder false;
 nonOrthCorr false;
 value $internalField;
}

The coupled patch fields look up the diffusivity field kappa by default (set the patch keyword diffusivity to use another name). This matches the field that conductTemperature registers.

Coupling

Interface type	Exchanged fields	Coupling mode
`heatTransferInterface`	`T` (temperature jump / heat flux via `regionCoupledTemperatureJump` / `regionCoupledHeatFlux`, using `kappa`)	partitioned (DNA)

heatTransferInterface only provides the jumpCoefficient (from heatTransferInterfaceCoeffs). The patch fields do the actual transfer. Monolithic coupling is commented out in multiRegionSystem::solve(), so only partitioned coupling is available at the moment.

Known Limitations

Coupled use only. selfCoupledFieldNames() is not overridden, so T is never solved unless it is DNA-coupled. A standalone (single-region) conductTemperature case does not advance T. Use laplacianFluid for standalone conduction.
No source terms. fvOptions are not read or applied.
Static mesh only. meshMotionCorrector() is a no-op and the equation contains no mesh-flux terms.
No time-step control. getMinDeltaT() returns GREAT; deltaT must be chosen by the user or limited by other regions.
Constant rho and cv in time. They are read once and never updated (NO_WRITE). Only kappa gets a boundary refresh in correct(), and its values are never recomputed (for example as a function of T).
No non-orthogonal corrector loop. The coupled solve path has no correctNonOrthogonal() loop, so nNonOrthogonalCorrectors in fvSolution is not used by this region.
No output/post-processing. postSolve() is a no-op. No derived fields (e.g. heat flux) are written.

Tutorials

Tutorial path	Description
`tutorials/conjugateHeatTransfer/flowOverHeatedPlate`	Flow over a heated plate (`pimpleFluid transportTemperature` + `conductTemperature`)
`tutorials/conjugateHeatTransfer/ShellAndTubeHeatExchanger`	Shell-and-tube heat exchanger, two fluid regions + `conductTemperature` solid
`tutorials/fluidStructureInteraction/heatedBeamInCrossFlow`	Heated beam in cross-flow, thermo-FSI (`solidStVK conductTemperature` solid)

References

Alkfri, A., Habes, C., Marschall, H., multiRegionFoam: A Unified Multiphysics Framework for Multi-Region Coupled Continuum-Physical Problems, Engineering with Computers, 2023. DOI: 10.1007/s00366-024-01974-4

multiPhysicsFoam – Solid