- The Darcy pressure and heat conduction equations have been developed independently up to this point.
- In this step, we couple them together.
$$$$-\nabla \cdot \frac{\mathbf{K}}{\mu} \nabla p = 0
\\
C\left( \frac{\partial T}{\partial t} + \epsilon \vec{u}\cdot\nabla T \right) - \nabla \cdot k \nabla T = 0$$$$
- Objects have been created for everything except the $$$\vec{u}\cdot\nabla T$$$ term.
- A
`Kernel`

, `DarcyConvection`

, will be developed for this term.
- We will also develop a more sophisticated
`Material`

that takes the heterogenous nature of our column into account.

Multiphysics Coupling

## Coupling Code

step06_coupled_darcy_heat_conduction/include/kernels/DarcyConvection.h

step06_coupled_darcy_heat_conduction/src/kernels/DarcyConvection.C

step06_coupled_darcy_heat_conduction/include/materials/PackedColumn.h

step06_coupled_darcy_heat_conduction/src/materials/PackedColumn.C

# Transient Function Inlet (6b)

- MOOSE supports the use of function strings, e.g.
`cos(x)`

, in the input file via `ParsedFunction`

objects.
- It is also possible to create C++
`Function`

objects that may be used by other objects

Functions

step06_coupled_darcy_heat_conduction/problems/step6b_transient_inflow.i

# Create a Test

- A simple test of
`DarcyConvection`

is created by:
- Creating an artificial pressure field using an AuxVariable
- Reducing the number of timesteps from the problem above

tutorials/darcy_thermo_mech/step06_coupled_darcy_heat_conduction/tests/kernels/darcy_convection/tests

tutorials/darcy_thermo_mech/step06_coupled_darcy_heat_conduction/tests/kernels/darcy_convection/darcy_convection.i