# Problem Overview
Consider a system containing two pressure vessels at differing temperatures. The vessels are connected via a pipe that contains a filter consisting of close-packed steel spheres. Predict the velocity and temperature of the fluid inside the filter.

[](image:206 width:475px)
[image:206 align:right]
    Schematic of Darcy Flow Problem


This problem mimics an experimental setup of Pamuk and Ozdemir (2012).

Pamuk and Ozdemir, ["Friction factor, permeability, and inertial coefficient of oscillating flow through porous media of packed balls"](http://www.sciencedirect.com/science/article/pii/S0894177711002640), Experimental Thermal and Fluid Science, v. 38, pp. 134-139, 2012.

# Governing Equations
A complete discussion of the governing equations is provided here: [Governing Equations](Problem)

# Tutorial Steps
[Step 1: Geometry and Diffusion](Step01)

[Step 2: Pressure Kernel](Step02)

[Step 3: Using Materials](Step03)

[Step 4: Velocity Aux](Step04)

[Step 5: Heat Conduction](Step05)

[Step 6: Darcy and HeatConduction Coupling](Step06)

[Step 7: Mesh Adaptivity](Step07)

[Step 8: Postprocessors](Step08)

[Step 9: Mechanics](Step09)

[Step 10: MultiApps](Step10)