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.

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", Experimental Thermal and Fluid Science, v. 38, pp. 134-139, 2012.

A complete discussion of the governing equations is provided here: Governing Equations

Step 1: Geometry and Diffusion