In order to better understand our system two theoretical models were created.  Each model had a unique temperature profile which was intended to further the understanding of our system and how it might react given certain conditions.

Our first profile, which is represented in Worksheet 1, had an idealized temperature distribution.  The temperature gradient was constant from the top of the column (which was held constant at 1.8K) to the base of the column (which was held constant at 296K).  Then the necessary area formula was applied to the column to get a theoretical thickness distribution for our assumed profile.  In hindsight this profile is not very representative of our whole system, but could easily be applied to either the lower section of the column (below the intake manifold) as a fundamental model.

Our second profile, which is presented in Worksheet 2, had an idealized temperature distribution, but also had a temperature constraint at 4.5K located somewhere between the top and base of the column.  This created two distinct temperature zones, each with its own governing temperature gradient.  The area function was applied to the overall temperature profile and a thickness for the column was obtained.  This profile was very similar to our actual system because of its two distinguished temperature zones which are separated by the intake manifold.