1. The Wine Cellar Problem
Ryley Hill and Dylan Snover

2. The Problem
Wine is best stored in an environment where temperature fluctuations are at a minimum. These temperature fluctuations occur at the surface both diurnally and seasonally. In order to determine the ideal depth at which to build our wine cellar, we must derive a solution to the following PDE.

3. The Problem

4. The Problem

5. Derivation of Heat Eq

6. Derivation Cont.

7. Derivation Cont.

8. Derivation Cont.

9. Derivation Cont.

10. Derivation Cont.

11. Equation Derived!

12. Physical meaning:

13. Physical Meaning Cont.

14. Note:

15. Optimal Depth

16. Optimal Depth:

17. Plotting the Analytical Solution..

18. Case Study (Napa, California) (Annual Cycle)

19. Daily Temperature Profile Napa, CA
Optimal Depth = 0.55 [m]
*Fine if you only want to keep your
wine for a single day...

20. Daily Temperature Profile (Annual Cycle Limits)
There is a big problem if we only
Assume a daily cycle!
We shall assume an annual cycle.
Fine wines need aging of course.

21. Annual Temperature Profile Napa, CA
Optimal Depth = 9.95 [m]

22. Work Cited
Solving Direct and Inverse Heat Conduction Problems, Taler J. Duda P.
USclimatedata.com