The Wine Cellar Problem

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Presentation transcript:

The Wine Cellar Problem Ryley Hill and Dylan Snover

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.

The Problem

The Problem

Derivation of Heat Eq

Derivation Cont.

Derivation Cont.

Derivation Cont.

Derivation Cont.

Derivation Cont.

Equation Derived!

Physical meaning:

Physical Meaning Cont.

Note:

Optimal Depth

Optimal Depth:

Plotting the Analytical Solution..

Case Study (Napa, California) (Annual Cycle)

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

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.

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

Work Cited Solving Direct and Inverse Heat Conduction Problems, Taler J. Duda P. https://ocw.mit.edu/courses/mathematics/18-303-linear-partial-differential-equations-fall-2006/lecture-notes/heateqni.pdf http://www.damtp.cam.ac.uk/user/dbs26/1BMethods/Heat.pdf https://www.wiley.com/college/borrelli/pdf/bcprob10.pdf USclimatedata.com