The Wine Cellar Problem Ryley Hill and Dylan
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-differentialequations-fall-2006/lecture-notes/heateqni. pdf http: //www. damtp. cam. ac. uk/user/dbs 26/1 BMethods/Heat. pdf https: //www. wiley. com/college/borrelli/pdf/bcprob 10. pdf USclimatedata. com
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