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 follow ID: 728743
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Slide1
The Wine Cellar Problem
Ryley Hill and Dylan SnoverSlide2
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.
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The ProblemSlide4
The Problem
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Derivation of Heat Eq
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Derivation Cont.
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Derivation Cont.
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Derivation Cont.
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Derivation Cont.
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Derivation Cont.
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Equation Derived!
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Physical meaning:
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Physical Meaning Cont.
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Note:
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Optimal Depth
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Optimal Depth:
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Plotting the Analytical Solution..
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Case Study (Napa, California) (Annual Cycle)
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Daily Temperature Profile Napa, CA
Optimal Depth = 0.55 [m]
*Fine if you only want to keep your
w
ine for a single day...Slide20
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.Slide21
Annual Temperature Profile Napa, CA
Optimal Depth = 9.95 [m]Slide22
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