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The Wine Cellar Problem Ryley Hill and Dylan Snover The Wine Cellar Problem Ryley Hill and Dylan Snover

The Wine Cellar Problem Ryley Hill and Dylan Snover - PowerPoint Presentation

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Uploaded On 2018-11-13

The Wine Cellar Problem Ryley Hill and Dylan Snover - PPT Presentation

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

cont derivation temperature problem derivation cont problem temperature depth pdf cycle annual optimal profile daily wine heat napa meaning

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Presentation Transcript

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.

Slide3

The ProblemSlide4

The Problem

 Slide5

Derivation of Heat Eq

 Slide6

Derivation Cont.

 Slide7

Derivation Cont.

 Slide8

Derivation Cont.

 Slide9

Derivation Cont.

 Slide10

Derivation Cont.

 Slide11

Equation Derived!

 Slide12

Physical meaning:

 Slide13

Physical Meaning Cont.

Slide14

Note:

 Slide15

Optimal Depth

 Slide16

Optimal Depth:

 Slide17

Plotting the Analytical Solution..

 Slide18

Case Study (Napa, California) (Annual Cycle)

 

 Slide19

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