Since my contribution to PALATE PRESS, I have developed a nice working relationship with my editor for the piece, Arthur Przebinda of winesooth.com. Over the weekend, he contacted me about an experiment he had performed looking at the temperature in wine shipping containers left in hot conditions. He wrote up the experiment for winebusiness.com, and you can find it here:

http://www.winebusiness.com/news/?go=getArticle&dataid=67958

A few more details about my back-of-the envelope analysis, for the scientifically inclined:

Assumptions (mostly made for simplicity):

- The liquid in the bottle is 750 mL (~0.75 kg) and has the same heat capacity as water, 4184 J/(kg*K) (Wine is 85-90% water)
- A wine bottle is a cylinder 27 cm long and 6 cm diameter
- The cylinder is encased in a 1 cm layer of styrofoam, thermal conductivity 0.033 W/(m*K)
- The liquid in the bottle is well-mixed (bouncing around in a truck, sure, why not?). This is important because it
*drastically*simplifies the problem. It assumes that the temperature throughout the container is the same. Good thing, too, because I HATE cylindical coordinates! - The initial temperature of the wine is cellar temperature, here approximated to 16C (60.8F)

Using the surface area, heat capacity, and thermal conductivities, plus the heat transfer coefficient of air, I was able to model this as a heat-transfer resistance problem. There are two resistances to heat transfer in series, convection from the air and conduction of the styrofoam. By combining the resistances you can treat them as one total resistance. This resistance relates to the heat flux into the container. The heat flux multiplied by the surface area and divided by the heat capacity of the fluid will give you the temperature change.

Since this system is not at steady state (that is, the temperature is changing with time), it can be modeled as a first-order differential equation:

This leads to an exponentially decaying increase in temperature (shown in the graph at winebusiness.com), the time constant of which (r) depends on the resistance (convective and conductive) and heat capacity and amount of fluid (750 g of wine vs. 1 gram of air).

Basically, air heats up a lot faster than liquids at a certain volume because (1) there is much less of it to heat up, and (2) energy transferred to gas is more efficiently displayed as a temperature increase than in liquids (particularly water, which has a hydrogen bond structure such that much of the energy input will go into breaking hydrogen bonds instead of making molecules move faster).

[…] I want to express my appreciation to Tom Mansell – wine blogger and PhD candidate in Chemical Engineering at Cornell University in Ithaca, NY – who did a lot of math to help us understand the possible temperature increase of wine inside an EPS shipper exposed to external temperatures in excess of 110°F. These estimates are also included in the article on WineBusiness.com. To be clear, these are projections. The numbers are the results of mathematical modeling. You can read Tom’s elaboration on how he did the math here. […]

Great explanation, Tom. Thank again for helping on this. It was vital to giving the final article more depth and substance.