Time required to cool down a botte of wine

[Andrea Vironda]

TL;DR Summary

Theory behind the cooling down of a bottle of wine

Good morning sirs,
I have a standard bottle of wine made by glass, 0.75l.
I suppose it's 20deg and I'd like to know how much time I need to lower the temperature of 4deg, considering outside it's winter, no wind, simple convection.

I read some theory and I discovered some reference to Nusselt number (ratio between heat transfer ways) and Rayleigh number.

They are very general, and I don't know very well hot to apply to my case, I simply want to know how much time I need to keep the bottle in the balcony to warm it down.

I could use Ansys but I think since this is a simple model, we can get some model in a more practical way.

 

[Chestermiller]

Well, you're on the right track. Let's see your overall energy balance so far.

 

[berkeman]

I simply want to know how much time I need to keep the bottle in the balcony to warm it down.

You could keep a metal bucket of water on your balcony, and then the cool-down time would be in minutes instead of an hour or two...

 

[jrmichler]

You say you have a Master's degree in Mechanical Engineering. You don't say how long ago you graduated, but all undergraduate ME programs have a course in heat transfer. That course covers how to estimate a heat transfer coefficient, and how to use that calculate the rate at which the temperature drops. Hint: The Nusselt number is used to calculate the film heat transfer coefficient.

Or you could set several bottles on the balcony, then open and drink them at regular intervals. That will tell you directly how long it takes to get it to the best temperature for drinking. Depending on how fast the wine cools, you might need to invite some friends to help.

 

[berkeman]

Depending on how fast the wine cools, you might need to invite some friends to help.

Road Trip!!

 

[Andrea Vironda]

Well, you're on the right track. Let's see your overall energy balance so far.

I know $\Delta=Q-W$. Here the work done is 0. $Q$ is function of external temperature, wine temperature, the bottle shape and the thickness of glass. Of course the substances are also important (maybe I can consider wine as water, as Jesus did).
I can use conduction Heat Transfer formula to calculate the rate of heat transfer (Fourier law), but I know only simple cases and flat surfaces, here we're speaking about a cylinder. But I don't know how to add convection to this.

 

[Chestermiller]

I know $\Delta=Q-W$. Here the work done is 0. $Q$ is function of external temperature, wine temperature, the bottle shape and the thickness of glass. Of course the substances are also important (maybe I can consider wine as water, as Jesus did).
I can use conduction Heat Transfer formula to calculate the rate of heat transfer (Fourier law), but I know only simple cases and flat surfaces, here we're speaking about a cylinder. But I don't know how to add convection to this.

In this situation, the internal energy and temperature are varying with time. So you need a transient heat balance: $$mC\frac{dT}{dt}=-UA(T-T_{surr})$$where U is the overall heat transfer coefficient and A is the surface area of the bottle; m is the mass of wine and C is its heat capacity.

 

[Andrea Vironda]

How can I estimate U and C?
For U I think I have to use the resistance equivalent with thermal conductivity of the glass wall (W/(m·K)) and convection heat transfer coefficient (W/(m2·K))
For C can I assume 2.5 kj/kg/K ?

 

[Chestermiller]

How can I estimate U and C?
For U I think I have to use the resistance equivalent with thermal conductivity of the glass wall (W/(m·K)) and convection heat transfer coefficient (W/(m2·K))
For C can I assume 2.5 kj/kg/K ?

I would use 4.186 for water and also include MC for the bottle.

 

[russ_watters]

You say you have a Master's degree in Mechanical Engineering. You don't say how long ago you graduated, but all undergraduate ME programs have a course in heat transfer. That course covers how to estimate a heat transfer coefficient, and how to use that calculate the rate at which the temperature drops. Hint: The Nusselt number is used to calculate the film heat transfer coefficient.

Or you could set several bottles on the balcony, then open and drink them at regular intervals. That will tell you directly how long it takes to get it to the best temperature for drinking. Depending on how fast the wine cools, you might need to invite some friends to help.

The problem for convective heat transfer here is that it is highly sensitive to small changes/specifics in the inputs (geometry, wind). It's very hard to get an accurate model. Imo, experimentation isn't just more fun it's much more accurate.

 

[Andrea Vironda]

I would use 4.186 for water and also include MC for the bottle.

What is MC? and how to deal with U? around 1E-2 W/(m2·K) I think it's suitable. In this case I would have dT/dt=-0.004 °/s

 

[256bits]

What is MC? and how to deal with U? around 1E-2 W/(m2·K) I think it's suitable. In this case I would have dT/dt=-0.004 °/s

MC ??
The glass bottle, along with the wine, also decreases in temperature.
mass of the glass bottle, and,
heat capacity of the glass bottle

If the glass bottle is thick, it would be significant.
If thin, then, possibly, the heat lost from the wine >> heat loss from the glass bottle, and you can neglect.

 

[Chestermiller]

What is MC? and how to deal with U? around 1E-2 W/(m2·K) I think it's suitable. In this case I would have dT/dt=-0.004 °/s

Transport Phenomena by Bird et al tabulates typical values of U for various situations with natural and forced convection.

 

[Andrea Vironda]

Transport Phenomena by Bird et al

I have the second edition (2002). I can see in §10.9 FREE CONVECTION the theory, but I can't find the tables. Also appendix E is mute

 

[Chestermiller]

Table 14.1-1

 

[Andrea Vironda]

Ok got, i created a model here, but I notice the starting rate would be -1.1 °C/s, too many in my opinion.
I think C or U must be revised.

 

[Chestermiller]

Ok got, i created a model here, but I notice the starting rate would be -1.1 °C/s, too many in my opinion.
I think C or U must be revised.

What numbers did you use?

 

[Andrea Vironda]

You can Open the link and have a look

 

[berkeman]

Also appendix E is mute

Mute (doesn't say anything at all)?

or Moot (doesn't say anything that applies here)?

 

[Chestermiller]

You can Open the link and have a look

what link?

 

[Andrea Vironda]

In post #16 there's a word, "here", that is in blue. Clic on it, it's stored on OneDrive. I put comments on all the variables i used

 

[Chestermiller]

In post #16 there's a word, "here", that is in blue. Clic on it, it's stored on OneDrive. I put comments on all the variables i used

1 W = 0.001 kJ/s

 

[berkeman]

it's stored on OneDrive.

That is not a reliable way to share information on PF. If the file goes away at some point, the thread becomes meaningless. Please upload a PDF copy of the file using the "Attach files" link below the Edit window. Thank you.