Experiment: How long does it take to go from 32 to 132!

[weedeater]

Since I started with Sous Vide a couple of years ago I have always wondered how long it actually takes to raise the internal temp of your meat to the set temperature on your Sous Vide apparatus. I decided to try a little experiment while I was cooking an “Eye of Round”.

For this experiment I started with an Eye of Round straight out of the freezer. It was place in a cooler and covered with cold water to aid in defrosting. Five hours later it was untraced but still ice cold. I cut the eye of Round in half and seasoned with my normal SPOG and sealed. I left the bag of the half for the experiment extra long. The reason for this was to allow the cutting of a slit in the top of the bag for a therm probe and still keep the top of the bag above water level in order to keep the therm dry.

The two half’s of Eye of Round then went into my cooler mod already at a steady 132 degrees. The half with the therm already inside was positioned so the the bag top where the therm entered would remain above the water line while the meat remained submerged. The temperature of the internal center of the 4” diameter Eye of Round was 32 degrees at the start. For purposes of this experiment I decided to record temps every 30 minutes until the meat center temp hit my target of 132 degrees.

It took a total of 4 hours for the meat to reach the target temp of 132 degrees. The chart below shows the actual data recorded.

Notice how quickly the meat rose in temperature initially and the closer you get to the target the slower it moves. I expected this but was a little surprised how quickly it moved initially. 32 degrees to 105 degrees in one hour. At the end a full hour to raise the last two degrees.


Here’s a pic of the experiment as it came out of the bath 21 hours later. The temp never moved off the 132 degree mark once achieved.

Here’s a final pic as I started to work on supper!

Weedeater

 

[bregent]

Nice. Baldwin's chart shows a cylinder going from frozen (32) to within 1F degree of bath temp would take 4 hours if the diameter was 60mm. Getting to within 2F takes 13% less time.

 

[Jonok]

Fascinating.

I wonder about 3 things:

1) Did you initially verify the water bath temp with your meat thermometer to assure that it correlated with the SV device sensor?

2) How much, if any, liquid was in the bag with the test meat and, since it was presumably in a suspended “open top” vacuum bag, did you do anything different to sink it relative to the other piece?

3) Since 48 qt (I’m assuming that you are using the same mod you wrote up a couple years ago) is a larger volume than most immersion SV devices are designed for, did you concomitantly record both the actual and SV machine measured temps at the same time points as the meat temp? This would test the theory that inadequate circulation is limiting convection heat transfer leading to an insulating “boundary layer” where heat transfer is primarily limited to conduction. (Suggesting that bigger isn’t necessarily better in terms of water bath size)

Neat idea overall, thanks!

 

[weedeater]

Thanks Jim for the observations. Now to your questions.

1. I did also monitor the temp of the SV bath with a second therm. It read dead on 132 degrees for the entire time except for about the first two minutes when the cold meat was introduced into the water. The temp of the water dropped to 131 degrees for a couple of minutes before recovering.

2. No additional liquid in the bag initially. Obviously as the meat cooks there is liquid produced which remains in the bag. No additional measures were needed to sink the test bag. It was initially vacuum sealed and the a small slit cut to introduce the sterilized temp probe. Since all air was itially removed none really re-entered the bag. Floating was not an issue.

3. As stated in response to question #1 I did monitor the temp of the bath water itself. It never varied on my therm be even a degree after the initial one degree drop. I probably should have used one of my other therms which reports 1/10th of a degree changes. Obviously there was some fluctuation at some level that was not picked up by the therm with 1 degree increments.

Bottom line the size of the insulated cooler is not too great a volume for the Anova 800 watt unit to keep up. It may be having to work really hard to keep up but I really don’t think that is an issue. One think I have noticed is that when cut off the water temp will rise about 3 degrees once the circulatory pump is shut off and then very slowly start to cool. The temp of the water if the cooler is closed will remain above 120 degrees for hours.

Weedeater

 

[Jonok]

Thanks for the reply.
The thermodynamics of this system are really fun to play with.
I had always assumed that there was enough flow (with my Joule placed in a similar-sized, prefilled and preheated cooler) to essentially provide an “infinite” production of heat, and sufficient flow that all one really had to do was assume a constant thermal conductivity, and then model the heat equilibration based on the difference in temperature.
It looks, though, from your numbers, like this isn’t actually the case.
I am inspired to dig out my old DiffEq book and to repeat your experiment to see how close it comes.

 

[dr k]

Taking a 1.5" steak out of a 37* fridge and resting it on a plate at 67* room temp will get the center to only 50* in two hours for just a 13* rise in the center since the fridge and room temps are only 30* apart. Kinda like the longer duration your meat took when getting closer to the 132* water temp.

 

[sigmo]

I love this sort of experimentation and the discussion.

Here's weedeater 's data graphed:

This should be a typical natural log function, just like a capacitor charging or discharging through a pure resistance. There's a bit of a discontinuity, but it's pretty close to what I'd expect. I'd like to have more points plotted in the lower end of the curve for more verification, but this does show the basic log curve pretty well.

Here's a site that talks about capacitor charge/discharge if you're not familiar with this.

https://www.electronics-tutorials.ws/rc/rc_1.html

It's really fairly simple, and it applies to a LOT of natural phenomenon we encounter. Examples that come to mind are water levels equalizing from one tank to another through a pipe, temperatures coming to equilibrium, etc.

But things can get complicated in a hurry.

For example: When the meat is frozen, I have wondered if the thermal resistance of the ever-thickening outer layer of thawed meat would be different from that of the still-frozen meat inside. I often sous vide steaks from frozen, and with great success. I just use the rule of thumb of giving the steaks an extra hour if they start frozen for steaks up to 1.5" thick.

But having the thermal resistance vary as the meat thaws definitely throws in an interesting twist!

And then there's the issue of the heat required to melt the ice. Latent heat of fusion. But it's not pure ice. And having been in my freezer, it starts off well below freezing, too!

https://www.engineeringtoolbox.com/latent-heat-melting-solids-d_96.html

Makes my head hurt!

As mentioned by bregent , this guy has done a lot of the math:

http://douglasbaldwin.com/sous-vide.html

Here's another experiment testing Baldwin's calculations:

http://www.sousvidecooking.org/douglas-baldwin-fish-sous-vide-cooking-table-correct-review/

Neat! You can see the natural log curve (just like a capacitor charge curve) that that experiment showed.

Another note you guys touched on was the issue of boundary layer effects, particularly with a non-stirred bath. My observation from 30+ years of designing data acquisition systems and temperature controls for laboratory use is that a well-stirred water bath is amazingly uniform. But a non-stirred bath can show surprising variations from place to place due to stratification, thermal loads presented by objects in the bath, stagnant zones, etc.

I really prefer an immersion circulator for sous vide versus a non-stirred system. The stirring keeps the temperature uniform and it "scours" the surfaces of the bags-o-food, keeping them in direct contact with water at the exact temperature you're trying to use. But there are a lot of non-stirred sous vide gadgets, and people seem to have good luck with them.