I have no trouble accepting the Physics. I dont disagree with your professorial explanations. I have no problem understanding schematics. Dare I say it, Im not an idiot.[/QUOTE
I know you're not and that's why I can't figure out why you can't seem to grasp what I am trying to tell you.
Where we differ is that you like your model, and I dont.
The reason I like it is because it works. If you look at the data I put up you will see that even with it's warts (some points don't fall exactly on the curve) the model fits the data very well.
For one thing, an ideal capacitor has no resistance.
The model, which again I reiterate fits the data very well as you can see is of an ideal capacitor connected to ideal voltage source. The purpose of a model is to accurately represent the real world to the point that one can use it to accurately predict what will happen without having to construct the system and also to give us insight as to how a system behaves. I took measurements every even minute i.e. 0, 2, 4... minutes. Clearly this model tells me very closely what I could expect to measure at odd minute (1, 3, 5..) intervals and it can predict quite accurately what the temperature will be after 60 minutes - way after I stopped taking data. It's a good model. I can see an objection to it if it didn't fit the real world but I don't think you can object just because you don't like it.
You may not like the model (though again I don't know why) but you will find it in any textbook that touches this subject, application notes for semiconductor devices etc. It is a well established model that has been verified over the years by thousands of engineers who have been using it to solve lots of problems and design lots of systems. I didn't invent it.
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As my experiment clearly showed conduction is not the means by which heat is transferred within the wort. It is convection. You can mention the thermal impedance of water as often as you want but for me to take it into consideration you will have to come up with some experimental data to show that it is a factor. Measurements that show a temperature gradient between the core of a fermenter and its walls would support your thinking. My experiment, done with a much smaller volume do not support your thinking.
A fermentor in a water bath is in no way an ideal system
. It doesn't have to be. It only has to be well described by the model.
The model fits my experimental data very well, as noted above. There is no denying this. You can argue that my small containers don't accurately model a carboy and you might be right. Theoretically there should be a gradient because convective transfer has an associated thermal impedance too. It is too small to see in my kitchen experiment. Perhaps it would not be with a carboy and probably would not be with a 30 bbl unitank.
You can probably guess my objection to the ceramic experiment.
Yes, but this tells me that you are missing the point. I have no data on the thermal characteristics of ceramics. They can vary all over the place. Adolf Coors used to package semiconductors in ceramics and presumably that packaging had high thermal conductivity but the ceramic container I used had an impedance of about 2.5 times that of the stainless steel one. What you should take from this is, what I think should be obvious, that different materials will present different thermal impedances and that, therefore, for a given heat flow, there will be different temperature drops across them.
One thing baffles me though; You dont have beer glasses? How do you drink beer?
I don't! I spend the summer in Quebec where 1) the beers are pretty bad and 2) the ciders are really good. During the summer I drink cider. I think I've had one beer since I got up here. It was advertized as a wit which I love but this was a typical Quebec brew - harshly phenolic.
More to the point - I wanted something that would hold at least a quart or two of water and wanted to containers about the same size. These two things met those requirements. I don't have any metal beer glasses anyway. Were I at home I would have used metal and glass beakers of the same size.
You keep repeating the obvious, as if I dont get it. Maybe if you keep hitting me over the head with it, the light will come on.
That's my hope anyway.
You refined your model, based on my objections.
No, I've stuck with the ideal cap model all along. I said that modeling the conductivity, should you want to do so, would involve a very complex model with thousands of caps to the point that it would not be a feasible model.
You admitted you were ignoring the thermal resistance of the water when I called you on it.
I did say I was ignoring it and gave reasons why I thought that was reasonable to do so. Experiment verified that it is.
You backpedaled on the heterogeneous heat in the fermenter.
Again, you didn't read or comprehend what I posted. I said that my experiments proved that convection alone was sufficient to allow us to ignore the effects of conductivity. I did say 'It isn't actually the yeast though, it's convection'. The yeast do, of course, provide the heat distributed throughout the medium so that a homogenous model is clearly the correct one but that, apparently, isn't a necessary condition for the simple model (and remember the OP was looking for a simple model) to work.
Then you act like I dont understand high school physics.
These last three things are things you have misinterpreted. What am I to think?
Maybe its the perennial conflict between engineers and technicians.
The laws of physics are the same for engineers and technicians. The thing I always found fascinating about good techs (I mean the really good ones) was that they had models of their own. I had no idea what they were but they did what a model is supposed to do - allow you to predict the behaviour of a system.
Once you take something off of paper and actually build it, it will have some unexpected behaviors.
That's why a model has to be verified. As I indicated in my post of yesterday I felt a little silly verifying a model this basic but in doing so I found out some stuff I didn't expect to (i.e. that conductivity of water isn't important and that loss through water/air interface is not significant).
If you fall in love with the model, it will circle around and bite you in the butt.
A large part of my career was spent modeling communications systems so I'm pretty familiar with their (models) strengths and weaknesses. The biggest problem I have with them is the widespread tendency of the model maker to change the model until it give him the answer he wants. One example of this would be Michael Mann tweaking the principal components from his climate data until the medieval warming period disappeared. Another would be you attempts to change the basic RC circuit model to get the results you wanted.
1. If heat is transferred between 2 bodies there will be a temperature drop/rise across the separator given by the product of the heat flow with the thermal impedance of the separator. If heat is flowing, that rise will always be present unless the separator is a perfect conductor of heat.
2. If the bodies are connected by a separator that has twice the thermal impedance of that in another identical system the drop across the separator will be, for a given heat flow, twice what it is in the other system. If the drop across the separators in the two systems is the same the heat flow in the first will be half what it is in the second.
3. In such systems the time constant (relaxation time, time to come to steady state, time to equilibrium...) is proportional to the thermal masses of the systems and the thermal impedance connecting them. If one system has a separator with twice the thermal impedance of another it will take twice as long for temperature to settle out.
Those are the facts. They can be verified in thousands of ways. Accept them or not. I hope you do.