Hot and Cold Water Temperature Stratification in Adiabatic Tank

• If the cold enters at the bottom, the hot leaves at the top and there is little mixing going on in the tank, as is the case with cylindrical domestic hot water storage tanks used routinely in the UK, then stratification will prevail.
• If the tank is open-topped, then the hot will leave at the top, principally as vapour.
• If there is no heat source in the tank, then its temperature will gradually fall.

Thanks for your answer, but I am talking about adiabetic cylinderical tank (no heat transfer to surrounding) and no discharge or charge. And I am curious about if there is heat transfer between water which has different temperature and interface zone (temperature mixing zone) becomes developed.

It doesn't matter what the tank is called.

• If there is little or no mixing between the hot and the cold that are already there , then stratification will prevail.
• If there is mixing and no heating, then eventually the contents will end up at one temperature. That which is causing the mixing has to be stronger than that which is causing stratification for this to happen.

<unsubscribes>

Thanks. To better understand, I hope I write an example.

Suppose that there is 10 m height adiabetic tank and 4.5 m in upper tank is filled with 100 °c water and 4.5 m in lower tank is filled with 50 °c water and 1 m is initial temperature mixing (interface zone) zone from 51 to 99 °c.

100 °c and 50 °c zone will become smaller as time goes by since temperature mixing zone is developed? Or 100 °c and 50 °c zone will be the same? Why? Is it because there is heat transfer within water which has different temperature?

And do you mean 100 °c and 50 °c zone will be the same if initial temperature mixing zone is small?

Please see stratification layers in the lake. Since 4 °c water is heavier, its water will be located in the bottom. If it is in an adiabetic condition, water temperaute of all zone will be the same in the end?

Since member PWSlack has left the building, I will just say that, so far you have described three distinctly different systems.

One cylindrical, one spherical and a lake.

Unless one rules out radiation, convection and conduction within the system, equilibrium throughout the strata will be achieved.

'...I have the feeling that the right word is adiabatic....'

.

Only if referring to something perfectly insulated.

.

It could possibly be adiabetic... if referring to something perfectly insulin-ated.

I thought that the "a" means "no" or "contrary" so that if we think about the seakness all who do not suffer are adiabetics!

Right. Which is why I said they would be perfectly (not imperfectly) insulin-ated. Insulin regulation would be just right for those with 'adiabetes'.

Since you have defined the 'problem' in strictly theoretical terms, I have to go with lyn.

PWSlack gave the example which first occurred to me of the water heater tank. But, as you pointed out, that is not adiabatic nor perfectly insulated. Of course, neither is the lake you give as an example.

I think, over an infinite period of time, the temperature would equalize. Heat transfer doesn't depend on mixing to take place. Imagine that no convection currents are present - hot water on top, cold on bottom. Over a long period of time, heat will transfer (via conduction) from top to bottom until the temperature is constant throughout the volume.

So, was your original question meant to be theoretical only, or apply to a real-world problem?

Thanks for answer all. If there are two soilds which have a different temperature and if two soilds are met, then the temperature will be equalized over some period. I understand this. Soild and water have the same characteristics though water has different density according to its temperature?

Well, we can take it to extremes and say that solids also have a different density, depending on their temperature.

Take a look at the thermal expansion properties of solids. I've performed practical experiments on one half inch cubes of plastics to determine the volume difference at different temperatures. Metals have this quality also.

Where are we going with this?

Once again, given your conditions, we will reach temperature equilibrium.

Although I rarely disagree with PWSlack, I believe that the water will reach equilibrium throughout the tank, given the conditions you describe.

I have no references at hand.

Best to suck it and see (otherwise known as 'have a go')

I suspect that stratification would gradually diminish due to Brownian motion. How quickly is the question.

Also, getting the water in with diff temps, & no mixing will be tricky.

P.S. No catfish.

P.P.S. Let us know!

Heat also travels through water by conduction, although not anywhere as well as through convection. After some period of time, the temperature will equalize through the whole tank.

I think you are correct in your assumption, the water temperature will never equalize (be the same at the bottom as at the top, or at all locations), at least on planet earth. This is even true of solids. The laws of thermodynamics apply, and as any heat loss or gain occurs (adiabatic systems are theoretical) heat moves locally across the material, producing differential temperature zones, and those zones correlate with density and pressure. I can envision a point in space that has no temperature fluctuation, and can see the spinning vessel placed at that point as having no stratification and achieving a temperature constant. (being in an adiabatic state). On earth, I don't think you could achieve that state, even on a temporary basis. Armchair physics is no place for most of us, so I stand ready to take a beat down.

Due to the nature of heat & fluids, the water will stratify, but at a temperature range fairly close to the average value. Expect a variation of 1-2C per metre (3ft). If you don't believe me, check the temperatures at the floor and ceiling of a closed room.

A factor to be considered is TIME.

The heat transfer by conduction depends on the temperature gradient i.e. the temperature change per length unit in the flux direction.

Let us assume that at t=0 there is a clear temperature step between the hot and cold fluids. The flux will be proportional (Fourier law) to the area, conductivity of fluid and the above mentioned gradient. In the first moment this gradient is very big fluid since the change is over a small distance. Due to the transfer the cold fluid will become hotter and the hot will cool. Those 2 fluids volumes have a thickness so that assuming a linear temperature variation versus distance the gradient will decrease and with it also the thermal flux. This continues more fluid will change temperature and the gradient will decrease even more. This means that heat transfer will be over time lower but as long as a gradient is present heat will flow from hot to cold. Time to reach same temperature is important but there is NO reason to have a gradient stable versus time. We have to understand that physic laws are not as we wish.

No time was specified. To me that means ∞.

You are right I did not want to go so far. Since the gradient decreases the heat flow decreases as well so that the time to reach a total temperature equilibrium is infinite.

What I wanted to stress is that as long as a gradient is present a heat conductive flow will occur = there is never a stable temperature gradient without external influences ( put in or take off energy). The system was supposed adiabatic which means without energy exchange with external sources.

I have seen the stratification occur in a tank where the water was mixed as it was heated. Once left still, the top became warmer than the bottom, and remained so even once it cooled to ambient temperature.

Have you tried the room temperature test? The air by the ceiling will be warmer than that at floor level. Heat Rises.

Where does the heat come from? By OP's definition there is no heat added, or lost, in this tank.

My reference was to experiments where the intention was to keep water at a specific temperature in a tank. It does not matter whether the tank is fully insulated or not (how does the OP suggest filling his tank with two different temperatures of water?).

Heat rises, therefore the top water will become at a higher temperature than the bottom layer. My take on this phenomenon is that the top fluid has more space to move than the lower particles, so the energy moves to where it can.

Then you are ignoring radiation and conduction as a means of heat transfer.

The water rises, here on earth, because it is less dense. Heat radiates, and is conducted, in all directions regardless of gravity.

No, I am not. They would play their part in mixing the hot top water with the cold bottom water.

But the result will not be the theoretical all-equal-eventually that some have predicted. The pressure on the bottom "layer" is greater than that at the top, so it will be more compact, have a little less room for movement, and thus be cooler.

These comments are based on recent experimentation, not any theoretical background.

Your reasoning is flawed, your logic is flawed, and your experiments are flawed.

And your reasoning is........?

You can't halt conduction, or radiation, until there is no place cooler than any other place.

Remember, the OP set the conditions. We should not alter them to suite our theories.

Dear Lyn,

do not insist.

Once more I notice that participants either do not understand the question or have a limited understanding of physics. You cannot convince somebody who has a belief, he will never accept another reason than his own.

I am sorry to be rude but but so many times discussions which could have been productive were killed by stubborn reactions , by trials to demonstrate the wrong idea by twisting physics.

Do not be sorry. I value your thoughts and know that everything you say is well reasoned, intelligent and thoughtful.

You and Lyn should get a room. It's awkward for the readers, like walking past a nude in the mall.

We, "suffer fools gladly".

Keep it coming.

Hubris is not an attribute. Suffer away.

I appreciate very much your selfcritic

I think 'self-critique' is probably the right term.....(just wish I had made the original comment, so that this comment could be ultra-apropos).

So if gravity will maintain a temperature gradient in a perfectly insulated container of fluid, can I use a thermocouple to extract some free energy?

No, because then you have broken the adibiatic seal by letting energy out the enclosed area. (Very little as electrical energy, as thermocouples work at the milivolt, milliamp level, but the cable itself will conduct heat to the surroundings)

Point taken. I'll replace the thermocouple with a more efficient heat engine and leave it inside.

I guess the point I was trying to make is that if gravity could maintain a temperature gradient, then that temperature gradient could be used as a source of energy in violation of the first law of thermodynamics.

If the tank is adiabatically sealed, heat will diffuse from the hot to the cold water until all the water is at the same temperature.

But then the energy would need to be used within the confines, and degrade back to heat......

Within the Earth's gravitational field, the gradient would exist, but it is small, perhaps one degree C per metre depth. I do not believe that your heat engine could do any useful work with that! And to keep the system adiabatic, could not communicate out of the enclosure, unless.....it is used to collect and store temperature data for later extraction/analysis.

How do you explain a temperature gradient? How can you ignore conduction and radiation?

Gravity will only come into play if the water is a different density and the hot water would rise, mixing with the cooler water, as it does.

Since we have infinite time, we will reach equilibrium.

Water column pressure?

Water is incompressible.

There is no density difference top to bottom, if we are on earth.

So, are you suggesting that pressure equals heat?

No, it is not! The difference may be slight , but it still exists.

Water is slightly compressible. The difference in density is the reason hot water rises and colder water sinks...unless you are talking about temperatures below ~4C.

.

You are still correct that conduction and convection (and actually a little effect from radiation) will lead to thermal equilibrium.

Careful.

Hot water rises because it is less dense than the water above it.

Now GM's telling me that water becomes more dense and compresses, thus making it hotter, but it doesn't then rise?

I can't reach that far.

I can't speak to the water becoming 'more dense and compressing, thus making it hotter....', because I'm not sure what that means exactly.

.

I can tell you that the density of water changes slightly but measurably with large changes in pressure and with just modest changes in temperature. The compressibility of water is an important factor in controlling reactivity in light water reactors and I thing in some liquid spring applications... though I might be mistaken, hydraulic fluid might exclusively be used.

.

The short answer is that nothing here on earth is really incompressible. The other short answer is that your original position remains correct, heat transfer will lead to thermal equilibrium.

We seem to be splitting atoms here and may have gotten off track, as we so often do.

I think I'll bow out now and rest my brain.

But then the energy would need to be used within the confines, and degrade back to heat.....

So in that case the inside of the tank gets warmer and warmer. Where does the energy come from? We have a water heater that requires no power.

No, the energy would be taken from the temperature differential, and used within the enclosed area to keep the net energy the same. We are only talking of displacing electrons to record temperature variations within the enclosed area. The data would only be recovered at the end of the experiment.

Water has a reasonably high thermal conductivity. It will therefore be impracticable to maintain a temperature gradient in this way, unless the vertical dimensions of the tank are large, there is no agitation, liquid transfer in/out, and the only source of heat is in the top layer of water. Perhaps one could maintain such a thermal gradient if: heat transfer of the container is prevented to a large extent, cooler water is trickled in at the bottom, 1 atm pressure steam (at precisely 100 C) is admitted at the top, and somewhere in the middle zone the median temperature is trickled out.

Thermal gradients can also exist where the bottom of the "vessel" is at the higher temperature, but these must rely on salt concentration gradient (or other solute of significant density) to prevent thermal convection.

The question was a theoretical one, it has NOTHING to do with practicality. In fact in practice the problem will never occur since when the hot water flows in it will immediately start to mix with the cold even if velocity is very low. And what you write sustains what I wrote : a gradient cannot be maintained without external influences this is contrary to the OP which specifies an ADIABATIC condition.

The last § is partly correct since solutions also do mix, which means that the upper less salty fluid will become more salty and the lower less so that a convection could occur (moving with) and this supposes a mass transfer since heat is con-vected by a mass movement.

The condition for a strata with hot down and cold up can be reached ONLY if 2 factors are satisfied: no possibility to mix and lower density higher. But this does NOT eliminate conduction so as you turn the problem temperature in an adiabatic system will be uniform after an infinite time.

Progression of heat depends on the heat diffusivity a=k/(ρ*Cp) [mm²/s].

k= conductivity [W/m°C] ρ= specific mass [kg/m^3] cp= specific heat [J/kg°C]

To give a feeling in comparison with other materials how water is positioned please look at following values:

Silver 165,3 / Gold 127 / Copper 117 / Al 98,8 / Steel 22,8 / N2 22 / Air 300°K 19 / SS304 4,2 / Water 25°C 0,143 /Oil engine 100°C 0,074.

We see that water is in the bottom range since k is small and cp important. Air considered a good insulation has in fact an "a" value a lot bigger than water .

Surprising no ? In fact what water has is a HIGH convection capability especially due to its very small viscosity.

Granted. What I had described was in no way adiabatic, but neither truly is any "real" system. Solar salt gradient ponds do exist, and work quite well thank you. In these, the evaporation of water results in higher density (by concentration) brine falling to the bottom, and in all instances that work, the bottom is a dark color to absorb insolation and raise the bottom temperature.

This same question was asked awhile back concerning gases.

http://cr4.globalspec.com/thread/82147