Thermal transfer between two barrels

[z-man]

Hi there and thanks in advance for any help,

I have two barrels, one barrel is 1m tall the other is 100m tall. The taller barrel has a diameter one quarter of the shorter one. Both barrels are filled with water. The two barrels are connected by a solid copper heat transfer unit.The bases of both barrels are at ground level. Both barrels are fully insulated and sealed from outside pressure.

The water in shorter barrel has a temperature of 80 degrees celsius, The water at the base of the taller barrel has a temperature of 30 degrees celsius.

My question comes in two parts.

1) Does heat get tranfered from the smaller barrel to the base of the taller barrel where the water pressure is much greater.

2) The heat will rise in the taller barrel. At the very top of the larger barrel where the pressure is smallest, will the temperature be higher than that of the shorter barrel.

 

[Mentz114]

The two barrels are connected by a solid copper heat transfer unit

How are they connected ? There's not enough information here.

 

[z-man]

Apologies,

The two barrels are next to each other, the equivalent of a thick copper peg goes through the sides of each barrel connecting them. This would allow heat to be transferred to the larger barrel but not any fluid transfer.

On rereading my question I should also add that the shorter barrel will be kept at its original temperature throughout.


The whole question came to me because, if I can heat the smaller barrel via a solar heat collection system, then I would be able to get about 80 degrees Centigrade. If the larger pipe is very tall and thin then eventually the heat would rise to the top. Because it is a sealed energy system, the most energetic water molecules would go the the very top. This add a few extra degrees of heat, concentrating the heat. If this is so then it may be useful to run a low temperature difference stirling engine.

I am not hoping to get more energy but a greater temperature in a smaller concentrated area.

Many thanks for your help

 

[russ_watters]

1. Yes. Pressure is irrelevant - heat travels from areas of high temperature to low temperature.
2. No. Heat doesn't get "concentrated". If your heat transfer is good, you'll have some amount of 80 degree water in the tall tank. It will flow upwards along the side of the tank, mixing somewhat with the cooler water around it.

 

[z-man]

Thanks for the reply, I agree with both of your answers.

If I may modify my question now.

If I remove the small barrel and add a heating element at the bottom of the large sealed barrel. I then heat the water at the bottom of this barrel to 80 degrees celsius. This would take a lot of energy because the heat would rise until the whole barrel is in a state of equilibrium. I would in effect have a very tall electric kettle or storage heater.

If I managed to heat the water at the bottom of the barrel to 80 degrees celsius. Would be the temperature at the top of the barrel be higher and is there an elegant formula for me to calculate it.

Thanks again for this additional question

 

[russ_watters]

If the temperature of the water flowing past the heating element never rises above 80C, then the temperature at the top never rises above 80C.