# Heat exchange limits question

• pkv

#### pkv

I am (slowly) learning thermodynamics. I find a lot of it puzzling and makes me formulate many conjetures; I hope any of you can help me with this one about heat exchange.

There is a closed hose loop filled with water; its temperature gradient goes from cold to hot from one extreme to the other.
The system is perfectly isolated from the surroundings, but the hose makes contact with itself creating a heat exchanger.
Water runs in the hose without friction, let's assume there is no pump / no pumping losses.
The length of the hose is large enough for complete heat exchange. Cold water reaches the hot end at the same hot temperature, and viceversa.

Questions:
Would this system remain at the same temperature at all its points indefinitely? Or do thermodynamics require this system to evolve to an average temperature some way?

There must be something, probably the change in density of the water plus gravity to make the water move. Think of Newton's second law, f=ma. The water will not accelerate without a force.

Temperature can create a force by making the fluid expand.

You need to include more things in your question to make it answerable.

Hi,
I specified "no friction" and set up the arrows, trying to convey the idea that the liquid is in movement due to inertia and there is no reason for it to stop.

My understanding of this system is that temperature in this idealized counterflow heat exchanger is completely exchanged, and therefore the cold extreme should remain cold, and the hot extreme remains hot "forever".
But I am pretty sure I am wrong and I am missing something important.

Hi,
I specified "no friction" and set up the arrows, trying to convey the idea that the liquid is in movement due to inertia and there is no reason for it to stop.

My understanding of this system is that temperature in this idealized counterflow heat exchanger is completely exchanged, and therefore the cold extreme should remain cold, and the hot extreme remains hot "forever".
But I am pretty sure I am wrong and I am missing something important.
The temperature throughout the system would eventually equilibrate at the average temperature, unless you were maintaining the cold end in contact with a cold reservoir and the hot end in contact with a hot reservoir. Under the latter circumstances, the system would reach a steady state.

Why don't you assume a heat transfer coefficient between the two parts of the hose in contact and model the transient heat transfer?

Chet