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Heat Recovery from waste water

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Imagine a tube inside a tube, the inner tube holds fresh cold tap water, the outer tube holds waste water from a shower, (as illustrated) the cold water is flowing to the left while the waste water is flowing to the right.

Assuming we shower for a very long time it becomes a matter of how long our tube is. Eventually the warm waste water will be just as cold as the tap water contained by it. Eventually the cold tap water will be just as hot as the waste water encaging it. This is not super hot, we need to add "conventional" hot water to make a comfortable mix. This however does mean the amount of incoming cold water is much smaller as the amount of warm water leaving though the drain. It will thus be more likely the cold water isn't cold enough to cool the drainage rather then the drainage not being hot enough to supply sufficient warm water to our exchanger. Different methods of dropping the water could be applied in order to preserve it's heat. Why use small drops if big splashes may consume far less heat? If you think about the limit of such heat exchanger it becomes a rather weird device. Say our shower is small and it is well isolated. There isn't any way for the heat to escape other then though the heat exchanger.

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