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What would be most effective way to transfer heat in the following situation?

Specific conditions: A vertical cylinder or pipe, 30-100cm long, 5-10 cm in diameter, heavily thermally insulated except at the bottom, placed in a solid medium (except at the top, which is in air) whose vertical temperature profile varies on an hourly basis and will change polarity (delta T=T_top - T_bot will change sign), and has a temperature difference of around 2-10ºC.

The bottom of the cylinder is attached to a heat "sink" embedded in the solid surrounding medium. The top has a thin insulation layer between it and the air.

The goal is to tie the top temperature as close to the bottom temperature as possible

On the right, not entirely to scale, the lagged vertical pipe is shown embedded in a solid medium whose temperature profile (on the left) varies during the day. Basal temperature is maintained at ambient (for that depth) with a heat sink embedded in the solid medium. The goal is to keep the top temperature as close to that of the base as possible by fluxing heat up and down through the pipe, and always compromised by the poorly insulating top lid.

My first thought was to use a solid metal cylinder (likely aluminum not copper for cost reasons) since conductive heat transport is agnostic to the top/bottom temperature polarity.

It's tempting to use free convection in a pipe using water etc, which is presumably far more effective at driving heat transport. However, if the top is warmer than the bottom, full-cylinder convection won't happen. Forced convection or pumping is out of the question.

What would be the best strategy here? Would a mix of metal conducting rods in a cylinder otherwise full of liquid be even better?

Update: diagram upload as requested.

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    $\begingroup$ What "polarity"? $\endgroup$ – Solar Mike Aug 3 '17 at 9:12
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    $\begingroup$ As the saying goes, ... "a picture paints a thousand words". A diagram would certainly make it easier to understand the situation. $\endgroup$ – Fred Aug 3 '17 at 11:56
  • $\begingroup$ Picture: will do! $\endgroup$ – Colin Stark Aug 3 '17 at 12:01
  • $\begingroup$ Polarity: hot vs cold, i.e. the temperature gradient imposed by the top & bottom boundary conditions will reverse periodically. $\endgroup$ – Colin Stark Aug 3 '17 at 12:02
  • $\begingroup$ If you stuffed a tube with rods and added water you would inhibit the water convective flow and so I suspect not gain much of anything over just using as much conductive metal as you can afford. $\endgroup$ – agentp Aug 3 '17 at 21:39
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Some solar water heating systems use a tube with a fluid that evaporates / condenses which moves the heat from end to end as you describe.

They are designed to work preferentially in one direction as one end has a bulb or larger diameter to better transfer the heat.

Will post an image when on the laptop, but, for the moment here is a link : http://www.apricus.com/html/solar_collector_heat_pipe.htm#.WYP5GYXRaaM

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  • $\begingroup$ Thanks! Question though: would such a solution not require rather substantial "hot top" temperatures for the evapo-condensation to work? And would it work "upside-down", in the sense that the moisture-rich air would have to sink to the bottom to condense? $\endgroup$ – Colin Stark Aug 4 '17 at 8:53
  • $\begingroup$ The fluid chosen would need to be matched to the temperatures : latent heat of vapourizatio / condensation... $\endgroup$ – Solar Mike Aug 4 '17 at 8:54

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