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I have designed a container which is heated up and has to heat up some tube-coils of water inside of it. This container is filled with a fluid that can help store and transfer the heat received from the container to the tube-coils.

My plan was to find some material that I can easily buy and which is not very expensive to fill the $636cm^3$ container.

It has to have a high coefficient of heat transfer, high heat capacity and an operating temperature of at least the range of 10-400 degrees Celsius. I will also need to calculate how much the volume changes when it goes from around -35 to 500 degrees Celsius.

I also think a high density and if the material is non-toxic might be a plus.

Does anybody know any fluid that could be used for this or somewhere where I could find such information?

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400 C is beyond long term use of any organic heat transfer fluid. Dow Corning boasts 427 C for one of its silicone fluids. Don't bet on that. Inorganic eutectic salts will long term decompose into corrosive volatiles. Best bet for a red hot closed system is fusible alloys of indium, gallium, and bismuth - beware of metal boiling points. Open systems will air oxidize. Accommodate sealed inert gas fill (argon) with a metal bellows add-on, preferably on a pipe extension away from the hot zone. Fill composition must be compatible with container composition. Mercury is out for toxicity and boiling point, 357 C. Thermal coefficient of linear expansion, solid vs. liquid alloy, must be looked up. The increment is cubed for volume change.

500 C (red heat) will change the metallurgy of stainless steels over time. They will harden (carbide precipitation), among other things. Don't try to drill a hole or tap a thread in stainless that has been soaked at red heat.

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Have you tried Wax?

'Paraffin wax is a white or colorless soft solid derivable from petroleum, coal or oil shale, that consists of a mixture of hydrocarbon molecules containing between twenty and forty carbon atoms. It is solid at room temperature and begins to melt above approximately 37 °C (99 °F);[1] its boiling point is >370 °C (698 °F).[2] Common applications for paraffin wax include lubrication, electrical insulation, and candles. [3] It is distinct from kerosene, another petroleum product that is sometimes called paraffin.

Paraffin candles are odorless, and bluish-white in color. Paraffin wax was first created in the 1850s, and marked a major advancement in candlemaking technology, as it burned more cleanly and reliably than tallow candles, and was cheaper to produce. [4]

In chemistry, paraffin is used synonymously with alkane, indicating hydrocarbons with the general formula CnH2n+2. The name is derived from Latin parum ("barely") + affinis, meaning "lacking affinity" or "lacking reactivity", referring to paraffin's unreactive nature.[5]"

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    $\begingroup$ Welcome to Chemistry.SE! Could you please site the source you took this from? $\endgroup$ – ringo May 9 '16 at 1:51

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