I have a steel vessel placed concentrically within a larger steel vessel, resulting in air-filled annulus (air gap) between the two vessel walls (figure below). Due to the existing vessel construction, the only way to heat the inner vessel is to externally heat the larger outer vessel. The air gap makes this extremely inefficient. I would like to fill the annulus with a liquid to help with the heat transfer. I am needing to heat the inner vessel to 400 degrees Fahrenheit. Since the liquid will be open to atmospheric pressure, a liquid that wont boil at 400degF and 1atm pressure is needed. A non-toxic fluid is needed (we don't want to be breathing any harmful fumes). Is it possible to dissolve a particular kind of salt into water to achieve this goal? Is there any other type of liquid to consider?
You can use a heat transfer oil like Mobiltherm 610. They also have some other oils that you can use, if you are able to shield the surface of the oil from the air. If you use a lower grade oil, it can still work, but the oil may slowly decompose.
Dont just buy some generic mineral oil, without checking if it will decompose or catch fire under the conditions you are expecting.
Heat transfer oils can be poured at room temperature, unlike some molten salt baths.
Phillips66Lubricants makes some heat transfer oils, but afaik none that can handle your temperatures in an open system.
Chevron has this line in the data sheet for HTOs: The oil surface in contact with air in open systems should not exceed 107°C (225°F)
A good starting suggestion is probably a mineral oil. These are often used in small scale labs for heating baths that need to reach temperatures much higher than boiling water. So they should be easily available and their properties are well known.
A possible alternative would be a molten salt mixture. Some of these are available even for low temperature situations but many are fine at higher temperatures (see this, for some examples, though it isn't a review for this sort of application, just an indication that such salts are available). Many molten salts are non-volatile and non-flammable but whether they are better than mineral oil will need some investigation.
Another alternative (though possibly more appropriate for lab-scale not large scale) is to use Armor metal beads. These are small metal beads that can be used as an alternative to liquids in heating baths in laboratories (either to avoid liquid contamination or to reach higher temperatures). They are quite expensive, but (obviously) are not flammable, can reach higher temperatures than many liquids and can be reused indefinitely.
This seems a very bad idea to me. Please tell us how you intend to heat the outer tank and some idea of actual dimensions; then consult a professional chemical engineer with experience in heating. There are industrial grade heating pads or sheets that reach 250C that can fit in very small spaces. Investigate also the possibility of inductive or infrared heating. This will involve some expense but if you can't use good, appropriate, equipment you should reconsider doing this.
One suggestion would be to fill the space with aluminized Mylar helium balloons; that will give more heat conductivity than air and they should not melt [mp~240C].