I'm trying to use a single 24VDC power supply but rig it to give a heating coil the equivalent of 24Volts but at +12/-12 in reference to ground for safety reasons. Is this as simple as a voltage divider with a high value resistor to ground? Would that work or just kind of short out the supply? Is the negative terminal of a power supply normally connected to ground or is it floating? Let me know if there's a cheap, simple way of accomplishing this aside from buying two 12V power supplies or one that outputs +/-12VDC. Thanks.
It depends on your power requirement. This question is a very classic one, a quick search on Google with the right keywords gave me this first result which explains why a simple voltage divider is not enough in most cases: the more you try to minimise the quiescent current of the divider, the less stiff the symmetry of the rails is (there is an offset in the virtual ground), as the offsets will increase with current draw.
Below are two solutions suggested by the author.
Even there the voltage divider should be replaced with a voltage reference (e.g. TLE2426) if the power draw is asymmetric (but it sounds like it won't).
You'll certainly recognise a push pull structure here, common in audio.
However this will NOT make the system safer, as there is still 24V across the heater. But 24V is still safe-ish in a dry environment.