You can certainly use a 24 V PSU for the heatbed, controlled from a 12 V board (i.e. RAMPS) - assuming that the heatbed is either designed for 24 V or is of a type that accepts dual supply voltage (be sure to use the correct input).
You have three choices:
- Modify the RAMPS board, using the built in MOSFET
- Use an external relay
- Use an external MOSFET (as you suggest)
Modifying the RAMPS
Assuming that you are actually using a RAMPS board:
From RepRapWiki - RAMPS 24V:
Modifying for 24v heated bed
You have to replace the 11 amp polyfuse, MF-R1100, with something else. This device is only rated for 16v. It will burn out and catch fire on 24volts. Most simply replace the polyfuse with a thick wire. Then wire in a 24v fuse with a inline fuse holder on the heated bed cables. Wire up 24 volt supply to the top two 11amp power sockets and its completed.
You can also use an external MOSFET with a separate 24v supply without any changes.
Thus, you can use 24 V, for just the heatbed, on a standard RAMPS board directly. However to do so, you need to modify the board and replace the fuse, as the standard fuse is only rated for 16 V and the current rating would be too high for a 24 V supply.
Just swap out the 11 amp polyfuse, MF-R1100, and replace it with a more suitably rated fuse. Alternatively, just replace the MF-R1100 with a thick wire and use an additional inline fuse holder with a 12/24 V fuse, and reduce the current rating of the fuse by half, i.e. 5 A.
As a 24 V heatbed will actually use less current than a 12 V heatbed, this is perfectly safe. In addition, the heatbed circuit on the RAMPS is isolated from the rest of the RAMPS control circuit, so there is no need to worry about using the two different voltages on the same board.
SSR
However, instead of a MOSFET, you might be better off using a relay, such as a FOTEK SSR-100 DD (which is a solid state relay module). Using a relay will isolate the two circuits. Nevertheless, you need to be aware that some (a lot?) of these Fostek SSRs are relabelled - that is to say that a 5 A SSR has the label replaced with one that says 10 A of 15 A, and the unscrupulous reseller bumps up the price accordingly. So, maybe choose a different brand of relay.
MOSFET
Assuming that you do not have a RAMPS board:
Wire up an external PCB with an appropriate MOSFET. For instance, you could just use the same MOSFET as the RAMPS board uses, which is one of these three (from RepRapWiki - RAMPS 1.4 - BOM):
STP55NF06L (MOSFET N-CH 60V 55A 18mΩ TO-220 @11A=+135*C )
IRLB8743PBF (MOSFET N-CH 30V 78A 3.2mΩ TO-220 @11A=+24*C)
IRLB3034PBF (MOSFET N-CH 40V 195A 1.7mΩ TO-220 @11A=+13*C)
From Re: best ramps 1.4 headbed mosfet upgrade:
IRLB8743pbf and IRLB3034pbf are good choices. IRF3205 and P55NF06 are bad choices, because they don't have guaranteed performance at 4.5V gate drive.
See also RAMPS 1.4 and external mosfets.