A friend of mine bought one of those maker bot type CNC 3d plastic oozing machines. I guess they need a hot plate to make the parts on so that the plastic doesn't cool too fast when the machine starts making the part.

He showed me a circuit board "resistor" plate and asked if i would make him a 7 x 7.5 inch plate. I attached a picture of the plate I made. It has 3.9 ohms resistance.

I powered it up to the maximum 3 AMPS my power supply could deliver and got it to heat up to about 110 degrees F

I guess they need it to go up to 240 degrees F

Assuming the PCB board can take that heat (I don't yet know if it can) instead of just increasing amperage to it I thought I would try and figure out how to calculate how much power the board would need.

There are 43 traces .085 in wide 6 5/8 inch long

About 285 inches. One ounce copper board.

Where do I start to calculate watts per square inch needed to get the surface temperature to 240 degrees?

From my 3 amp test raising the temp from 70 to 110 (40 degree rise) I would think a rough estimate to get up another 130 degrees would take 130/40 or another 3.25 x 3 amps another 9.75 amps so roughly 13 amps

So 13 x 3.9 is 50 volts. This would require an expensive DC supply compared to what I think he should use noted below.

That is the traditional wing it method I typically use but I know someone who had a good math/physics background would put a pencil and calculator to it with some fancy graphs and all. is there anyone here that could give that a go? It would be a very nice introduction to thermal dynamics.

By the way I suggested a $19.00 plug in hotplate with a good adjustable heat setting and an aluminum plate or I could use some nice 1/4 inch SS tube heaters from OMEGA and embed them in an aluminum plate and run it on 110VAC using a zero cross SSR.