Hi,
We are making an egg-fryer from a 7cm x 7cm PCB. (single sided, 2 oz copper covered with conformal coat), It will have a 0.5R resistor made on it with PCB tracks.
If we put 10A through it, how long will it take to heat up the copper to 180degC? (ambient is 25degC)
If you search "pcb heater design" on YouTube, you'll find several guys who have experimented with designing pcb heaters for several different applications.
Heat input = Watts x time.
Heat required = mass (m) x specific heat (sh) x rise in temperature (dt).
You need to know those parameters for each of the components of the system and also take into account insulation below the heater panel.
Your putting 50 Joules into your copper ( I²R = 10² x 0.5) That will give a ~150°C rise in one gram of copper in one second and it'll keep going until it melts. However, the weight of your copper is unknown (to us) and the rate of heat loss is also going to be a big factor.