Thermal conductivity of a metalic bar

1. The problem statement, all variables and given/known data

we have a metalic bar with thermal condutivity of 200w/(m*k) it has an area of 20 cm^2 which is in contact with with an heater that delivers 200 W and is at 300ºC. the metalic bar has a thickness of 1cm

The two questions are:
a) once the system have entered a stationary state what's the temprature of the other of the side of the bar that is not in contact with the heater?
b) calculate the flux going through the metalic bar

2. Relevant equations



3. The attempt at a solution

well I haven't got far, I know that the flux of heat going to a surface is J=-k*grad(T) and from that I get that there is no flux going out the side walls of the bar.
I also concluded that at the stationary state the side of the bar wich is not in contact with the heater wont be at 300ºC for in that case the flux of heat would be zero.
I think that if the board is in contact with something at the other end then it should be always at roam temperature because if it goes above that temperature there will be a discontinuity in the temprerature and it will result in an infinite flux.

Now I don't know what else to do.

Thank you