Say I have a flat rectangular bar of aluminum with a known volume. Sitting directly on top of that piece of aluminum is a rectangular circuit board made of FR4 (standard circuit board material). I can raise and lower the temperature of the aluminum very rapidly and I can monitor the temperature of the aluminum instantaneously but I cannot monitor the temperature of the circuit board directly. We can assume that the entire aluminum piece heats and cools evenly as does the circuit board.
If I know that I want to raise the temperature of the circuit board from 30°C to 200°C linearly in 90 seconds what calculations would I need to do to determine how fast i need to raise the temperature of the aluminum.
( I am tagging this incorrectly because there isn't a good tag for it and I can't add tags yet!)