In order to be more clear
Say that the resistor gives off a temp 50C (constant)
In the original case: Let it be that the lower surface of the 2nd disk has a 30C temp and the running water's temp increases by 2C (from 20C to 22C) while touching that lower surface
1st level: Resistor at 50C...
What happens in an heat flow apparatus when you reduce the length of the disk?
The apparatus is this
1st level: A resistor to produce heat
2nd level: A metal disk with known thermal conductivity coefficient
3rd level: A metal disk with an unknown thermal conductivity coefficient
4th level...