It all comes down to this equation:
DT/DTmax = 1 - (Q / Qmax)
This shows that the amount of cooling in oC is proportional to the amount of heat that must be removed.
With your suggested setup of two Peltiers on top of one Peltier, the bottom one will give little cooling because it must remove a lot of heat relativ to its rating. The second two Peltiers will not only hav eto remove the heat from the CPU, but also the power consumed by the first Peltier, which in the case of a 172W device operated at full power could be as much as 270W. This means that the second two Peltiers will also be operating close to their limit and so they will give very little cooling.
In the other case, with just the two more powerful Peltiers, they will be operating well below their limit, so you should get a DT closer to DTmax, which is more than the not-much + not-much in the other case.
|