I would like to cool a small device, with a size of 45x45 mm² and a thermal load of ~40 W. Currently, I have a cooling system available, capable of cooling a thermal load of 52 W, and a cold plate with the dimensions of 60x80 mm². Due to the size difference I expect a small drop in the efficiency.
Is there a way to calculate that drop, and to estimate if I still can use that cooling device? As a naive approximation I would take the difference in the area size ($80\cdot60-45^2=2775$), which is approximately 60 % of the original cold plate. Can I therefore expect a loss of 60 % of the original cooling capacity, i.e. I only can cool a thermal load of 30 W for the given dimensions, or is that approach wrong?