The way I look at the problem is that the only variable is geometry of our cold plate, all the rest is constant and therefore has no influence on the outcome/3D characteristics of the cold plate.
Yes, you are right, with different peltiers you will need different cold plates and for each combination of 'block side' set of characteristics and 'cpu side' size/thermal output there is one optimal shape of the cold plate.
What I am saying is that for a prticular setup there is only one best 3D shape of a cold plate providing the best performance for given material.
Performance of the whole assembly with only variable being cold plate (we stick with Cu here) is only governed by its shape, which pretty obvious.
Now, how to arrive at this 'shape'?
Start from ideal conditions being cpu die in perfect vacuum and what happens with its thermal output, where and how energy propagates. then introduce an environment and make it also uniform (same as perfect vacuum but with additional set of 'modifiers being properties on a material defining our environment). We are talkin here about the half of infinite space represented by half-sphere.
It is certain that at particular distance from energy source measurable value of emitted energy is going to be so close to zero that for our purposes it is going to be zero. This boundary condition is important for us.
now imagine the same thing but for TECs cold side.
Shapes of 'energy clouds' each of them are different. For now thay are at infinite distance from each other and have no influence on each other.
Start decreasing the distance between the two (treating enviro. as one).
At some point 'thermal energy clouds' of different polarity (lts say hot is + cold is -) will start to overlap.
We are interested in the 'overlap' condition. Cals are simple here (I am still at theoretically perfect situation where there are no external influences contaminating test universum). It dead easy to calculate temp of each point within 'tec' (thermal energy cloud) for each source. Where they overlap we simply do some adding to arrive at effective temp.
At this stage we need to introduce time and thermal energy pressure (thermal gradient dependant) to establish the ideal distance between two sources. Shape will be decided by the oputcome of isotherms interference pattern.
By examining this model I concluded that the optimal distance is where isotherms of both sources meet at their 'flat fragments' and are equal in size (plains). Due to TEC modules isothermal plain is 'wider' than CPUs at the same distance from each of them, distancee from CPU is going to be longer than that from TEC to allow CPUs 'tec' to expand to needed width (the further from source the larger the plain and we want it to be as small as possible).
I hope it is cogerent nuff to be digestible.
Please do not reply saying that I am desribing things extremely basic since they are not for all members
If you want to b0llock it do it constructively. please
P.S. Experimental methodology is pretty neat. Use moulds for shapes and lead to replace Cu since it is easily obtainable and melts even easier. To create a moulde use sth like clay-like material and plywood shape cut-outs axial initial shaping. The whole thing is easy but requires massive amount of time and workman hours...
