Is it possible to use 12 x LM2596 modules to charge a 12s LiFePO4 battery pack by connecting the inputs of the lm2596 modules in series and using a single power supply in the input?
Let me give example of 4s battery pack.
Input connections:
1. IN+ module 1 connected to +ve of 20V
2. IN- module 1 connected to IN+ of module 2
3. IN- module 2 connected to IN+ of module 3
4. IN- module 3 connected to IN+ of module 4
5. IN- module 4 connected to -ve of 20V power supply
Output connections:
4 cells connected in series. Cell 1 being connected being towards negative side and cell 4 being towards the positive side.
Output of modules set to 3.5V.
1. Out+ module 1 connected to cell 4 +ve
2. Out- module 1 & Out+ module 2 connected to cell 4 -ve & cell 3 +ve
3. Out- module 2 & Out+ module 3 connected to cell 3 -ve & cell 2 +ve
4. Out- module 3 & Out+ module 4 connected to cell 2 -ve & cell 1 +ve
5. Out- module 4 connected to -ve of cell 4.
Will this work?

 

When I drew the circuit diagram I understood that this arrangement will not work as I am shorting the inputs and outputs

 

If you can use isolated converters, it could work.