OK, so if I want to freeze a block of something and keep it there, I have to know something about its heat transfer to the environment.
I'll know I can keep the hot side at 50C with some regulated sink system (i.e., fan control)
then I'll know I want dT of 50C, and I can use 1.5A @ 5V, 3A @ 10V, 4.5A @ 13V, etc.
But I'll have to use the second chart to know what current I need to pump the equivalent heat power, which is over 3A @ dT of 50C
So my water did not freeze because there was too much heat transfer into my tin and system on the cold side.
OT
Heat transfer was my least favorite course, and probably because the professor was a tenured penis. Every semester the kids that failed the semester before would circulate a petition to have him removed. He was a bold MF'er, would proudly announce at the beginning of the semester that half the class would not pass. And he was right. He also justified the difficulty of his program, meaning it was so hard that nobody could get 100% because if they did, he would not know how far they really could go.