Capitalisation of "Section" and "Chapter" in a Ph.D. Thesis
"In Chapter 3, it was shown that..." 


This seems correct. "Chapter 3" is the name of the third chapter. Names are capitalised.


  "In the previous Section, a method was presented to..."


This seems wrong. "Section" is not referring to the previous section by name, therefore no capital.


  "The graph in Figure 3 shows..."


Correct. Same as the first example.

So the rule (I use) is, if it is a proper name, then use a capital. This means, if it is of the form "Section $n$", where $n$ is a number, then it needs a capital.