I would use one of the following two forms:
- A plate divides the tube into a primary and a secondary part
- A plate divides the tube into primary and secondary parts.
The meaning is much the same, the difference is one of style, and of emphasis. In the first case the difference between the two parts is emphasized, while in the second the fact that they are both parts of the tube is emphasized. Normally a repeated article in a parallel construction can be omitted with no change of meaning. But here using "a primary and secondary" without the second "a" feels wrong, although I can't specify any rule that it violates. Perhaps my mind wants to parse "a primary and secondary part" as if there was one part that was both primary and secondary, but that makes no sense in this contest. In any case I would not omit the second "a", but I won't assert that it is wrong to do so.
As a comment points out the form:
A plate divides the tube into primary and secondary parts.
could imply many parts, some primary and some secondary (in which case the plate or the tube would need to include several bends). One way to clarify this would be:
A plate divides the tube into two parts; one primary and one secondary.
I would also mention the related sentence:
Plates divide the tube into several parts.
Here the multiple parts must be plural.