What is the purpose of the air inlets on an A320neo's pylon (LEAP-1A)? Passive cooling, air bleed like in the 707, or something else?
Compressed (hot) air is taken from the engines (before combustion) for pressurization and air conditioning. This air has to pass through a PCE (cooled by air from the fan) before heading to the PACKs at about 200°C. The PCE is typically located in the pylon due to space constraints.
CFM56-5 (A320) bleed users; source: slideplayer.com.br
The largest of turbofans don't have the PCE inside the pylon, and instead have them in the cold bypass stream (as shown below), as does the 737 due to its short pylon (or almost nonexistent pylon on the -3/4/500 series).
Source: Boeing via leehamnews.com