G500 First Officer reported both air conditioning packs failed and they diverted to a nearby airport.

Narrative

We were climbing through FL390 when a CAS message for a Left air conditioning Pack Hot was displayed. We used the checklist and turned off the left pack switch. That CAS message went away after 15 seconds. One minute later; the Right air conditioning Pack Hot CAS message was displayed. We asked ATC for a lower altitude and we were cleared to FL300. As we descended; the right pack overheat message went away. We leveled at FL300 and turned both air conditioning packs on and noticed the pack outlet temperatures were abnormally hot. They were around 80 degrees when they should be 35 degrees. We asked ATC for a divert to ZZZ and we landed safely. The Maintenance Technicians found that the air conditioning Y-Duct in the aft equipment bay was damaged. The Y-duct doors did not open properly with damage at the hinge pin area. The doors did not swing freely to the open position. In addition; the fiberglass Y-duct was torn in areas surrounding the Y-duct door on both sides. The Y-duct was replaced and the aircraft returned to service.