Download location of pdf files saved in the of Academia app

Android usage Linux based kernel and security, so every app runs in its own sandbox. Although storing app specific files depends on the developer most of them store in app specific folders which again can either be accessible by user or not. If you can't find any app specific folder created on your sdCard(external storage) look for /Android/data/yourAppSpecificPackageFolder [in your case /Android/data/com.academia.academia] in internal storage, you can look for folders within this. It can be stored as it is(.pdf) or some other format which default applications might not understand(so you can't open it).
If you don't find here then it might be in /data/data/yourAppSpecificPackageFolder for which you need to have rooted device.