Internal energy is primarily associated with fixed volume, closed processes where dU = CvdT holds. Enthalpy is associated with open, fixed pressure processes where dH = CpdT holds. In open processes the product stream is running into space already occupied by something else and that something else needs to be moved somewhere. The additional work required is contained in the PV term in your H = U  + PV formula. Hence either in chemistry lab experiments or industrial processes, we generally work w