An EGR cooler reduces intake charge temps. This makes EGR more effective at controlling NOx. This allows automakers to use less EGR and meet the same emissions or use the same amount of EGR and meet more stringent emissions.
It also ups the power slightly (when EGR is used) because less heat energy is lost to the cooling system and more of it stays in the gas where the piston can extract work from it.

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green 85 300SD 200K miles "Das Schlepper Frog" With a OM603 TBO360 turbo ( To be intercooled someday )( Kalifornistani emissons )
white 79 300SD 200K'ish miles "Farfegnugen" (RIP - cracked crank)
desert storm primer 63 T-bird "The Undead" (long term hibernation)

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