wuzak
Captain
The exposed pipe may have been cheap and easy but it can't have been very effective. The surface area is too small to have an appreciable cooling effect. Look at a your car radiator and calculate the surface area of all those fins. In addition it must have had a disastrous effect on the aerodynamics. The P-47 installation is much better aerodynamically it wasn't just moved inside for aesthetics. The typical American practice of hanging the turbocharger in breeze was not a good idea. It may not have been too critical for bombers cruising at 160 mph but for fighters it would affect performance.
The other thing to note is that turbulent flow is what you want for heat transfer but not what you want for drag. I've always been surprised that the leading edge intercooler of the P-38 worked at all.
For the exhaust pipe to turbo you don't actually want heat transfer, but a small amount may have been required in order for the turbine blades to live.
Leaving the exhaust exposed to outside air may have given the required amount.
The P-47 layout also had a longer path to the turbo, so some heat would have been lost.
Temperature difference is the other main factor s heat transfer. In the case of exhausts compared to outside air at altitude, the temperature difference is substantial.