Hp pavilion a450n problem fan is running on high and keeps shutting down

First off - have you ever cleaned inside the case? You'd be very surprised how much dust often builds up inside a PC. After that it sounds like you might have another fan which has failed. PCs often have more than one inside and they also have temperature sensors to keep the CPU cool. If a case fan has failed it would not have air flowing inside to cool off the other components and then the CPU sensor would kick the processor fan into "overdrive". One thing to note; the difference between a two wire fan and a three wire fan is that the third wire is used to confirm the speed of the fan. Fans are usually easy to replace - just get the right size and the same right plug.