I am doing air cooler modeling for the first time. I wanna know if we considering the expansion in the nozzle boxes of the air cooler? if yes, how do we model that, i mean where is the fixed point from which expansions are considered?

Of course you must consider nozzle expansion. There are lots of posts on air cooler modelling, it can be a complex issue. Try using the forum 'search' facility.

FOR AIR COOLER MOSTLY THE INLET IS FIXED BUT IT IS CLEARLY MENTIONED ON VENDOR DRAWING AS STATIONARY HEADER.

so you mean the only expansion to be considered is the nozzle axial expansion?