You have designed two heat exchangers to do the same thermal ‘‘job’’ [i.e., they have the same q and total tube-side mass flow rate m₁ t (kg/s)]. A comparison of these heat exchangers shows the following:

 

Assume constant and identical fluid properties for both heat exchangers.

(a) Calculate P/Ps, where the subscript s is for the smooth tube.

(b) Calculate p/ps.

(c) Suppose that P/Ps is 0.8; how would you alter the rough tube exchanger geometry to make P/Ps = 1, keeping the same rough tube length? Give quantitative estimates considering no change in the friction factor.

(d) How would you expect UA to change for part (c)? Give explicit reasons whether it will increase, decrease, or will have no change.

 

Property Heat transfer area 4 (m) Number of tubes N, Smooth Tube 13.62 100 Rough Tube 9.80 120