In gas turbine recuperators, the exhaust gases are used to heat the incoming air and Cmin/Cmax is therefore approximately equal to unity. Show that for this case e = NTU/(1 + NTU) for counterflow and e = 1/2 (1 – e– 2NTU) for parallel flow.

Question

GIVEN

• Gas turbine recuperator

• Cmin /Cmax ? 1

FIND Show that

(a) e = NTU/(1 + NTU) for counterflow

(b) e = 1/2 (1 – e– 2NTU) for parallel flow

SKETCH

Answer 1

(a) From the solution for counterflow



Applying L’Hopital’s rule



(b) For parallel flow, the effectiveness