A counterflow concentric heat exchanger is used to cool oil

A counterflow, concentric heat exchanger is used to cool oil for a gas turbine engine The flow rate of cooling water through the inner tube is 0.2 kg/sec, while the flow rate of oil through the outer annulus is 0.1 kg/sec. The oil and water enter at temperatures of 100 C and 30 C, respectively. What is the heat transfer rate of this heat exchanger and the fluid exit temperature if the heat exchanger is 66 m long ?

Solution

Solution:

A is pi/4 (0.045^2 - 0.025^2) (66)

A = 0.0725 m2

mo = 0.1 , Cpo=2 ; mcpo = 0.2

mw= 0.2 , Cpw = 4.2 ; mcpw= 0.84

C = 0.2/0.84 = 0.23

Efficiency is given by 1- e^-(1-C)(NTU)/(1-(C)(e)^-(1-C)(NTU)

where NTU is given by UA/(mco)

(here U is not mentioned im given question therefore writing down all steps after this)

Effieciency is also given by = mco (100-Tof)/(mco)(70)

= 100-Tof/70

knowing eff Tof that is fluid exit temo can be calculated.

then mco (100-Tof) = mcw (Twi - 30)

knowing Tof, Twi can be calculated as heat loss by oil will be equal to heat gain by water which will be heat transfer rate for heat exchanger.