Question

Steam enters a counterflow heat exchanger operating at steady state at 0.07 MPa with a quality of 0.9 and exits at the same pressure as saturated liquid. The steam mass flow rate is 1.3 kg/min. A separate stream of air with a mass flow rate of 100 kg/min enters at 30^oC and exits at 60^oC. The ideal gas model with c_p = 1.005 kJ/kg·K can be assumed for air. Kinetic and potential energy effects are negligible.

Determine the temperature of the entering steam, in ^oC.
For the overall heat exchanger as the control volume, what is the rate of heat transfer, in kW.

Answer 1

Steam enters counterflow heat exchanger at steady state P1 = 0.07 MPa and x = 0.9

Tsat = 89.93 C

saturated specific enthalpy of liquid hL = 376.68 kj/kg

Saturated specific enthalpy of vapor, hg = 2659.41 kj/kg

Enthalpy inlet ,

h1 = (1-x)*hL + xhg = (1-0.9)*376.68 + 0.9*2659.41

h1 = 2431.13 kj/kg.

Outlet steam condition : saturated liquid with same pressure P2= 0.07 MPa

Ts = T2 = 89.93 C

h2 = hL = 376.68 kj/kg

Heat transfer rate, : mass flow rate of steam m = 1.3kg/min = 1.3/60 kg/s = 0.02166 kg/s

Q = m(h1 - h2) =( 0.0216kg/s )*(2431.13 - 376.68) = 51kj/s = 51kW

a) heat transfer from steam to air = 51 kW

m(CpsteamT1 - CpliquidT2) = 51 kW

(0.0216kg/s)(2.041*T1 - 4.205*T2) = 51

2.041*T1 - 4.205*89.93 = 2361.11

T1 = 1342 C

Entering steam temperature T1 = 1342 C

B) rate of heat transfer Q = 51 kW