Steam enters a counterflow heat exchanger operating at stead

Steam enters a counterflow heat exchanger operating at steady state at 0.07 MPa (0.7 bar with a specific enthalpy of 2431.6 kJ/kg and exists at the same pressure as a saturated liquid. The stream mass flow rate is 0.025 kg/s. A separate stream of air with a mass flow rate of 1.667 kg/s enters at 30 degree C and exits at 60 degree C. Use Table A-22 to determine any properties of air. Neglect the effects of kinetic and potential energy. Determine: The quality of the entering steam (-) The rate of heat transfer between the heat exchanger and its surroundings (kW), be sure to indicate direction

Solution

The specific enthalapy of the steam entering the heat exchanger =2431.6kJ/kg at the pressure of 0.07MPa.

From the steam tables at Pressure of 0.07MPa,

h_g=2659.4kJ/kg. h_f= 376.68kJ/kg.

h_x=h_f+x(h_g-h_f);

2431.6= 376.68+x(2659.4-376.68);

The quality of the steam x=90.02%.

Rate of heat lost by the steam= m(h1-h2);

The steam leaving as the saturated liquid. the enthalapy of the stea when leaving the exchanger = 376.68kJ/kg.

Rate of heat lost by the steam = 0.025*(2431.6-376.68) = 51.373kW.

Rate of heat gained by the air = m*c_p*(T2-T1) = 1.667*1.005*(60-30) = 50.26 kW.

The rate of heat transfer between the heat exchanger and its surroundings = 1.11295kW. The heat is transferrred from the heat exchanger to the Surroundings.