Question

Water at 600ºC, 10 MPa enters the “hot” side of a well-insulated heat exchanger with a flowrate of 0.1 kg/s and exits as saturated liquid.   Water enters the “cold” side of the heat exchanger at 10ºC, 100 kPa with a flowrate of 0.5 kg/s. Find (a) the rate of heat transfer (in kW) between the two fluids and (b) the exit temperature of the cold water (in ºC).

Answer 1

a) For the hot water which is at the inlet at Th1 = 600oC

the mass flow rate of hot water, mh = 0.1 kg/s

at the outlet of hot water given that it exits as saturated liquid i.e temperature at the outlet

Th2 = 310.997oC [steam table]

enthalpy of steam at 10MPa and 600oC = 3625.8 kJ/kg [steam table]

now enthalpy of steam at saturated vapour condition at 10 MPa = 2725.5 kJ/kg [steam table]

Latent heat require to get to the saturated liquid at 10MPa = 1317.4 kJ/kg [steam table]

so, Total heat transfer from hot fluid per unit mass = (enthalpy of steam at 10MPa and 600oC) -(enthalpy of steam at saturated vapour condition at 10 MPa) + (Latent heat require to get to the saturated liquid at 10MPa)

Total heat transfer from hot fluid per unit mass = 3625.8 -2725.5 +1317.4 =2217.7 kJ/kg

or

directly (3625.8- enthalpy of saturated liquid at 10MPa)

Total heat transfer from hot fluid = 2217.7* 0.1 =221.77kW

b) exit temperature of cold fluid

Total heat transfer from hot fluid = Total heat transfer to the cold fluid (1)

specific heat of water ,cpc=4.2 kJ/kg.K

the mass flow rate of cold fluid. mc = 0.5 kg/s

Total heat transfer to cold fluid = mccpc (Tc2  - Tc1)

where Tc1 is the inlet temperature of cold fluid

and Tc2 is the outlet temperature of cold fluid

Total heat transfer to cold fluid = 0.5 *4.2*( Tc2 - 10)

put all these in equation 1

221.7 = 0.5 *4.2*( Tc2 - 10)

Tc2 = 115.57 oC

But saturation temperature at 100 kPa =99.606oC [steam table]

and 221.7 KW is less than the latent heat of 0.5 kg of water at 100kPa which is 2257.4 *0.5 = 1128.7 kW, [steam table]

hence, heat transfer from the hot fluid is not sufficient to completely vapourize the cold fluid

so,

the outlet temperature of cold fluid = 99.606oC