Question

An insulated heat exchanger uses geothermal water to heat water for a chemical plant. Water enters the heat exchanger at a rate of 36 kg/s and is heated from 23 ∘∘C to 69 ∘∘C. The geothermal water enters the exchanger at a rate of 41.4 kg/s and at an initial temperature of 130 ∘∘C. The specific heat of the geothermal water is 4.31 kJ/(kg K). Determine the rate of heat transfer between the two streams and the rate of entropy generation for the heat exchange process. (Assume constant specific heats and that neither stream undergoes a phase change during the process.)

rate of heat transfer _____ kW

rate of entropy generation ______ kW/K

answer to part a is 6922.08 kW

Answer 1

Answer to part a

Here we have all data for Water and hence we can find the rate of heat transfer with the help of that dat

H = m*Cp*dT = (36)*(4.18)*(69-23) =6922.08 KW

now in order to calculate Entropy generation we will first to find the final temperature of geothermal water

for that we will do enthalpy balance

Enthalpy of water = Enthalpy og geothermal water

6922.08 = m*Cp*dT =41.4*4.31*(130-T)

From above equation, T =91.2 oc

Now entropy is given by

we will have to calculate for the system hence the total entropy generation will be due to the two

Here temperature will be in Kelvin

For water, Tinitial = 23 oC =296.15 K, Tfinal =342.15 K

For geothermal water, Tinitial = 130 oC =403.15 K, T final =91.2 =364.35 K

Change in entropy = entropy generation ( for this case ) = 3.67 KW/K