Igure P4.57 provides steady-state operating data for a parallel flow heat exchanger in which there are separate streams of air and water. Each stream experiences no significant change in pressure. Stray heat transfer with the surroundings of the heat exchanger and kinetic and potential energy effects can be ignored. The ideal gas model applies to the air. If each stream exits at the same temperature, determine the value of that temperature, in K.

the approximate temperature is equal to 533 K

Explanation:

the conditions given by the exercise are as follows:

P1=pressure at state 1 as saturated vapor=1 bar

m1=m2=mass flow rate at state 1=10 kg/s

P3=pressure of air at state 3=1 bar

T3=temperature of air at state 3=1200 K

m3=m4=mass flow rate of air=5 kg/s

The energy balance heat gained is equal to heat loss:

m1(h2-h1)=m3(h3-h4)=m3Cp(T3-T2) (eq. 1)

From saturated water tables:

h1=hg=2675.5 kJ/kg

Cp=1.004 kJ/kgK

if T2=240°C=513 K

From the superheated water tables we have at 513 K and 1 bar:

h2=2954.5 kJ/kg

Replacing values in equation 1:

10*(2954.5-2675.5)=5*1.004*(1200-513)

2790≠3448.74

We need to try another temperature

if T=260°C=533K

at 533K and 1 bar h2=2994.35 kJ/kg

Replacing in equation 1:

10*(2994.35-2675.5)=5*1.004*(1200-533)

3188.5≠3348.34

We observe that the difference is increasing. At this temperature, is approximately equal, thus the approximate temperature is equal to 533 K

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