Question 6.CSGP.84: In a co-flowing (same direction) heat exchanger 1 kg/s air a......

In a co-flowing (same direction) heat exchanger 1 kg/s air at 500 K flows into one channel and 2 kg/s air flows into the neighboring channel at 300 K. If it is infinitely long what is the exit temperature? Sketch the variation of T in the two flows.

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C.V. mixing section (no W˙,Q˙\dot{ W }, \dot{ Q })

Continuity Eq.:      m˙1=m˙3 and m˙2=m˙4\dot{ m }_1=\dot{ m }_3 \text { and } \dot{ m }_2=\dot{ m }_4

Energy Eq.6.10:    m˙1h1+m˙2h2=m˙1h3+m˙2h4\dot{ m }_1 h _1+\dot{ m }_2 h _2=\dot{ m }_1 h _3+\dot{ m }_2 h _4

Same exit T:      h3=h4=[m˙1h1+m˙2h2]/[m˙1+m˙2]h _3= h _4=\left[\dot{ m }_1 h _1+\dot{ m }_2 h _2\right] /\left[\dot{ m }_1+\dot{ m }_2\right]

Using conctant specific heat

T3=T4=m˙1m˙1+m˙2T1+m˙2m˙1+m˙2T2=13×500+23×300=367KT _3= T _4=\frac{\dot{ m }_1}{\dot{ m }_1+\dot{ m }_2} T _1+\frac{\dot{ m }_2}{\dot{ m }_1+\dot{ m }_2} T _2=\frac{1}{3} \times 500+\frac{2}{3} \times 300= 3 6 7 \,K

69

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