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Question

# Steam enters a counterflow heat exchanger operating at steady state at 0.07 MPa with a specific enthalpy of 2431.6 kJ/kg and exits at the same pressure as saturated liquid. The steam mass flow rate is 1.5 kg/min. A separate stream of air with a mass flow rate of 100 kg/min enters at $30^{\circ}C$ and exits at $60^{\circ}C.$. The ideal gas model with $c_{p}= 1.005 \: kJ/kg \cdot K$ can be assumed for air. Kinetic and potential energy effects are negligible. Determine (a) the quality of the entering steam and (b) the rate of heat transfer between the heat exchanger and its surroundings, in kW.

Solution

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Given:

• $p_1=p_2=0.07 \space \text{MPa}=0.7 \space \text{bar}$
• $h_1=2431.6 \space \frac{\text{kJ}}{\text{kg}}$
• $\dot m_1=1.5 \space \frac{\text{kg}}{\text{min}}$
• $\dot m_3=100 \space \frac{\text{kg}}{\text{min}}$
• $T_3=30 \space ^{\circ} \text{C}=303 \space \text{K}$
• $T_4=60 \space ^{\circ} \text{C}=333 \space \text{K}$
• $c_p=1.005 \space \frac{\text{kJ}}{\text{kg} \cdot \text{K}}$

Steam is cooled in a counter-flow heat exchanger by air at steady-state operation. Kinetic and potential energy effects are negligible. The quality of the entering steam and the rate of heat transfer between the heat exchanger and its surroundings are to be determined.

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