Question 2.11: A heat exchanger has an overall heat transfer coefficient of...
A heat exchanger has an overall heat transfer coefficient of 120 W/m2K. Superheated steam enters the tubes at 250 °C and exits the exchanger at 400 °C. Hot gases on the shell side enter at 900 °C and exchange heat with the steam. The capacity rate of steam is 200 000 W/K and that of the gases is 300 000 W/K. What is the effectiveness? Using the formula for NTU for a counter-current shell and tube, determine the required surface area of the heat exchanger. What is the temperature of the gases leaving the exchanger?
The actual heat transfer is q = C_{steam} \times (400 – 250) = 30 MW.
q_{min} = C_{min}(900 – 250) = 130 MW. The effectiveness, \epsilon = q/q_{min} = 30/130 = 0.23.
We know that NTU = UA/C_{min} = 120 \times A/200 000. From the formula for a single counter-flow tube and shell exchanger:
Therefore, A = 0.285 × 200 000/120 = 475 m². The gases exit temperature is determined by: q = C_{gases}(900 – T_{exit}), 30 \times 106 = 300 000 \times (900 – T_{exit}), and T_{exit} = 800 °C.