Question 9.30: A process requires a flow of 4 kg/s of purified water at 340......
A process requires a flow of 4 kg/s of purified water at 340 K to be heated from 320 K by 8 kg/s of untreated water which can be available at 380, 370, 360 or 350 K. Estimate the heat transfer surfaces of one shell pass, two tube pass heat exchangers suitable for these duties. In all cases, the mean heat capacity of the water streams is 4.18 kJ/kg K and the overall coefficient of heat transfer is 1.5 kW/m² K.
For the untreated water: GC_{p} = (8.0 x 4.18) = 33.44 kW/K
For the purified water: GC_{p} = (4.0 x 4.18) = 16.72 kW/K
Thus:
and: {\frac{G_{1}C_{p_{1}}}{G_{2}C_{p_{2}}}}={\frac{16.72}{33.44}}=0.5
From equation 9.235:
\eta=\frac{G_{2}C_{p_{2}}(T_{22}-T_{21})}{G_{1}C_{p_{1}}(T_{11}-T_{21})} (9.235)
\eta=\frac{4.0\times4.18(340-320)}{4.0\times4.18(T_{11}-320)}= \frac{20}{(T_{11}-320)}.
Thus η may be calculated from this equation using values of T_{11} = 380, 370, 360 or 350 K and then N obtained from Figure 9.85b. The area required is then calculated from:
A={\frac{\operatorname{N}(G C_{p})_{\operatorname*{min}}}{U}} (equation 9.236)
to give the following results:
Obviously, the use of a higher untreated water temperature is attractive in minimising the area required, although in practice any advantages would be offset by increased water costs, and an optimisation procedure would be necessary in obtaining the most effective design.
| T_{11} (K) | η ( – ) | N ( – ) | A (m²) |
| 380 | 0.33 | 0.45 | 5.0 |
| 370 | 0.4 | 0.6 | 6.6 |
| 360 | 0.5 | 0.9 | 10.0 |
| 350 | 0.67 | 1.7 | 18.9 |
