2.96 kg/s of a process fluid is evaporated at 444 K up to a final temperature of 478 K in a tubular unit using steam at 1720KN / (m ^ 2) Unfortunately the mode of operation permits the buildup of scale inside the tubes equivalent to a resistance of 0.00176m ^ 2 * K / W and this has to be removed periodically at an annual cost of £ 8500. It is proposed to retube the exchanger with alloy tubes and it is estimated that due to the resulting reduction in scale formation, equivalent to a resistance of 0.00123m ^ 2 * K / W the annual cleaning costs will be £ 1750. If the present unit can be operated for five years, for how long will the modified unit be operated to produce the same annual profit?
[10 MARKS]
The following additional information is given:
Latent heat of process fluid = 1093 KJ/kg
Value of process fluid = 1.55 £/Mg
Outside film coefficient of steam = 8.52 kW/m²K
Inside film coefficient of process fluid = 1.42 kW/m²K
Installed cost of existing evaporator = I = 295A ^ 0.8 * f
Installed cost of modified evaporator = 1 = 797A ^ 0.8 * f
Where A, m ^ 2 the heat transfer area.
Fixed charges = 40% of installed cost
Cost of steam £ 1.65/1000 kg
Interest rate on capital = 8%
The following resistances are given for the original and the modified one.1/h_{0} = 0.11737,1/h_{1} = 0.70423 scale=1.76000,For the modified tubing 1/h_{o} = 0.11737, 1/h_{1} = 0.70423, Scales 1.23000 m²k/W