1. (a) Process water with a specific heat capacity of 4.182 kJ kg-1 K-1 flows at a rate of 0.050 kg s-1 through a heat exchanger where its temperature is increased from 16°C to 85°C. Heat is supplied by exhaust gases (mean specific heat capacity 1.075 kJ kg-1 K-1) which enter the heat exchanger at a temperature of 420°C. If the mass flowrate of the exhaust gases is 0.044 kg s-1, determine their outlet temperature.
(b) The heat exchanger in Question 1 (a) above is of the double-pipe type, and the fluids are in counter flow. If the overall heat transfer coefficient is 35 W m-2 K-1, calculate the size of the heat transfer surface.
(c) What would be the new heat transfer area if the fluids were in parallel flow?
(d) Describe what is wrong with the sketch of the temperature profiles for the parallel-flow heat exchanger shown in FIGURE 1 and draw the correct version.
2. (a) The data in TABLE 1 below relates to a specific heat exchanger. A reliable colleague has looked up an effectiveness chart and says that the effectiveness in the given operating conditions is 0.82.
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'Hot' fluid
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'Cold' fluid
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Mass flowrate kg s-1
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0.7
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0.6
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Specific heat capacity kJ kg-1 K-1
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1.8
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4.2
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Inlet temperature
°C
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140
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15
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TABLE 1
Area of heat transfer surface 14 m2.
Overall heat transfer coefficient 360 W m-2 K-1. Determine:
(i) the two outlet temperatures
(ii) the heat transfer rate.
(b) Another colleague, who is not altogether reliable, has analysed the heat exchanger, referred to in Question 2 (a), using the correction- factor method and he claims that the correction factor is 0.595. Confirm whether he is correct or not.
3. (a) Dry saturated steam at a temperature of 180ºC is to be produced in a fire tube boiler from the cooling of 50 000 kg h-1 of flue gases from a pressurised combustion process. The gases enter the tubes of the boiler at 1600ºC and leave at 200ºC. The feed water is externally preheated to 180ºC before entering the boiler.
The mean specific heat capacity of the flue gases is 1.15 kJ kg-1 K-1. The latent heat of vaporisation of the water at 180ºC is 2015 kJ kg-1. Feed water temperature = 180ºC.
Determine the amount of steam produced per hour, if the total heat loss is 10% of the heat available for steam raising.
(b) The overall heat transfer coefficient based on the outside area of the tubes is given as 54 W m-2 K-1. Determine the area of heat transfer required to perform this duty.
(c) The tubes within the boiler are to be 25 mm inside diameter with a wall thickness of 3 mm. The average flue gas velocity through the tubes to maintain the overall heat transfer coefficient value and to minimise pressure losses is to be more than 22 m s-1 and less than 28 m s-1.
Assuming that the average density of the flue gases is 1.108 kg m-3, calculate:
(i) the minimum and maximum number of tubes in each pass
(ii) the overall length of tubes at each of these numbers of tubes
(iii) the minimum number of tube passes in each case, if the length of a boiler tube is to be less than 5 metres.