# Heat exchangers

1. Nov 24, 2014

### Mitch1

1. The problem statement, all variables and given/known data

1. If the flue gases exiting the boiler are used to preheat the water fed to the boiler from a temperature of 28 C to 90 C and assuming:
• a mean specific heat capacity for water over this temperature range to be 4.2 kJ kg–1 K–1

• a mean molar heat capacity for the flue gases up to 300oC to be 31 kJ kmol–1 K–1

• 10% of the heat required to heat the water is lost in the heat exchanger

• all water entering the system is converted to steam

determine the final outlet temperature of the flue gas
2. Relevant equations

pw = (mole fraction)water × total pressure

3. The attempt at a solution
I'm not sure where to start off on this once as it does not state any pressure the steam is at, I thought you needed a pressure to multiply by the mole fraction to then obtain a temperature using steam tables?
Any help/suggestions on equations would be much appreciated -thanks

2. Nov 24, 2014

### Bystander

The boiler feed is in the liquid phase.

3. Nov 24, 2014

### Mitch1

Thanks for your reply, so is there a different equation that is used? Because you do not need to use specific heat capacity when using the method I described I believe

4. Nov 24, 2014

### Bystander

This is the second (nth?) part of the flame temperature question isn't it? Vapor pressure of water at 90 C is less than 1 atm, and the steam generation occurs in the boiler.

There are some parameters missing here --- water feed rate, flue gas generation/flow rate?

5. Nov 24, 2014

### Mitch1

Yes it is the final part there is one after the flame temp question that I believe to have completed just the notes are not very clear,
The flow rate of flue gas is 1400 kmol h^-1
And it does not state any water feed rate, what is the equation that you are intending on using please

6. Nov 24, 2014

### Bystander

From the earlier part, "steam at 5atm?" Gauge or absolute? So, you've got 1400 kmol/h at whatever heat content from 300 C to flame T (again from earlier) generating however much steam it takes to soak up that much heat (liquid heat capacity from 90 C to 5atm steam T plus enthalpy of vaporization at 5 atm.), be it gauge or absolute, giving you the water feed rate.

'Nuff of a start?

7. Nov 24, 2014

### Mitch1

Thanks for the explanation would you be willing to give me a formula to use I might be able to tackle it and give it a go that way
Thanks

8. Nov 24, 2014

### Bystander

Total heat in (flue gas flow rate at flame T x heat content) = Total heat out (sum of pre-heat/0.9, plus heat content of steam (or, heat content of flue gas x flue gas flow rate between flame T and 300 C, which is the steam generated, minus losses if they mention it's not a perfect boiler) ) --- I think I got everything, but double-check it.

9. Nov 24, 2014

### Mitch1

Thanks mate I will give it ago using this!

10. Nov 25, 2014

### Mitch1

What would the usual difference be between inlet and outlet temperatures with regards to flue gas as I have worked it out although it barely differs from the inlet temp (around4 degrees) surely I have gone wrong?

11. Nov 25, 2014

### Bystander

This is for the feed water pre-heat? What did you get for feed rate?

12. Nov 25, 2014

### Mitch1

2113 kg/hr? I used the liquid heat cp 90c + 5bar + enthalpy of vaporisation 5 bar
4.208+2.32+2107=2113

13. Nov 25, 2014

### Bystander

Lemme see --- 2113 x 4.2 x 62 = 555 kJ/h; and (31kJ/kmol x 1400 kmol/h)/.9 = 48.2 kJ/h; goes into 555 11.4 times for an 11.4 K delta T. And, you evaporated water in the pre-heat, I'll bet ---- pre-heat T gets to 90 C, at 5 atm., so it can't evaporate.

"Are we there yet?"

14. Nov 25, 2014

### Mitch1

I'm not sure hahah! So what is the 11.4 difference in temperature?

15. Nov 25, 2014

### Bystander

That's how much the flue gas exhausted from the boiler at 300 C is further cooled by running it through the pre-heater.

16. Nov 25, 2014

### Mitch1

Ah so it is simply 300- 11.4 to give the outlet temperature of the flue gas?

17. Nov 25, 2014

### Bystander

That's the way I'd play it.

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