# Homework Help: Calculating Mass Flow Rate of Steam

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1. Jan 10, 2017

### sjh94

1. The problem statement, all variables and given/known data
If 5% of the heat available for steam production is lost to the
atmosphere, determine the amount of steam raised per hour when the
total flow of flue gases is 1400 kmol h-1.

qmH = 1400 kmol h-1

Flue gas temperatures:
Inlet = 1832°C
Outlet = 300°C

Water temperature:
Inlet = 90°C
Steam produced at 5 barg = 159°C

Latent Heat of Steam @ 5 barg = 2085 kJkg-1 (hfg)

Specific heat capacity of water = 4.18 kJ kg-1 k-1 (Cpc)

2. The attempt at a solution:

The specific heat capacity of the flue gas is not given, therefore I am missing 'cph' and cannot use the equation below:

If I could work out the heat transfer rate then I would be able to use the equation below to find the the mass flow of the steam??

Any help would be much appreciated.
Thanks.

2. Jan 10, 2017

### BvU

Hello sjh,

Seems to me the problem statement you were given is incomplete indeed. Otherwise your expressions are fine.
Perhaps there is a context ? Or else you are supposed to look it up somewhere and use an approximate value ? Somewhat strange, when the input temperature of the flue gas is given with such a high accuracy (on the other hand the 5% looks like a crude estimate) .

3. Jan 10, 2017

### sjh94

I should have mentioned that a previous question asked me to calculate the flame temperature, this is why the temperature is so precise.

I emailed my tutor with the following question:

'To my understanding I would require the specific heat capacity of the flue gases to use in this equation?

Is this correct? as the question doesn't state what the specific heat capacity is for the flue gas?'

'That sounds sensible, yet as you mentioned the question doesn't state what the specific heat capacity is for the flue gases. So you need to think of other way to calculate the heat available, maybe you can use the steam table.'

Don't know if this helps further, thanks.

4. Jan 10, 2017

### BvU

HI,
I'm afraid I don't see any inroads and the steam table doesn't help me for the process side.
@Chestermiller : am I overlooking something ?

After reading a bit better: Note that

is a bit deficient on the steam side: it only describes the phase transition; you also have to heat the water from 90°C to 159°C

5. Jan 10, 2017

### Staff: Mentor

This can't be done unless you know the composition or the heat capacity of the fluid gas. Is this the second part of a problem?

6. Jan 10, 2017

### sjh94

Hi,

Yes I have already calculated the flue gas composition, below is what I got:

There is 10% excess air provided in combustion, this is why I have a small amount of oxygen in flue gas.

7. Jan 10, 2017

### BvU

Do your 'steam tables' also have properties for these gases ? As in Cengel, for instance ?

8. Jan 10, 2017

### sjh94

I have been provided with this table, which shows enthalpy of combustion gases.

I used these values when determining my flame temperature by calculating the heat content for each component = number of moles * enthalpy of component
Then added the heat content per combustion gas to give me my total

I calculated the total heat input per kmol of fuel to be 2349 kJ (maybe be right, maybe wrong).

I then used this value to determine my flame temperature, I started with a flame temperature of 1800°C which gave me a total heat content of 2305 kJ.

So I knew my flame temperature was higher, therefore I did the same with a flame temperature of 1900°C.
This gave me a heat content of 2448kJ which is higher than my calculated heat input of 2349 kJ. So my flame temperature was between 1800 and 1900, from these 2 results I produced a straight line graph and ended up with 1832°C.

Make sense?

The chart below should be kJ kmol-1 not MJ, I think.

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9. Jan 10, 2017

### Staff: Mentor

So look up the heat capacities of these gases at the two extreme temperatures, and take their temperature average. Then take their molar average.

10. Jan 10, 2017

### Staff: Mentor

11. Jan 10, 2017

### BvU

So instead of $c_p \Delta T$ you use $\Delta H$ -- much better.

So much for answering your original post #1. The exercise is growing a bit bigger with your post #8 !

You can compare with Cengel....

12. Feb 5, 2017

### evoke1l1

13. Feb 6, 2017

### BvU

Enthalpy difference

14. Feb 6, 2017

### evoke1l1

Ahh I see! It makes sense to me now. Many thanks.