Tube gas exit temperature in fire tube?

[Cool SH]

Hello ladies and gentlemen,

My objective is to find the tube exit gas temperature in fire tube boiler. I know the rate of heat transfer, Q=m.c.delta T, should be equal between gas and water side. Anyway, I have work out the analysis as attached. However, I just cannot seem to get the final temperature, which is 240 deg C.

Can anyone please point out on what my mistake is?

Thank you in advanced.

EDIT: This is not a homework. This is a real life problem. I measured the temperature at site; 240 deg c. I want to verify with theoretical calculation.

 

[lappygamer]

I'm not precisely sure what the system looks like, but since it is a boiler I would expect to see the latent heat of vaporization included. I don't see it in your equation.

 

[georgeverghese]

Agreed, with the latent heat of vaporisation included (with Tsat=186degC, Psat is 1000kpag), the corrected equation would be

2409x1.133x(1045-T2) = [2056x4.31x(186-70)] + (2056x1988.5); which doesnt give a sensible result, so there are some other errors also. T1 seems rather low for example, so is the mass rate for Mg.

 

[chicopee]

All fire tube boilers that I am accustomed are two or four passes. Your drawing shows a single pass. Normally flue gas temperature to the stack will be around 350 dF depending on the dew point that you are minding for the boiler location. The initial water of 70 dF is not appropriate in your analysis. It would be more suitable as an initial condition in a numerical analysis using time, tube length and increase in the cooling medium internal energy increments. You need to develop a computer program or spread sheet to solve this problem.

 

[Cool SH]

Thank you for your time.

It was weekend, so I didn't reply. Just finished Avengers Infinity War, greatest movie of 2018.

Anyway back to the question, just to answer chicopee, this is a reverse flame fire tube boiler. I think i didn't sketch the overall of the system. You can check it out in the latest link.

My understanding of heat transfer in between fire/gases and water is like this. The water act as insulation to prevent the tube from overheating (part of the function beside to supply steam). That's why flue tube is submerged within the water level all the time. No steam is in contact with the flue tube. Phase change from water to steam take place above the flue tube. Therefore, the enthalpy, h doesn't play a role in heat transfer between gases and water.

Water input from feedwater pump is t1=70 deg C. The Temperature of flue gas into the tube is T1=1045 deg C. The steam output is at 10.35 bar, which is equal to 186 deg C according to steam table. So I take temperature of water, t2=186 deg C, just before it is form into steam.

Or is my understanding wrong all the time?

I appreciate all the help. Thanks


EDIT: Wait, maybe I should consider radiation heat transfer in the flue gas tube? Given by Stefan-Boltzmann Equation?

 

[chicopee]

The temperature in the firebox may be 1045 dC but it will not be that as the hot gases travel thru the tubes. There will be a temperature drop thru the tubes. Yes radiation heat transfer will take place inside the firebox and inside the tubes. You will also have to contend with heat loss thru the boiler insulation and any exposed bare metal surfaces. For such type of boilers, past experiences has shown a steam generation of five to 7.5 lbm/ hr-sq ft of heating surfaces which is one method of determining the size of pressure relief valves. At best the heat transfer efficiency for such boilers is low somewhere around 60 to 75% (ie heat output in terms of the steam generated to heat input from the combusted fuel within the firebox). The heat input within the firebox is about 80% of the energy content of the fuel.
If you are still intend of analyzing with heat transfer equations, numerical analysis is the way and with each time step taken you want to calculate a bulk water temperature before proceeding to the next time element. Let me tell you that such analysis will be a beast to develop as I have done a somewhat similar but simpler analysis a few decades ago by hand calculations and hand held calculator.

 

[Cool SH]

Chicopee, what you mentioned about the efficiency is near to what I had calculated; 83%. So far I had done the excel sheet. I am stuck at here.

Actually part of the reason why I take up this challenge is to understand better the mechanisms behind the boiler. The process is more important than the answer. I believe by this exercise will make me a better engineer, instead of just follow and agree with others about the final output.

You said you had done a simpler calculation decades ago, can you help me by telling what's the hand on calculation you used? Any input is appreciated.

Thank you.

 

[chicopee]

There are tons of books in libraries about boiler information that will help you with your goal. Don't rely on the internet for research because it will be lacking in details. If you intend to continue with your analysis, I would first calculate heat transfer in a simpler system such as for a single tube surrounded by a volume of water, then by several tubes immersed in water, firebox surrounded by water, separately, and then an assembly of all. That way you'll get a better feel for the problem.