
#1
Mar1507, 01:50 PM

P: 46

Hi,
I would like some help/orientation about heating furnaces. The issue is around the heating of steel billets (continuous cast billets). The furnace needs to heat a load of 104 billets placed face to face along its longitudinal axis from ambient temperature to ± 1,150°C. Each billet has this dimensions: 140 mm x 140 mm cross section, and 12.7 m. length. The furnace burns a mixture of natural gas and air. So, where in the Internet can I find theoretical models to calculate or design a furnace for such an application? Thank you. 



#2
Mar1507, 03:43 PM

Mentor
P: 22,007

Well, the simplest approach is with the efficiency of the furnace (almost always about 85% noncondensing and 95%, condensing) and the energy capacity of methane. You can caluclate it directly. Methane has a heat content of about 1000 btu/cubic ft.
The toughest part is figuring out how much capacity you need and you didn't provide the most critical piece of information: how fast you want to do the heating. 



#3
Mar1507, 04:47 PM

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P: 22,007

I read and posted in the thread just as I was leaving work and probably should have thought about it on my ride home before posting. Anyway, it is more complicated....
I haven't ever designed a furnace before, so I can't be certain of what is really important, but I suspect: The furnace will quickly reach an equilibrium temp not far below the adiabatic flame temp of methane in 100% stoichiometric air: 1950C. This temp can be adjusted via excess air. The heat loss to the environment will be nontrivial at high temp, so you'll need to calculate it for both convection and radiation. This gives you your required furnace output. The heat transfer to your billets starts off high, but that just means you will be transfering it to the billets instead of through the furnace walls at first  when you end, of course, the heat transfer to the billets is zero. So you can probably ignore this in your calculations for furnace capacity unless the heat transfer through the furnace walls is actually not that high. The exhaust will be used to preheat the intake air, but will still leave pretty hot, so your efficiency from that standpoint will be much less than the 8595% I mentioned above. It isn't all that difficult to calculate, though, from the temperature and airflow. The toughest part will actually be the heat transfer of the billets themselves. It is convective and convective heat transfer is virtually impossible to calculate from scratch. If you have an example of a similar furnace to use as a model to find a heat transfer coefficient, that would help a lot. Also, the arflow and furnace capacity are dependent on each other and the higher the airflow, the more convective heat transfer you get. So that is how you can control the time to heat the billets. Except for the convective heat transfer to the billets, the rest is relatively straightforward. You may want to pick up a used thermo and heat transfer textbook. You should be able to follow the necessary parts. 



#4
Mar1607, 12:04 PM

P: 46

Evaluating furnace heating capacity.
Russ,
OK. Thanks a lot. Well, as you mention, it can be helpful if one has a furnace sample...so I was thinking in handling the problem beginning with the basics. A good starting point could be this: suppose we have a furnace with an atmosphere at 1,200 °C ( at this point let´s forget about the burning process needed to get this atmosphere). Next, suppose that the floor of the furnace has billets placed side by side as described on the thread starting text. This can be viewed as a solid body 140 mm thick, 12.7 m. wide and 14.56 m. long. Then I would like if someone can help me with an example of how to calculate the time needed for this body to reach a uniform temperature of 1,150°C (top thru bottom). Thank you. 



#5
Mar1607, 07:00 PM

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To get a numerical answer, you need some quantites that you can only really find by experiment: the convective heat transfer coefficient between the metal and the gas, and the emissivities of the metal and the furnace walls, for radiative heat transfer. The radiation heating will be significant, and makes the problem much harder than just convective heating. The practical way to get an answer, given all the input quantities, would be a computer simulation. I would be dubious about the assumption that the stack of billets is "one block" of metal. I would expect there would be a significant amount of thermal resistance between adjacent billets in the same horizontal "layer" because of small air gaps, which are good insulators if there is no way for convection to occur. Presumably there would be better thermal contact in the vertical direction  assuming the billets have flat smooth surfaces with no oxidation or corrosion. If that doesn't apply, all bets are off. 



#6
Mar2007, 03:33 PM

P: 46





#7
Mar2107, 08:18 PM

P: 46

About the book by Carslaw & Jaeger, "Conduction of heat in solids"...do you think that someone with a B.A. degree in Engineering can undersatand the contents? Or is it a book for higher degrees of education?




#8
Mar2207, 07:45 AM

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C&J was written "before computers" so the amount of maths needed to do anything back then was heavier compared with a modern course. If the maths in this thread http://www.physicsforums.com/showthread.php?t=161722 looks way over your head, you will be struggling. If you understand the question in that thread but don't know how to answer it, you will probably be OK using the results if you take the derivations on trust. Plan B would be to check out some of the open source finite element packages on the web and solve it numerically. (Sorry, I don't have any experience of those programs so I can't give you a recommendation). 



#9
Mar2307, 04:46 PM

P: 46

OK...I understand the question but I don´t know how to answer it... About plan B: Where can I look for "...some of the open source finite element packages on the web..." ? An example of keywords to type on a search engine to go to the right place(s)? Thank you 



#10
Mar2307, 05:22 PM

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The sticky thread in this forum has some links to FE software
http://www.physicsforums.com/showthread.php?t=58902 



#11
Mar2407, 09:15 AM

P: 46

Thanks a lot, AlephZero!
You have helped me quite a lot.... 



#12
Mar2407, 01:11 PM

Admin
P: 21,637

Is this a batch furnace? Are the bars (or billets) in contact or separated  that would affect thermal conductance? One could use an atmosphere to increase the heat up rate of the charge. One could use a lumped parameter model based on mass and thermal conductivity of the steel. I think most furnace design methods are proprietary since they can provide a competitive advantage to the furnace designer. 



#13
Mar2407, 08:02 PM

P: 46

I think you are right about proprietary methods. Also if a company is specialist in designing and manufacturing heating furnaces, they can do investigation and measuring of data, so they can evaluate about their calculations method and correct and improve them. But still I hope someone could find somewhere a theoretical calculation method that could help a nonexpert to get an idea about heating power, fuel consumption, time needed to heat uniformly the charge, etc. What is a "lumped parameter model"? Do you know about a lumped parameter model based on mass and thermal conductivity of the steel? I already found and purchased a used copy of the book by Carslaw & Jaeger, because I want to learn something about heat transfer in solid bodies. From my years at the University I only recall about heat transfer through walls, layers of different materials, pipes, fluids in motion, etc. But nothing close to a heating furnace. 



#14
Mar2407, 08:04 PM

P: 46





#15
Mar2407, 09:24 PM

Admin
P: 21,637

Going from 100 to 130 mm increases the charge by 69% with the larger 140 mm size essentially doubling the furnace charge from the original design.
Are there thermocouples in the furnace? So the furnace is loaded with 2 billets in two minutes, and at the opposite end, the charge is removed, one billet/minute, or one billet is removed at one time, so 2 billets/2 minutes. That doesn't leave much time for soaking. So one would appear to be assuming a density of steel of about 7870 kg/m³, for a 1 MT billet of 0.127m³. The energy required to heat one billet is simply the mass (1000 kg) * c_{p} * deltaT (1150°C  25°C), where c_{p} is the specific heat, which is a function of temperature. Using sp. ht of 700, one billet require about 788 MJ. At room temperature c_{p} is about 450500 J/kgK, and at higher temperatures it increases to about 600 J/kgK and higher. It's best to find a materials property book or datasheet for the particular steel, which presumably one's company has. One type of steel from Sandvik has the following thermophysical properties. Temperature (°C) 20, 100, 200, 400, 556*, 600, 800  *curie temperature Specfic Heat (J/kgK) 481, 517, 559, 663, 918, 778, 715 Thermal conductivity (W/mK) 11.7, 12.8, 14.3, 17.1, 19.5, 19.7, 22.9 But it's best to use the particular data for the steel being heated. 



#16
Mar2507, 10:39 AM

P: 46





#17
Mar2507, 12:41 PM

P: 46





#18
Mar2507, 02:44 PM

Admin
P: 21,637

OK  so billets are loaded in one end and drop out the other side. I take it they are loaded sideways, hence the furnace 12.7 m wide by 14.65 m long ( = 104 * 0.14 m). Well, the heat up and cool down times would be twice as long, roughly, assuming the heat transfer coeffient and hotcold temperature difference remains unchanged. What was the heat up time of the 100 mm sq billet? There is a lot of thermal inertia in the charge (billets which are already hot), which ~ 100 x the cold billet. So based on 104 billets, one being removed each minute, the soak time is ~104 minutes, so at least about 11/2 hrs soak time at temp. Has anyone used an optical pyrometer to measure the temperatured during cooldown of billet? 


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