# Evaluating furnace heating capacity.

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.

## Answers and Replies

russ_watters
Mentor
Well, the simplest approach is with the efficiency of the furnace (almost always about 85% non-condensing 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.

russ_watters
Mentor
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 non-trivial 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 85-95% 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.

Last edited:
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.

AlephZero
Homework Helper
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.

If you want to look up the equations, see the standard book by Carslaw and Jaeger, "Conduction of heat in solids". The solution is a Fourier series - FWIW Fourier invented "his" series to solve this type of problem.

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.

If you want to look up the equations, see the standard book by Carslaw and Jaeger, "Conduction of heat in solids". The solution is a Fourier series - FWIW Fourier invented "his" series to solve this type of problem.

Well, I guess first I´ll better grab my old book about Fourier series and try to remember those matters....

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?

AlephZero
Homework Helper
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?

Sorry, I don't have a copy right now otherwise I would scan you a page from so you can see for yourself. I haven't been working on heat transfer for quite a while, and I gave my copy of C&J to the guy who took over from me!

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 https://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).

Sorry, I don't have a copy right now otherwise I would scan you a page from so you can see for yourself. I haven't been working on heat transfer for quite a while, and I gave my copy of C&J to the guy who took over from me!

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 https://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).

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

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

Astronuc
Staff Emeritus
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?
That's a pretty good sized charge. I think most heat treat furnaces these days are electric, and given the length I would imagine one would want 4 or 5 controlled zones unless one is not too concerned with temperature uniformity.

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.

That's a pretty good sized charge. I think most heat treat furnaces these days are electric, and given the length I would imagine one would want 4 or 5 controlled zones unless one is not too concerned with temperature uniformity.

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.

The furnace is old (built in 1969). It´s of semi-continuous feed and discharge ( typically every 2 minutes you feed in two billets simultaneously, and every minute you discharge a billet at the time on the opposite side). Originally it had 2 rows of burners (gas/air) located above the charge, one row at approx. 2/3 of the lenght far away from the charging side, and the other row practically above the discharge zone. At that time the billet size was 100 mm x 100mm x 12.7 mts. (1 mton weight). The billets go side by side (contact along the full lenght) once they are inside the furnace. After years of operation, the billet size was increased to 130 mm x 130 mm x 12.7 mts. without any revamp in the furnace. It operated OK. But when the decision was made to go to 140 mm x 140 mm x 12.7 mts. and also to increase production rate from 100 mtons/hour to 120 mtons/hour, an engineering/construction company got the contract to do the job. They came out with a solution based on 8 additional burners, located below the billet charge, near the charging zone. They did a good job. The increased production rate is indeed reached, and exceeded.
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 non-expert 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.

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.

I forgot: the book has not yet arrived at my mailbox yet....

Astronuc
Staff Emeritus
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) * cp * delta-T (1150°C - 25°C), where cp is the specific heat, which is a function of temperature. Using sp. ht of 700, one billet require about 788 MJ.

At room temperature cp is about 450-500 J/kg-K, and at higher temperatures it increases to about 600 J/kg-K 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/kg-K) 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.

Are there thermocouples in the furnace?

Yes, as I remember at least 3; located on the roof.

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.

If we discharge a billet per minute, but we have 104 billets in the furnace, this means that we have 104 minutes to heat one particular billet....

Astronuc
Staff Emeritus
If we discharge a billet per minute, but we have 104 billets in the furnace, this means that we have 104 minutes to heat one particular billet....
Oh, OK, I got it now.

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 hot-cold 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 1-1/2 hrs soak time at temp.

Has anyone used an optical pyrometer to measure the temperatured during cooldown of billet?

What was the heat up time of the 100 mm sq billet?

The heat up time was 86 minutes...

You should look, I think, at books published by Jones & Laughlin, Carnegie, or US Steel. They used many similar furnaces over the years and put out material about these. The information is probably more practical than theoretical. Try Google Books for anything by these 3 companies. Certainly a BS in engineering is sufficient; we still have some steel mill retrofit outfits around and, for the most part, those folks are BS or MS.

Here is a link to a ppt file for heating of slabs

http://www.combustionsoftware.com/new_features.htm

select heating of bars. Hope this helps!

Sailer,

Thanks a lot. That software package seems to be capable of doing precisely the kind of calculations and simulations that I was looking for since almost a year from now. The time waiting was really worthwile...

Thanks a lot again