heat transfer rate

[MRSSPOCK]

Hi.

This question has probably came up many times, so hopefully someone can direct me to a relevant thread, or elsewhere.

I just want a very basic rule of thumb, or a basic chart, which gives a rough estimate of how long it takes to heat up a piece of metal, while sitting in hot air, i.e. air without a circulating fan.

I realise this is a very complicates subject as regards the calculations, but I'm sure there is a simple way to arrive at an approximation?

Suppose for example a 20°C, 3mm thick mild steel plate, 1m x 1m placed in air at 500°C.

How long does it take the plate to reach 500°C throughout, i.e. both sides of the plate are exposed to the same 500°C air temperature.

I did find a calculator here,

http://www.faculty.virginia.edu/ribando/modules/OneDTransient/index.htm

but I have no idea how to use it.

I was hoping for something more basic.

Thanks

 

[racookpe1978]

How much basic heat transfer theory have you had?

Remember: NO Homework nor schoolwork here.

How accurate an answer do you need?
What geometry is the thin-walled plate - Horizontal I guess, right?
The hot gas is not moving, but what keeps it hot? Are you assuming the hot gas cools down as the plate heats up? Or does the hot gas get slowly replaced so it stays at a constant temperature somehow?
When the original plate at 20 deg C is put in the hot gas, are you assuming the gas doesn't leak out, or do you have to re-heat the gas as if the plate were on a conveyor belt?
What "gas" is in the room? Hot air? Combustion products? Nitrogen? CO2?

Use this link, then register to use the Maya Heat Transfer calculator.

http://www.mayahtt.com/maya-support/thermal-wizard

 

[IRstuff]

To the first order, it cannot be any faster than thermal mass divided by natural convection heat flow.

TTFN
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[willard3]

Rules of thumb will bite you in the butt. You will have to do the thermodynamics.

 

[chicopee]

"... You will have to do the thermodynamics." willard3, I think that you meant: You will have to do the heat transfer.

 

[chicopee]

3mm is pretty thin so I would venture a guess of under 2 minutes.

 

[racookpe1978]

Well, technically, the plate will never reach "exactly" 500 deg if placed in still air at 500 deg, but it will get very close in only a few minutes.

Based on a 1/2 mm steel cookie sheet placed in a 500 F deg oven, you actually need longer to re-heat the oven back to 500 deg F (after opening the door, loading the cookie sheet, and re-closing the door) than you need to heat the cookie sheet from room temperature to the current oven air temperature of 480, 490, or 500 deg. In the real world, I'd assume the oven was a continuous-loaded oven heated from below with a mix of forced and natural convection - the trays loaded on a roller or conveyor belt.

But what accuracy, how "close" to the 500 deg does he really want/need/care about? There will always be a little bit of thermal lag between air and tray since the tray has mass, and forced convection or radiant transfer is not in the problem statement for some reason. (At 500 deg C walls, there will be a lot of that!)

Therefore, his problem cannot be solved in the real world given the little information provided. 8<)

(Are all school textbooks this bad at asking word problems as they try to relate to the real world? )

 

[MRSSPOCK]

I'm not really trying to split the atom.

I think the general tone of my initial post made it very clear that I was only trying to find a rule of thumb. How a rule of thumb is quantified is anybodies guess, but it is a term that has been around for years and is generally interpreted by assessment of the context in which it is written.

I didn't ask anyone to do anything on my behalf, such as HOMEWORK. I merely asked for someone to point me in the general direction where I might find more help.

The example given was purely hypothetical, and was given solely to help provide an idea of the scale of things I had in mind. (Okay, I should have noted the plate orientation).

My question didn't even ask anything about the surroundings or the source of the heat, because that was nothing to do with the what I wanted to know. The idea was to assume a limitless supply of 500°C air.

I purposely kept it simple to avoid complications which seem to have been introduced unnecessarily.

Yes, they're important if you want an accurate answer, but as I said, the context of the question makes it clear that accuracy wasn't a big issue.

I did state hot air, so no need for the question about nitrogen etc.

I imagine someone will understand what my question means.

I'm not in a position to go study thermodynamics to get a better understanding, hence I came to eng-TIPS, to find a a few TIPS, as the name would suggest.

Not to get accused of wanting someone else to do my HOMEWORK and solve my hypothetical question.

Give me a break.

 

[IRstuff]

again, thermal mass divided by natural convection heat flow provides a lower bound

TTFN
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[FredRosse]

"Suppose for example a 20°C, 3mm thick mild steel plate, 1m x 1m placed in air at 500°C.......................How long does it take the plate to reach 500°C throughout?"

In fact, it will never reach 500C, that answer is exactly correct, and the only solution for which a correct answer is found based on your question.

In practical terms, since you are probably not looking for the mathematically correct answer "it will never reach 500C", I aasume you mean "very nearly 500C"?? This example will have several answers depending on boundary conditions. Getting to 400C, or 450C or 495C, or 499C ,any of these temperatures might (or might not) be considered "close enough", but each would have far different answers.

Beyond this example, how about a piece of mild steel that has the same mass, but is about 150mm diameter and 150mm long. That piece would heat up at a far slower rate because it has far less heat transfer surface area.

So the answer is, there is no simple rule of thumb here, too many relevant variables to allow simplification. With an oven held at exactly 500C, you could put a piece of metal into the oven, and it would reach 499C in a few seconds (a thin piece of wire), and put another piece of metal into the same oven, and it would take days to reach 499C (a 20 ton steel ingot). That is not to say that the 20 tons of steel would always heat very slowly, for example if the 20 tons of steel was in the form of very thin sheet metal corrigations, with plenty of surface area exposed to the environs of the oven, then it might heat up as quickly as the thin piece of wire.

 

[DmitryKalganov]

I propose to use a simple rule - split heating time into several intervals. Why there is no overheating of the coolant? workpiece will be heated for a long time