Plate heat loss

[melvrohack]

I have a problem where I need to write a simple program to estimate the temperature of a steel (stainless & Ti) plate ranging in size from W:80-100" L:100-400" H:0.25-2". The surface temperature of the plate is measured as the plate is initially placed on a cooling bed. There is no forced air flow. The plate needs to cool to a desired temperature (200-500F) before the plate can be removed from the table. The table is a series of parallel steel bars ~2" thick, spaced ~2' apart. Is there a simple equation that can be applied to estimate the time required to reach a target temperature.
Thanks
Rick....

 

[IRstuff]

nope,
thanks.

Is this homework?

TTFN

FAQ731-376

 

[melvrohack]

No, this is a processing line where I need to ensure the plate has cooled done to an acceptable temperature (material handling requirements for Ti and contact with rubber suction cups Ti & SS). I am sure that the program could be imperical with a bunch of lookups, but I would prefer a manageable "model" with material specific constants.
thanks

 

[MintJulep]

If it's really important, wouldn't it be better to simply measure?

 

[melvrohack]

The piece has to "walk" on the table to an exit position. The rate of the walk it determined by the cooling time required. Plus the mechanics of the equipment do not permit a pyro at the exit postion(s).
Thanks

 

[IRstuff]

There are going to be several components:
>> radiation to surroundings
>> convection to air
>> conduction to rollers

There are lots of heat transfer books that can help you. There's even a free one, online:

http://web.mit.edu/lienhard/

http://www/ahtt.html

TTFN

FAQ731-376

 

[prex]

As the boundary conditions to the plate are essentially always the same and only the dimensions and the mass vary, you could take a simple model where the plate is considered as having a uniform temperature.
The equation is:
cMdT=hATdt
where
c=specific heat of material
M=mass of plate
T=temperature difference of plate with respect to the surroundings
h=heat transfer coefficient
A=surface of plate (both faces)
t=time
This equation easily solves into an exponential that allows to calculate the time for going from a given initial temperature to a colder one.
Of course the problem is that you don't know h, you don't know the temperature of the surrounding, and someone might even say that assuming a linear relationship for the heat exchange is arbitrary, as radiation exchange is important in this case.
However:
-the assumption of linear exchange will be certainly acceptable
-you should give a good estimate of the (average) temperature of the surrounding: I guess that 30 to 50°C would be a good guess, assuming there is no enclosure around the plate
-if you can measure the cooling rate for one or two plates then you are done, determining h from measurements.
You'll get something that will work probably better than any complex thermal calculation based on what can be found in books.

prex

http://www.xcalcs.com

: Online tools for structural design

http://www.megamag.it

: Magnetic brakes for fun rides

http://www.levitans.com

: Air bearing pads

 

[corus]

You must live near the equator prex! Generally the surroundings are taken to be about 20C where I am. For a heat transfer coefficient use a value of about 10-12 W/m^2 K as a rough figure. As prex says the actual value is non-linear due to radiation and natural convection terms in the true value of h.

corus

 

[prex]

corus,
my assumption of 30 to 50°C is because there is a likely non negligible exchange through the supporting bars, and this will appear as done towards a hotter temperature.
The same holds for the heat exchange coefficient: the measured value should be higher than 10 W/m²°K due to the exchange though the bars. I don't expect however something in excess of 15 W/m²°K.

prex

http://www.xcalcs.com

: Online tools for structural design

http://www.megamag.it

: Magnetic brakes for fun rides

http://www.levitans.com

: Air bearing pads

 

[SylvestreW]

While a calculation will give you a realiable bracket, if you truly want to optimize the process, direct measurements and statistical analysis will provide a much better level of comfort and reliability.
just my $0.02

 

[melvrohack]

Thanks for the information! I will study the suggested doc's and see what I can come up with (should be a challange for a "dumb" EE).

One quick question, the plates are laying horz. Can I assume that both sides cool equally. There is no forced air due to Ti metallurgical reasons (sorry don't know why, just adhearing to requirements specified by metallurgists.

I did some investigation about temperature measurement, and a pyro is available, but the pyro is used as a safety device to protect the equipment and the temp specs are not within the required range for the metallurgical requirements. Software is cheaper than engineering a measuring system and associated maintenance with such a device. I agree that a pyro might be the most optimal solution, and will keep that in mind should calculations not be adaquate.

Again,
Thanks

 

[IRstuff]

There's no way that software is going to get you the correct answer under EVERY single possible environmental condition. A pyrometer or even a thermocouple will give you real-time and exact temperature and allow you determine the movement rate of the slab.

TTFN

FAQ731-376

 

[IRstuff]

see:

http://www.tufts.edu/as/tampl/en43/lecture_notes/ch5.html

TTFN

FAQ731-376

 

[prex]

rohack,
I would say that if you cannot make at least a few sample measurements, you won't go far and will be left with uncertainties in the order of 100% for the travel time.
More: if there are safety concerns connected with the withdrawal af a too hot plate, then I guess you'll need a check by reading the temperature at the end.
So you should seriously consider doing all that with one or two pyros.
If you really need to tightly control the travel time, there is a mixed solution, than can solve both your constraints: guess a travel time before starting and no pyro at the exit.
You can put a pyro at mid distance, another one at the start position (but this one is not necessary if the starting temperature is constant or known): then start the travel with a speed calculated as I proposed above taking h=15 W/m²°K for the whole surface of the plate (see below), check the resulting temperature at mid distance and adjust the speed for the second half (or stop the movement for a while). This procedure will also allow you to adjust the value of h by the readings, guessing a better starting speed with experience.
Concerning the exchange on the lower face, then of course, as the reference by IRstuff confirms, convection is almost absent there. However radiation is still present and it adds for more than 50% to the total exchange at your temeperatures. Also on the lower face you have the supporting bars, that, depending on how they are supported and connected to their supports, contribute to the exchange...
Trust me, this is a complex phenomenon (like most heat transfer problems) and a detailed calculation won't give you much.

prex

http://www.xcalcs.com

: Online tools for structural design

http://www.megamag.it

: Magnetic brakes for fun rides

http://www.levitans.com

: Air bearing pads

 

[unclesyd]

Since it appears that you don't need the accuracy of the higher accuracy IR Pyrometers, you might want to look at the hand held models used by the all the racing teams and hot rodders. For about $150.00 you can get a very good one or two mediocre ones.

The software that we used for very similar type of heat transfer studies was from Fluent. You could purchase a very good IR setup for far less than the cost of using this software, very very good but expensive.

 

[sailoday28]

If one follows the path of a particle, or say a lumped mass with constant density and specific heat then an energy balance is
rho*C(DT/dt)= net Q (1)
rho=density, C= specific heat,
T=temperature, t= time, and Q=heat transfer + to partice and negative from particle Q= Q(t)

But DT/dt= partial of T wrt time + u patial of T wrt x (2)
u= velocity and x spatial coordinate. u=dx/dt

Does this make sense to the readers? If not, I will not pursue where I'm headed.

 

[sailoday28]

Units of Q USA units BTU/hr/unit volume

 

[MintJulep]

Unclesyd's mention of CFD triggered a memory of a presentation I attended some years ago.

Look into Proper Orthogonal Decomposition. It's a cool technique that allow you to transform the solution of a complex numerical model - such as CFD - into a much simpler alegbraic model, suitable for real-time calculation.