Heated Plate In Air

[rjsfocus]

I am trying to model a system and so far haven't been able to do exactly what I want. I have a plate, heated by electric heater cartridges, about 4000 watts total. For now I will assume the surface temperature is the same as the internal temperature, unless anyone knows of a good way to do that. The plate is in air, no air flow. I know that an object in air that is cold will decrease by:
dT/dt=kA(Tobj-Tair). What I don't know how to do is find the temperature of the plate when an internal heat source is added. I am thinking it is similar to that of a car going against the force of drag in air, but I don't know the equations.
Similarly, I was hoping to see if I can model the change in air temperature around the plate too. When the plate is heated, the air temperature changes as well, effecting the plate temperature. This may be a little too complicated, but I haven't found much out there so far.
Any help would be great, I appreciate it.

 

[IRstuff]

What exactly are you trying to calculate? Is this a transient or steady state problem?

TTFN
faq731-376

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[rjsfocus]

I have a heat plate that is used basically to melt plastic, and I need it kept at a relatively constant temperature, so the surface temperature is what I need. It isn't really steady state. It is like an oven, energy is supplied until a set temperature is reached, then turned off to a set point, then turned back on. It never reaches steady state, and I plan on doing a Simulink model once I know the calculations. I just can't figure out how to link everything together.

 

[IRstuff]

If it's under control, then the temperature ought not be moving a whole lot, so it could be treated as steady state. Otherwise, you are simply looking at using the heater to replace the lost heat content. The timing and amplitude is part and parcel to the control loop, so you should be talking to your control loop guy.

TTFN
faq731-376

Need help writing a question or understanding a reply? forum1529

 

[rjsfocus]

I was hoping to model the response under a number of different parameters. Such as, how well does it respond to when it is larger, more surface area. Or if the temperature of the air is different. it is more of an excersise of designing it and modeling the system before we build it so we have an idea of what we are looking at. Is there any equation/calculation that can be derived to show an object in air that is given an energy and cooled at the same time?

 

[dvd]

A few comments:

1. A plate in air will be exposed to air flow due to natural convection.
2. A plate in air will radiate to other objects.
3. The plastic material will require energy to melt, and thus will affect the plate temperature.
4. If the plate surface temperature is not controlled the plastic nearest the plate may become too hot before the outer plastic softens.

 

[rjsfocus]

Thanks for the comments, those were parameters I was thinking of using but I am just not sure how to use them. Would there be a way to determine how much energy is used when melting the plastic, and how much the temperature of the plates drops? I know the cycle time of the machine, and it would be great if I can model how the temperature reacts when we are running the line faster than we should.

 

[IRstuff]

It seems to me that this appears to be backwards, i.e., you appear to be doing analysis without doing a design first, and without identifying the requirements first.

TTFN
faq731-376

Need help writing a question or understanding a reply? forum1529

 

[rjsfocus]

What is going on is we have a design already in place in the plant. Its basically a large plate with a set of heater cartridges inside. We have problems keeping the temperature steady when trying to run the line. I am changing what I originally wanted to see. What I am curious of is how fast the temperature rebounds after each time it comes in contact with the plastic. I know how much energy is put into the plate, and I'm curious to see how much is removed when it comes in contact with the plastic. If I can get really creative with it, I can model it all in Simulink, using a step and switch command to turn on and off the heater, while also putting in features for the plastic melt as well.
For now, I am just curious to the plastic contact. What happens to the temperature when it comes down onto the plastic, or specifically, how to model that temperature drop.

 

[rjsfocus]

I am going to start from scratch on this one now. Just to start, I want to see how hot my plate can get with constant energy. If 4000 watts is applied to a plate, of volume V and Area A, in a steady state temperature of T, how hot can it get, and over what period of time?

 

[racookpe1978]

Check the Mayan web page: They have some pre-defined heat transfer problem pages that you can input your parameters in: still air, vertical heated plate, room temperature, etc and the calculator will figure out the convection, radiation, and Nusul;t numbers, etc.

 

[rjsfocus]

I'm not sure what the Mayan web page is?

 

[ione]

http://www.thermal-wizard.com/tmwiz/default.htm

Regards

 

[rjsfocus]

This is my understanding so far. I can cool an object, the equation dT/dt=kA(Tplate-Tair) can be integrated and I can see what happens when the heat is turned off, and there is only cooling of the air. But what happens when I turn the energy back on. I know that qcond=Q/t, where Q=MC(T(t)-Tinitial). T(t) is the temperature at some time T. If solving that alone, you get the equation. Assuming Tinitial=Tair, you can solve T(t)=(qcond*t/MC)+Tair. I just don't know how to link the two together. The best analogy is the force of a car against the force of drag, but I haven't figured it out yet. I'm expecting a curve of temp over time to be a basic curve, reaching steady state at some temperature. Any ideas would be greatly appreciated.

 

[chicopee]

You should calculate the Boit number and if it turns out to be less than 0.1 then you can assume the temperature distribution thru the thickness of the plate to be uniform. So when you melt plastic, probably around 350dF, the surface and internal temperature of the plate will drop slightly but should remain somewhat uniform throughout the thickness. That equation yours, Q=MC(T(t)-Tinitial),is time dependent and s/b represented as Q=MC(T(t)-Tinitial)/dt and that should be equal to the heat input to the plat minus convective and radiation heat losses and minus the heat absorbed by the plastic. To further reduce the temperature fluctuation during the process, you should consider increasing the mass of the plate which will change the Boit number to a new value.

 

[MisterE2]

you seem to be going back and forth a bit about the effects of air and the effects of the plastic applied to the metal plate. The air doesn't affect the temperature of the plate anywhere near the amount the plastic does, you're comparing convection at low temperatures with no air flow to conduction at low temperatures. Why not simplify a bit and say, the air has little effect except on very high temperatures and the plastic is treated as a thermoplastic, can be remolded, so no extra energy expended from denaturing. From there, estimate the volume of plastic melted, the plate volume, and do the following to calculate the rebound time, 4000W to 4000J/s
Tnew = Told + Cp*Vplate*Power*Time

now, if you want to add convection effects do a very low airflow over the plate and subtract the heat flux

 

[prex]

Your equation dT/dt=kA(Tobj-Tair) is wrong. Should be Q=kA(Tobj-Tair) , where Q is the amount of heat (energy) per unit time (so it is a power) required to keep the object at Tobj (k being power per unit surface per degree of temperature).
To account for the heat absorbed by the plastic you need to know the mass you melt per unit time (as it is a batch process, this will be an average value) and the amount of heat required to heat up and melt a unit mass of plastic (you'll likely find this in a material data sheet). Add this power to Q above and you get the average power required by your process: the heating system should be capable of delivering at least this power (likely with the addition of a substantial margin).
If I understand correctly your problem, this should be what you are looking for.

prex
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