What is the temp of this? I need an equation.

[ducatidd]

Hi everyone, and thanks for looking at my problem here.

Please view attached pic which shows two bodies sitting at a distance "R" from eachother, first the rectangle is at 100C degrees and the circle is unknown, my question is there an equation that will help me find the temp. of the circle as a function of "R"?
Thanks
A

 

[zdas04]

Is the question for a High Scool Physics class or a College Thermo class?

David

 

[IRstuff]

"is there an equation that will help me find the temp"

Yes, there are lots of them, start here:

http://en.wikipedia.org/wiki/Heat_transfer#Newton.27s_law_of_cooling

TTFN

FAQ731-376

 

[ducatidd]

first, thank you for the comments guys.
its actualy neither high school or college, its a problem that iam facing at work, i have these two bodies that iam trying to find a relationship between them in a function of thier distance from eachother. there is air between them so they are in conviction if u think about it, however, the conviction effect is so minimal due to the low air velocity however, radiation is what's really effecting it. anythoughts/
Thanks

 

[JKEngineer]

If you restrict the exchange between them to radiation, then the equations for transfer between them "simplify". ("" means: sort of) You need to deal with the emissivity of each surface and the view factor between them. In addition, assuming a steady state condition, you will need to write the equations for the circular body's dumping of heat back to its surroundings. This would be both convective and radiative losses. They will depend on the thermal conductivity and size of the circular object. The convective will also depend on the temperature of the surrounding air at the circular object. You will also have to include re-radiation from the circular object to the world, both at its front and at the back. All this assumes that the source temperature is "fixed" - that is, it has enough energy supply to maintain the 100C.

Given the physical properties and dimensions, this is doable, altough could get tedious.
Jack


Jack M. Kleinfeld, P.E. Kleinfeld Technical Services, Inc.
Infrared Thermography, Finite Element Analysis, Process Engineering

http://www.KleinfeldTechnical.com

 

[IRstuff]

Your comment about convection is only partly correct. Convection is a actually a combination of conduction of heat from the surface to the medium, and the medium's buoyancy causing the heated medium to rise.

If R is sufficiently small, you get direct conduction. A slightly larger R results in some mutual convection. Only beyond those two conditions would you be safe in ignoring convection transport to the second object.

However, depending on the material of heated part, you can get sufficient convection cooling to change the radiated energy, so CAVEATs abound

Furthermore, you have not specified what the boundaries of this system are, how far away they are, etc.

TTFN

FAQ731-376

 

[ducatidd]

Well the issue here is I am trying to measure the distance between both the rectangle and the circle, however, due to the extreme temperatures the rectangle is usualy at, I cann't place a sensor to measure how far the circle is from the ractangle, so what I thought of doing is measing the temperature differential and based on that i will be able to find the distance R.

In terms of boundry conditions. imagine if the circle is sitting inside of a furnace, where the rectangle is a huge heat sink, and the temperature is always constant at that surface. The circle would be your temperature sensor here. there is no air movement iside of that furnace, thus in my opinion convection can be voided.

thanks for ur help guys, let me know what u think of the above.

 

[JKEngineer]

ducatidd,
You really need to tell us more.

What approximate distances are involved, what sizes. What temperatures are we dealing with? You say the circle is in the furnace and the rectangle is a heat sink. Then you say that the temperature of the rectangle is too high to deal with.

What type of access is there? Measurements can be made from outside, perhaps.
Jack

Jack M. Kleinfeld, P.E. Kleinfeld Technical Services, Inc.
Infrared Thermography, Finite Element Analysis, Process Engineering

http://www.KleinfeldTechnical.com

 

[Twoballcane]

I think what you are looking for is qtotal=qradiation+qconvection. qradiation is straight forward, but qconvection can be tricky because to find the heat transfer coefficient is a iteration calculation. I guess in short there is no one simple equation. If you want to further this analysis, I suggest getting a heat transfer book and go head long into the theories.

Good luck!


Tobalcane
"If you avoid failure, you also avoid success."

 

[ducatidd]

Guys,

• The rectangle is a furnace (hot plate, heat source....etc ), I threw in the 100 C as an example but in fact it's around 400C degrees.
• The circle is suppose to be my temperature sensor.
• The distance between the rectangle and the circle (my temp. sensor) varies between 2mm-20mm.

What I am basically trying to do, is place a sensor above the rectangle where the heat is coming from, and based on the readings signal that I receive from the temperature sensor, I could then calculate how far they are apart. Unfortunately, I can't physically go in and measure this distance due to the high temperatures, so I thought this would be an alternative method measuring that distance "R".
Thanks,

 

[JKEngineer]

I don't think it has any chance of working.

Your distances are NOT so large as to be able to neglect convection.

I am sure that there are physical methods to measure the distances.

Jack

Jack M. Kleinfeld, P.E. Kleinfeld Technical Services, Inc.
Infrared Thermography, Finite Element Analysis, Process Engineering

http://www.KleinfeldTechnical.com

 

[IRstuff]

I agree with Jack. Your sensor of choice cannot be used to estimate distance.

What exactly is the intent? What difference does it make what the distance to the sensor is? If the intent to "calibrate" the sensor, then you're using the wrong sensor. Perhaps an infrared pyrometer would be more appropriate.

I recommend that you explain what you're trying to accomplish, and maybe, there'll be a more direct solution to the actual problem, rather than to deal with your point solution.

TTFN

FAQ731-376

 

[ducatidd]

My intent is to measure that distance "R", however, I am not able to do so because it is inside of a furnace so I thought maybe I could measure the temperature differential by placing a temp. sensor (the circle in the diagram) and from there I could find the distance.
Thanks

 

[Twoballcane]

I think you are thinking of Fourier's law for conduction where, if you wanted, you can find what temp at a certain distance within the solid. However, radiation and convection are different. Radiation depends on the emissivity factor and the temp of the body and the nearest body. Convection depends on the heat transfer coefficient surface temp and ambient temp. Distance (or your R), I think, is not a factor.

Tobalcane
"If you avoid failure, you also avoid success."

 

[IRstuff]

What is the significance of the distance you're trying to measure, and what accuracy are you looking for? How how will the sensor location get?

> laser on fiber-optic?

> proximity sensor?

TTFN

FAQ731-376

 

[Zoobie]

I think you missed the point of IRStuff's recommendation. Why do you need to know the distance? What kind of furnace is this? You are unable to place a distance measurement device in the furnace yet you seem to be able to place a temperature sensor inside. Why is this?

There are numerous types of instruments that can measure distances

 

[ducatidd]

Guys,
Thank you much for all of ur comments but due to the confidentiality of this project, i am unable to disclose more info on this type of project, however, i could tell u that a temp. sensor is very easy to find and use for appl;ications that run at or around 500-600 C, thus i was thinking if i use a temp. sensor to measure the temperature and based on that I could calculate the distance then it would help me avoid using proximaty sensors.
thanks

 

[Bribyk]

This "could" be done but your method sounds very difficult to get an accurate distance measurement. Temperature is probably the most difficult variable to measure accurately and you would have to control a lot of variables very carefully to be able to correlate temperature and distance. Surely there's an easier and more accurate method available...

 

[racookpe1978]

If these two parts are in a furnace you KNOW the distance between them. They aren't going to move between the time of placement, and the time of removal - unless they are on a bed traveling through th efurnace. If so - problem is still soluable: the realtive distance between is going to be known - because that won't change with distance travel through the furnace.

If radiation between the two is a concern - place a plate of reflective (bright) metal between the two and separate them thermodynamically. If one has to retain heat that is being to the second - same solution. If one is heating up the second too much so the second is being damaged in some way - run them at two different shifts, or in two different batches, or with a second pice of the same type so both of the same parts get the same treatment with no loss of production time.

Solve the problem, don't try to spend a lot of time calculating something you can measure. You claim that measuring temperature with a probe is simple, and maintaining temperature (of the parts) is what you need to do. These is little else that needs to be "calculated" - when the absolute best you can theorectically calculate for a perfect part in a perfect world in a perfect furnace is - at best - merely an approximation of the "real temperature" that you should measure "for real" .

 

[IRstuff]

Bolts are cheap and easy to find, as well, but they won't do the task.

In all your postings, you've yet to actually specify the accuracy and range of the distance measurements you apparently want. Until you do so, you're not going to get much in the way of meaningful answers.

TTFN

FAQ731-376