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Electrical Heating

Electrical Heating

Electrical Heating

(OP)
I'm looking for an equation that will give me the temperature of a heating element if I know the following:

- resistivity (in ohms mm^2/m)
- length (in meters)
- cross-sectional area (in meters or mm)
- power applied (in watts)

Do I need anything else? I'm trying to build a computer model. Thanks.

RE: Electrical Heating

(OP)
Nope, this is for an aerospace application I'm working to develop. I can't go into details because it's kind of sensitive right now. I could wait until August when I'm starting my next Master's degree and go find a professor to help me out, but this is easier and probably faster. I appreciate the concern about school work, though.

RE: Electrical Heating

You will need at least the following (assuming you are heating an airstream):

Emissivity of the element.

Emissivity of surfaces in direct view of the element.

Geometry and distances from element to surfaces in view.

Convective heat transfer coefficient between element and airstream.

RE: Electrical Heating

(OP)
MintJulep - I'm trying to calculate how hot the element will get. I have the information I provided in my first post. Thank you.

RE: Electrical Heating

I'm not sure how you are going to model this if you don't know enough about heat transfer to know that you were missing at least half of the critical parameters.  

Perhaps you need to download a textbook? http://web.mit.edu/lienhard/www/ahtt.html is free, as is OpenCourseWare: http://ocw.mit.edu/courses/mechanical-engineering/2-51-intermediate-heat-and-mass-transfer-fall-2008/

TTFN

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RE: Electrical Heating

Mass and specific heat of material, duration of power applied and initial temperature of the material.

Use Q(kW)*T(sec) = m(kg)Cp(kJ/kgC)(T1-T2)(C) to get the maximum temperature (if you have to get actual temperature, you should consider convective and radiation losses)

RE: Electrical Heating

(OP)
IRstuff: For my model, I intended only to increase power (in watts) to see how the temperature increased. I know this is a very simple approach because as temperature increases, resistivity will decrease. I'm just trying to figure out how hot a material (with a given resistivity in Ohm-mm^2/m) will get when power (in watts) is applied. Maybe this isn't a thermodynamics question as much as it is an electrical engineering question?

quark: I don't have the specific heat, I have a resistivity. I'm basically building an electric heater and I need to know, based on the resistivity of the material, how hot it will get when power is applied.

RE: Electrical Heating

(OP)
quark: Found Cp for my material. How do I account for the fact that it will eventually stop heating up? I know I can't just apply power and have it heat to infinity.

RE: Electrical Heating

"temperature increases, resistivity will decrease"  ??? Resistivity in most metals used for heaters INCREASE as temperature increases.

What exactly is your academic status?  For someone supposedly doing a Master's program, you seem to not know conservation of energy.  I repeat my suggestion that you review the fundamentals of heat transfer.

TTFN

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RE: Electrical Heating

(OP)
IRstuff - I'm specifically talking about ceramics, not metals, but I know it increases for metals. I took one thermodynamics course seven years ago and have never used it since. I intend to look over the material you provided me, thank you.

RE: Electrical Heating

If you "know" the power applied in watts than resistivity, conductivity, and any other electrical characteristic is redundant.

Energy in = Energy out + Energy stored

Energy stored is temperature on specific heat capacity.

For energy out you'll need the parameters that I listed above.

 

RE: Electrical Heating

You need to figure out both the electrical energy entering the heater and the thermal energy leaving the heater to determine its temperature. The power entering and the thermal power leaving will balance at the steady-state temperature. See if you can't find a copy of Incropera and Dewitt; it's a good reference for thermal problems.

RE: Electrical Heating

(OP)
MintJulep - watts doesn't equal temperature. I used quark's equation and got a result. I'm now wondering the limit of that equation...I can't heat infinitely.

RE: Electrical Heating

Quark's equation is for Joule heat only, and is not applicable to your specific question.  I suggest that you look up heat transfer in Wikipedia, if nowhere else and adhere to energy conservation: http://en.wikipedia.org/wiki/Heat_transfer.  Of particular importance are radiation: http://en.wikipedia.org/wiki/Thermal_radiation
and convection:
http://en.wikipedia.org/wiki/Convective_heat_transfer

TTFN

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RE: Electrical Heating

(OP)
Thanks IRstuff. I'm going to go look at the book you posted.

RE: Electrical Heating

In Quarks's equation Energy out = 0.

As Quark correctly noted, you need to consider convection and radiation.

RE: Electrical Heating

(OP)
I found an solution to my problem in the book IRstuff posted (Example 2.8), however it involves an h-bar. At the beginning of the book is a calculation:

h-bar = q/delta-T

where:

q = power/area

Can I use:

input power/area of element

in the calculation of h-bar? So say I have 4000 W going into an element of 4.7124E-3 m^2, so q = 8.4882E5 W/m^2, and delta-T = some theoretical maximum (say 1850-dec C) - some theoretical starting value (say 20-dec C), so delta-T = 1830-deg, giving an h-bar of 463.8361. I then calculate T = 1404.6K (using the calculations in Example 2.8), which I plug back into my delta-T and iterate to get a final T = 1271.4K = 998.4-deg C.

Does this make sense? Am I doing this correctly? The example iterates a temperature in calculating h-rad (again, I use the same theoretical maximum of 1850-deg C and a minimum of 20-deg C to do this and iterate with the 1404.6K), so that's how I came up with the idea to use theoretical values for the h-bar calculation and iterate. Thanks for the help with this.

RE: Electrical Heating

It should be a relatively  easy problem if you took heat transfer, however, you have defined the problem well. For instance your OP did not state that it was ceramics  you were heating; secondly you have not defined the size and position (horizontal, vertical,slanted, curved) of the ceramics; thirdly is the ceramic emitting on both sides or only one and what about the heated space or objects,what are they and how foar are they.  Then you can start applyings the principles particularly those involving ratiation and convective heat transfer as aluded in the above replies.

RE: Electrical Heating

(OP)
I'm not in school at this time. I'm not sure if I will be going back to school in the fall. I appreciate the help I have received so far. If I do enroll in classes in the fall, I will hunt down a thermodynamics professor and talk to them.

RE: Electrical Heating

You should discuss your problem with a heat transfer professor, not a thermo. one.

RE: Electrical Heating

(OP)
Thanks chicopee. I'll look into it if I go back to school in the fall.

RE: Electrical Heating

I love chicopee's answer- all well thought except for that those obvious missing words- substitute understood for took and ...have NOT defined.....  
"It should be a relatively  easy problem if you took heat transfer, however, you have defined the problem well. For instance your OP did not state that it was ceramics  you were heating; secondly you have not defined the size and position (horizontal, vertical,slanted, curved) of the ceramics; thirdly is the ceramic emitting on both sides or only one and what about the heated space or objects,what are they and how foar are they.  Then you can start applyings the principles particularly those involving ratiation and convective heat transfer as aluded in the above replies."

RE: Electrical Heating

(OP)
chicopee and cloa -
I am heating a ceramic element that is a tube folded in half. It will be emitting on both sides, but one side will be close to a wall. I know the emissivity, the thermal conductivity, and the specific heat capacity. What additional information do I need to solve this problem? Thank you.

RE: Electrical Heating

How is the heat being applied?  How "close" is "close to a wall?"
What comprises the wall surface (standard wallboard, or is it a metallic component?)

Cloa also mentioned other factors that need to be considered.

Is it possible to provide a sketch so we're all speaking to the same problem?

Otherwise, is this something where you can build a prototype and test?  Being able to input real data into a program should make it easier to model the component's behavior under other conditions.

 

Patricia Lougheed

******

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