Electrical Heating

[pbhuter]

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.

 

[IRstuff]

Is this for school?

TTFN

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Chinese prisoner wins Nobel Peace Prize

 

[pbhuter]

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.

 

[MintJulep]

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.

 

[pbhuter]

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

 

[IRstuff]

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/

http://www/ahtt.html

is free, as is OpenCourseWare:

http://ocw.mit.edu/courses/mechanic...ntermediate-heat-and-mass-transfer-fall-2008/

TTFN

FAQ731-376
Chinese prisoner wins Nobel Peace Prize

 

[quark]

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)

 

[pbhuter]

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.

 

[pbhuter]

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.

 

[IRstuff]

"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

FAQ731-376
Chinese prisoner wins Nobel Peace Prize

 

[pbhuter]

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.

 

[MintJulep]

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.

 

[flash3780]

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.

 

[pbhuter]

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.

 

[IRstuff]

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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Chinese prisoner wins Nobel Peace Prize

 

[pbhuter]

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

 

[MintJulep]

In Quarks's equation Energy out = 0.

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

 

[pbhuter]

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.

 

[IRstuff]

No, that particular example was a way to empirically calculate the htc from the measured delta_T and the applied power.

You really need to discuss this with your professor. This site is not intended for tutorials at this level.

TTFN

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[chicopee]

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.