Ok I have what I believe is a relatively simple calculation but I can't track down my equation and I don't have any textbooks at my disposal.

Working with a ceramic nozzle tip at 1250-1475 deg C which is attached to and Aluminum brace. I need to find the temperature of the ceramic 19-21 cms down the nozzle. I am only looking at it through pure conduction through the ceramic. the thermal conductivity of nozzle is 35 W/mk. Going to measure thickness soon. Can anyone point me in the direction of the equations or laws i need?

Thank You
Thor

Sorry correction. That is 1250-1475 K.

Doesn't Aluminum melt at about 670°C? So that would be the upper limit of the aluminum temperature. Conduction simply requires the thermal conductivity of the material, and its dimensions, for which you may need to do a heat spreading correction. Wikipedia gives you a start: http://en.wikipedia.org/wiki/Heat_conduction#Conductance
Lienhard has a free HT text: http://web.mit.edu/lienhard/www/ahtt.html

TTFN
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I fail to see the simplicity in this? It sound like FEM work to me?

How is the geomety of the nozzle? What is the ambient temperature of the surrounding medium? What is the temperature of the aluminium?

If your geometry is basic you may be lucky and somebody one did some nomogram like stuff or set up some fairly simple differential equation. But i dont recall any just now. I resently saw studies of a choke valve during start whith cold gas and high dP where the aim was to check temperature profile because of an unfortunate flange sealing material. That was pretty advanced stuff (at least to an engineer like me .

Best regards

Morten

You may need to be careful with this setup. You are using something close to a Aluminum Silica Ceramic which is relatively conductive (similar to carbon steel). Aluminum may melt at 660 C but many alloys turn to putty at 520 C and lose considerable strength leading up to this point. The ceramic thickness will be very important. This example should be helpful http://www.syvum.com/cgi/online/serve.cgi/eng/heat/heat1101.html

Comprehension is not understanding. Understanding is not wisdom. And it is wisdom that gives us the ability to apply what we know, to our real world situations

The temperature of the aluminum is what I was trying to find. Thank you for the responses. I was afraid of the temperature at the aluminum will be too high to operate safely. Thank you again.

You haven't provided enough information for anyone to even guess at what the temperature distribution might be, though.

A brute force approach might be to take the ratio of σ_cer/σ_al times the temperature delta relative to ambient. The result is the temperature at the interface assuming equal effective physical thermal path lengths. I get about 220°C with that, and the same numbers give a heat flux of about 29 W/cm²

TTFN
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I wasn't looking for someone to do it for me. I knew what I needed and was looking for some guidance.

I think the OP has a 21 cm long nozzle, tip at 1475 K, of some unspecified diameter clamped to an aluminum plate of some unspecified thickness, exposed to ambient, a perfectly doable problem,
He just wants minimum guidance to do it him/herself.

So far he/she hasn't gotten the help needed because of poor clarity of the description.

I would suggest that he/she post a drawing of the system to get the help.

I don't see how the OP can ignore the radiation heat loss/heat gain ... That hot at that close a distance, its going to be a larger percentage than "negligible".

But, I'm more used to the radiation heat transfer from the welding tip and arc, cooled somewhat by the gas flow around the nozzle and arc (MIG).

A point source at 1475 at a distance of 21 cm from a plate won't add much temperature to the interface.