Predicting Temperature of PolySi Ring with Current Input

[chenxianghao]

Hi, I am working on a project that involves some electrical expertise. I am actually mechanical in training.

Anyway, the situation is that I have a polySi ring that I am going to heat up using a certain amount of current. Is there a way that I can predict the temperature of the ring with the value of the current? I know the resistance and resistivity of the polySi.

To put it simply, is there a way I can know the temperature of a certain object by knowing the amount of current input into it?

Thanks in advance!

 

[Gokul43201]

You would need to know some additional details - what is the temperature and the nature of thermal contact to the surroundings, what is the thermal conductivity (and specific heat, if you care about transients) of the polySi ring, what are its dimensions, and is there any airflow? In the case of current densities that are large enough to make the ring very hot, you need to also know if there's any surface treatment that determines the emissivity.

In essence, you want to balance the heat generated from the current with the heat lost to the surroundings through conduction, convection and radiation (the latter can be neglected if the ring temperature does not increase by say, around 100C). And this is not a simple calculation, even for a simple geometry, especially since the resistivity of polySi is a temperature dependent value (i.e., you have to solve a pair of coupled differential equations subject to various boundary conditions). The method of choice for a problem like this is to resort to a finite element computation using a platform like COMSOL or ANSYS.

 

[chenxianghao]

Hi Gokul! Thanks for the reply!

Let's assume that it is a perfect conductor for now. So all the current that goes into the ring is used for heating. Is there a certain formula that we can relate the Current I and the Temperature reached by the ring?

I am not able to to know the amount of heat lost to the environment (through either convection or other method), I do not have the necessary equipment to do the measurement. I do have a thermometer (a concentric ring which is bigger then the heater) measuring the temperature emitted, what I want to know is whether this temperature (that is recorded) is accurate per say by my calculation, if there is one that I can relate the current to the temperature reached in the ring.

 

[sophiecentaur]

Hi.
The answer to your original question is, basically, NO, I'm afraid.
The maximum temperature it reaches after switch on will be when the electrical power supplied is balanced by the heat lost. The heat lost depends not only on surface temperature but how easily the heat can be taken away. Just think of the temperature reached by a 3kW (say 13A) water heater element (around 100C), compared with the temperature reached by a 100W (0.5A) lightbulb filament (3000C).
You really couldn't predict what temperature your ring will reach without some actual tests under the conditions you expect it to experience. Gokul43201 stated it in a more academic way but you don't seem to know the conditions in enough detail. If you are after a particular temperature, you could stabilise it by using a thermal regulator.

(Btw, the important quantity is Power not Current; the volts count!.)

 

[Carl Pugh]

If you assume all the heat goes into the polySI ring, then joules into the ring is E*I*time. This will be true if the ring is heated before energy can be dissipated. Milliseconds or maybe seconds.

If time is seconds or minutes, you can calculate the maximum temperature rise possible and then the actual temperature rise will be something less.

Then using Thermal Capacity/Specific Heat, calculate the temperature rise.

 

[sophiecentaur]

That's a good point. As long as you're not talking about constant conditions you can say that
(Energy in) =(Thermal Mass X temperature rise) before any heat is 'lost' to the surroundings.
I have a feeling it will only be a useful answer if you are intending to be brief, though.
Don't forget, you still need to know the Power not the Current, though.

 

[Gokul43201]

The problem with this (adiabatic approximation) is that the modeled temperature is going to rise linearly with time. So then, what is a meaningful value of time to use? If your temperature rise is 1K in the first microsecond, what is it after 1 second? A million K, or a whole lot less? And how much? Such a calculation is useful to set an upper bound, if you had a usable number to plug in for a time. It could also be useful to extract a rough estimate of some time-averaged mean temperature if you had a pulsed current with a very short pulse width. But even so, it would be wise to estimate a dissipation time constant (for comparison), using the effective heat transfer coefficient, effective surface area and heat capacity of the ring.

 

[sophiecentaur]

Agreed. You wouldn't want to have to wait 30minutes between measurements.
As usual, in engineering, the numbers count. We need more details. How many Watts are involved etc.?