I may want to write a patent on this, so I prefer not to say, sorry

In that case, I suggest you employ a knowledgeable patent agent. If you don’t know the physics of the heating of wires, and your patent depends on it, it’s going to be an easy patent to break.

 

In most jurisdictions, to get a patent the idea has to be novel and non-obvious to anyone 'skilled in the art'. What you've told us so far is neither.

 

Hi,

I need to calculate the temperature of a wire, due electric current passing through, and I have no idea how to do that. I need it for a device that I want assemble.

I'm using one single thread (strand) of speaker cable, like you can see in this picture:

View attachment 258135


Again, Just a single thread that I'm pulling out of the cable.

The length of the wire will be about 50 cm, and I'll connect it to a power supply of 12V DC, and 2A current.

What will be the temperature of the thread after about 1 minute?

Will it reach 60°C ?

I tried to look up for it at Google but the calculations are too complicated for me :-(

Please help me figure this out, if possible also show me the calculation so I can calculate it for other currents.

Thanks very much.

Hello there,

Let me see if i understand you correctly first.

You are saying you want to calculate the temperature of a wire that is conducting a certain amount of current, and you want to know the time it takes to reach a certain temperature.

If this is correct, then strictly speaking this is not a simple calculation as there are many things to consider.
Again strictly speaking, you may have to go back to the sort of first principles which would mean using the Heat Equation (Fourier) because you not only want to solve for the final temperature you also want to solve for the time it takes to reach a given temperature, and that is really described by a two variable differential equation known as a Partial Differential Equation.
However, to do that many things have to be very clearly defined. A few include these:
1. Specific heat capacity of the wire.
2. Heat insulation factor of the wire insulation.
3. End point heat sink characteristics.
4. Of course the current and the wire diameter.

So again strictly speaking you are asking for a lot here which makes me think that the person that asked this question expected a simple approximation that was taught to you before this or else you are in a Master's or PhD program of study.

There are some approximations based on surface area, but i cant be sure if that would be good enough for your study or not because you are a little vague about what you can use to solve this.
As a first step, you might try calculating the final temperature of a resistor of a certain uniform shape. However, getting to the time data for that will also be more complicated.

Many you can find an approximate formula online. Keep in mind the insulation plays an important role too if there was no insulation it would be just the surface area which would allow quite a bit of cooling, but with a insulation jacket that was a perfect insulator for heat the wire would eventually overheat with 1 microampere of current. So some of these variables make a huge difference on the calculation.

BTW a complete profile of the wire being heated over time requires a 3d graph plot and that is again because there are a few things that vary, the temperature along the wire (x), and the time (t) it reaches that temperature. If you concentrate on one point along the wire (x) then you still have to solve for the temperature in time which would be a function like:
T=f(t)
but for the entire solution along the wire it would be:
T=F(x,t)

So you see you have to be more specific ab out what you really want to do.

A typical problem using the Heat Equation is to have a long metal bar with perfect insulation around it except at the two ends. The two ends are then assigned a driving temperature at time t=0 and then the temperature along each point (x) of the bar is then calculated for all time.

 

High current adjustable power supplies aren't that expensive. I would recommend something like this:
https://www.amazon.com/LW-K3010D-Adjustable-Switching-Regulated-Spectrophotometer/dp/B07512KQDW/ref=sr_1_4?crid=376HZK6C0GHV6&keywords=Variable+power+supplies&qid=1642702160&sprefix=variable+power+supplies,aps,119&sr=8-4
using something like that you can adjust the temperature of the wire to whatever you want.

 

Hello there,

Let me see if i understand you correctly first.

You are saying you want to calculate the temperature of a wire that is conducting a certain amount of current, and you want to know the time it takes to reach a certain temperature.

If this is correct, then strictly speaking this is not a simple calculation as there are many things to consider.
Again strictly speaking, you may have to go back to the sort of first principles which would mean using the Heat Equation (Fourier) because you not only want to solve for the final temperature you also want to solve for the time it takes to reach a given temperature, and that is really described by a two variable differential equation known as a Partial Differential Equation.
However, to do that many things have to be very clearly defined. A few include these:
1. Specific heat capacity of the wire.
2. Heat insulation factor of the wire insulation.
3. End point heat sink characteristics.
4. Of course the current and the wire diameter.

So again strictly speaking you are asking for a lot here which makes me think that the person that asked this question expected a simple approximation that was taught to you before this or else you are in a Master's or PhD program of study.

There are some approximations based on surface area, but i cant be sure if that would be good enough for your study or not because you are a little vague about what you can use to solve this.
As a first step, you might try calculating the final temperature of a resistor of a certain uniform shape. However, getting to the time data for that will also be more complicated.

Many you can find an approximate formula online. Keep in mind the insulation plays an important role too if there was no insulation it would be just the surface area which would allow quite a bit of cooling, but with a insulation jacket that was a perfect insulator for heat the wire would eventually overheat with 1 microampere of current. So some of these variables make a huge difference on the calculation.

BTW a complete profile of the wire being heated over time requires a 3d graph plot and that is again because there are a few things that vary, the temperature along the wire (x), and the time (t) it reaches that temperature. If you concentrate on one point along the wire (x) then you still have to solve for the temperature in time which would be a function like:
T=f(t)
but for the entire solution along the wire it would be:
T=F(x,t)

So you see you have to be more specific ab out what you really want to do.

A typical problem using the Heat Equation is to have a long metal bar with perfect insulation around it except at the two ends. The two ends are then assigned a driving temperature at time t=0 and then the temperature along each point (x) of the bar is then calculated for all time.

Thanks very much for trying to help, but I already got to a conclusion that it will be much faster and easier through try and error. I linked to 3 videos on Nichrome wire warming on the previous page (almost at the bottom), from what I saw there I'm now very confident that I can make my wire warm to 50-60 °C in about a few seconds, just perfect for what I need.

I will probably have to use some resisters to lower the wire temperature so it will not become too hot... rich people's problems
Thanks anyway!

 

High current adjustable power supplies aren't that expensive. I would recommend something like this:
https://www.amazon.com/LW-K3010D-Adjustable-Switching-Regulated-Spectrophotometer/dp/B07512KQDW/ref=sr_1_4?crid=376HZK6C0GHV6&keywords=Variable+power+supplies&qid=1642702160&sprefix=variable+power+supplies,aps,119&sr=8-4
using something like that you can adjust the temperature of the wire to whatever you want.

Thanks (I already worked with such power supplies in the past) but it's too "Heavy" and complicated for what I need... I want my device to be much simpler and compact... I think that maybe I will use a small Potentiometer in order to control the current and the temperature.

 

With the little amount of information you are willing to disclose, the best answer to your question is, "try it". The worst that can happen is you'll either burn yourself or you'll get disappointed.

 

With the little amount of information you are willing to disclose, the best answer to your question is, "try it". The worst that can happen is you'll either burn yourself or you'll get disappointed.

Yes, Trial and error will be the best method here.

And I will be very carful not to burn myself or anything else

 

Thanks very much for trying to help, but I already got to a conclusion that it will be much faster and easier through try and error. I linked to 3 videos on Nichrome wire warming on the previous page (almost at the bottom), from what I saw there I'm now very confident that I can make my wire warm to 50-60 °C in about a few seconds, just perfect for what I need.

I will probably have to use some resisters to lower the wire temperature so it will not become too hot... rich people's problems
Thanks anyway!

Ok sure. From your first post it sounded like you wanted to actually calculate this which is entirely different than actually running it in real life. In that case there are still a couple things to think about.

First, the method of control.
Since you need around 2 amps you probably wont be able to use a potentiometer because strictly speaking those are usually for very low currents like 1ma or maybe 10ma.
What you may be able to use is a "reostat" which is sort of like a potentiometer but is usually made for higher currents like 1amp or something. The wattage of this device has to match the application however just like any other resistor so you have to calculate the max power and buy one that will meet that requirement as well as the proper resistance. The only thing here is that this is just a method of adjustment not really a control method. This means that as you adjust the reostat the wire will heat up and you have to adjust it some more and then again until you get it to the right temperature. The problem then is that once you apply the load (in this case the load is a thermal sink) the wire will cool so you have to adjust the reostat again and once the load is removed you might have to quickly turn the reostat so the wire does not melt and break apart.

A control method is a way to keep the wire at a given temperature. You find a way to masure the temperature and then use an automatic control to keep it at that temperature even with load.
For a resistance wire, you can probably get away with measuring the resistance and correlate that to the temperature of the wire. It will however be the average temperature of the wire because many parts of the wire are unobservable unless you get more sophisticated.
Given that you can do this, it should work out very well.
The circuitry is quite simple really.

Having said all that, you still may be able to get away with just the reostat. You can also consider a small variac to adjust the input to a unregulated DC power supply. The reostat will waste power the variac much less.

 

Note: As soon as the warm wire touches anything, the temp will drop.

 

Ok sure. From your first post it sounded like you wanted to actually calculate this which is entirely different than actually running it in real life. In that case there are still a couple things to think about.

First, the method of control.

Since you need around 2 amps you probably wont be able to use a potentiometer because strictly speaking those are usually for very low currents like 1ma or maybe 10ma.

What you may be able to use is a "rheostat" which is sort of like a potentiometer but is usually made for higher currents like 1amp or something. The wattage of this device has to match the application however just like any other resistor so you have to calculate the max power and buy one that will meet that requirement as well as the proper resistance. The only thing here is that this is just a method of adjustment not really a control method. This means that as you adjust the rheostat the wire will heat up and you have to adjust it some more and then again until you get it to the right temperature.

The problem then is that once you apply the load (in this case the load is a thermal sink) the wire will cool so you have to adjust the rheostat again and once the load is removed you might have to quickly turn the rheostat so the wire does not melt and break apart.

A control method is a way to keep the wire at a given temperature. You find a way to measure the temperature and then use an automatic control to keep it at that temperature even with load.

For a resistance wire, you can probably get away with measuring the resistance and correlate that to the temperature of the wire. It will however be the average temperature of the wire because many parts of the wire are unobservable unless you get more sophisticated.

Given that you can do this, it should work out very well.
The circuitry is quite simple really.

Having said all that, you still may be able to get away with just the rheostat. You can also consider a small variance to adjust the input to a unregulated DC power supply. The rheostat will waste power the variance much less.

Thanks, I appreciate it, but I think that rheostat is a little too massive (and expensive) for what I was planning, and same for the variance (did you mean Transformer?). Also using a control method is a little complicated for me now.

One idea that I thought of, is maybe using the Nichrome wire itself as a potentiometer. As I understand, the Nichrome wire has a pretty high resistance, so if I use a small metal ring or conductor that I slide across the wire from one end to the other, maybe I can use it in order to control the current very easily.

I also thought about using a 2A Fuse (in case of using a 12V, 2A power supply) in order to protect the power supply and prevent over current. Maybe I'll even use two fuses just to make it safer.

Also, I found a charger of 12V, 0.250mA that I used for an emergency lamp that I threw (because it stopped working), maybe I can use it, if I'll find out that this relatively small current is enough to warm the wire. In this case, maybe it will be possible for me to use a regular potentiometer.

 

Thanks, I appreciate it, but I think that rheostat is a little too massive (and expensive) for what I was planning, and same for the variance (did you mean Transformer?). Also using a control method is a little complicated for me now.

One idea that I thought of, is maybe using the Nichrome wire itself as a potentiometer. As I understand, the Nichrome wire has a pretty high resistance, so if I use a small metal ring or conductor that I slide across the wire from one end to the other, maybe I can use it in order to control the current very easily.

I also thought about using a 2A Fuse (in case of using a 12V, 2A power supply) in order to protect the power supply and prevent over current. Maybe I'll even use two fuses just to make it safer.

Also, I found a charger of 12V, 0.250mA that I used for an emergency lamp that I threw (because it stopped working), maybe I can use it, if I'll find out that this relatively small current is enough to warm the wire. In this case, maybe it will be possible for me to use a regular potentiometer.

Well if you dont want to buy a reostat then you can roll your own.
Use maybe a 1k pot and connect it to the base of an NPN transistor. Connect the emitter to your load (wire), connect the collector to the positive power supply rail. That gives you adjustable current of a higher value than you can get from a simple pot.
If you really need 2 amps then you might have to use two NPN transistors. The first transistor emitter connects to the second transistor base, the second transistor emitter connects to the load. The two collectors connect to the positive supply rail. The pot connects as a voltage divider to the emitter of the first transistor.
The second transistor has to handle most of the power so maybe a 10 amp unit. The first transistor can be a general purpose smaller unit. The cost wont be very high.
What this forms is a super voltage follower that can sort of amplify the current of the pot to a much higher value. This arrangement is often referred to as a Darlington Compound or just Darlington Transistor. One such device is the TIP141G but there are many more out there.
A different type of Darlington Compound known as a Sziklai Darlington is constructed from one NPN and one PNP and has advantages over the standard Q1 emitter to Q2 base Darlington. I dont know if they sell these in single packages like they do with the TIP141G however. Since these transistors have very high gain in the area of 1000, that means 1ma in the pot can adjust 1 amp in the load, and 2ma in the pot can adjust 2 amps in the load, roughly speaking.
So there you go, one transistor and one potentiometer. The transistor probably needs a heat sink though.

It's just fine if you dont want to do that either it's always your choice. It does make things a little easier to adjust though.

The nichrome wire idea may or may not work depending on the load. You may end up needing too long of a nichrome wire to do the job effectively. If it does work however, you may be able to suspend it between two heat resistant poles and use an alligator clip to move along the wire to adjust resistance. A drawback is it may get too hot, so this is something that has to be tried with your load.

The adjustable power supplies that can handle 5 amps are readily available for around 65 dollars USD. They have adjustable current limit also so they dont blow out or overpower your circuit. Max voltage around 30v unless you want to pay more, and you may find one that goes up to 10 amps. You can use these for various tests on electronic stuff.