temperature - Help Understanding How Long It Will Take To Heat My Wire

I am trying to find out how many Amperes I will need to reach a certain temperature in a certain time (Milliseconds)

I need a thick wire to slow the melting of the wire. "Nichrome is the wire I'll be using" now in the American Gauge. I want to use 12 as its thick but not too thick and on Wikipedia, when I was checking how many amps I will need to reach a specific temperature using that gauge type it said I will need around 39.03A to reach around 1400F but in what time period will I reach that? Thicker wires are much slower to heat up but smaller wires are very weak.

P S I am very new to the American Wire Gauge so forgive me if I'm wrong.

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I need a thicker, more sturdy wire that can put in a high PSI environment and still reach temperatures of 2-4 millisecond. The problems i see is thicker wire don't have as much resistance and a smaller mutil-twisted smaller wire. Is there away i can change that and still reach my desired temp of 1400F?

Answer

James Clerk Maxwell popularized this method of dimensional analysis; in fact, before him, dimensions were a mishmash, unstandardized, and such analysis was impossible.

I'll give you silicon, which has specific-heat about 3X higher than tungsten.

At 2 picoJoules/(cubic_micron*degree Centigrade), suppose we want to short the output driver of a microcontroller? That driver is 100 micron * 100micron (its a powerful transistor), with 0.1 amp short-circuit ability. Assume 2.5 volts.

How long before the transistor reaches 1,025 degrees Centigrade? starts at 25C.

Our power is I*V = 0.1amp * 2.5 volts = 0.25 watts, or 250Billion picoJoules/second. The volume of silicon? Assume we'll only heat the top 100microns of the Integrated Circuit during our experiment (that depth has a thermal TimeConstant of 114 microseconds, and in that time "most" of the heat remains in that 100micron thickness. Our total volume is 100*100*100U or 10^6 cubic microns.

What is our rate-of-change-of-temperature? we want degrees/second as dimensions for our answer.

The only bit of info we have with seconds is the power: 4 seconds/joule

We want to cancel the "joules" so multiply 4seconds/joule by specific-heat of silicon

$$4 seconds/joule * 2 picoJoule/(cubicmicron * degree Cent) $$

Our rate of temperature rise is $$8 picoseconds/(cubicmicron *degree Cent)$$

And we have 1Million cubicmicrons of silicon. We need to cancel 'cubicmicron' in our answer, so multiply the answer by 10^6 cubicmicron, and we get

$$8 Million picoseconds/degree Cent$$ or $$8microseconds/degree Centigrade$$

We wanted 1,000degree Cent increase in temperature, thus 8,000 microseconds or 8 milliSeconds is the answer.

We initially assumed ALL THE HEAT would remain inside 100*100*100 micron cube. In 8 milliSeconds, heat will have moved outside the cube. A different method is needed for a correct answer.

And thank Maxwell, also the investigator of viscosity, for this method.