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  1. I know what battery I wish to use (3.7 V 140 mAh which I can swap for larger mAh battery)

  2. I know what length of wire (3.5 inches or 7 inches depending on which ever would work better)

  3. I know what temperature (110 F)

  4. I know the the wire only needs to stay on for 10 seconds at a time

  5. I don't know which diameter/gauge wire to use

I stuck at math and can't seem to google-fu my way into finding something that will give me the ability to calculate what nichrome wire to use. There was one site that would give let input the given parameters, but the lowest known temperature I could use was 400 F.

I need the math that let me calculate which diameter/gauge and with what resistance will give me 110 F temperature over either 3.5 or 7 inch wire using a 3.7V battery.

Please forgive any of my blaring misunderstandings or ignorances/deficiencies in formality of how to inquire this information.

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  • \$\begingroup\$ You could start at Temperature in a wire to see what's involved. For a wire at around 43 °C, radiation will not be the dominant effect, so you will need to work out the losses due to air flow too. \$\endgroup\$ – Andrew Morton Feb 6 '18 at 9:21
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The first thing you need to figure out is how much power per unit length it takes to maintain the wire at 43 °C (110 °F). That depends on things you haven't told us. The ambient temperature and thermal conductivity of whatever the wire is touching will make a large difference.

Calculating the power required to maintain a particular wire temperature is probably not possible since too many things will be unknown. The best method to find the answer is to try it.

Get some wire, connect it to a lab supply, and see how much current it takes to keep it at the desired temperature. This doesn't need to be nichrome. Just about any wire can handle 43 °C. When find the setting that yields the desired result, record the current and the voltage drop across a known length of wire. The current times the voltage is the power being put into that wire.

From the power into a known length, you find the total power into your desired length. The power into a resistance is:

    W = V2 / Ω

where W is the power in watts, V the voltage across the resistance, and Ω the resistance in Ohms. If you are going to apply a fixed voltage, like your 3.7 V battery, then flip this around to find the resistance:

    Ω = V2 / W

Now you look at wire resistance tables to find some that has the desired resistance over that length.

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  • \$\begingroup\$ Im looking for more equations than those. More or less, im looking for equation where i can plug it temperature, length, and input voltage (doesnt show the equations, but kinda like this -easycalculation.com/engineering/electrical/…) Isn't there some calculus that can derive the needed diameter of Nichrome wire for all the values given \$\endgroup\$ – Robert Anderson Feb 4 '18 at 18:09
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    \$\begingroup\$ @RobertAnderson TBH, doing the experiment is the best way at this scale. \$\endgroup\$ – Andrew Morton Feb 4 '18 at 18:23
  • \$\begingroup\$ Experimenting requires buying various gauges of nichrome wire and trial and error. I was inquiring if there are exact mathematical ways of calculating whats specified. \$\endgroup\$ – Robert Anderson Feb 4 '18 at 18:29
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    \$\begingroup\$ @Robert: Please read the answer again properly. It explains that you don't need to buy various gauges and how to do the experimental measurements and calculations. This is an engineering site. \$\endgroup\$ – Transistor Feb 4 '18 at 20:48
  • \$\begingroup\$ i understand the nature of what was explained. The Manhattan project did more math than experimenting because fissile material was expensive and not yet abundant. They didn't detonate many experimental bombs to find the best way to derive the first working bomb. They did the math first, second, third, and several orders of magnitudes more. I know i could experiment math wise and refer to the tables to; i'm asking is there a way to calculate this more directly... the link above does at least half of what i am asking... ANYBODY know how to math this? \$\endgroup\$ – Robert Anderson Feb 5 '18 at 21:24

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