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I have two Cr20Ni80 nichrome wires having 1m length each, 24 SWG and a resistance of 4.390 Ohm/m. I need to heat up a furnace to 450 degree Celsius. How can I calculate the supply voltage and current for the purpose? I need some formulas to design a power supply to power this nichrome wire. Is there any relation between temperature, voltage and current?

The furnace has a base diameter of 54cm and top diameter of 34cm with a height of 40cm. Total volume is 61869cm^3 and is made of mild steel with no insulation.

Also I need to know: Can I power it using AC or DC supply?

If I give a constant supply for some time, will the nichrome wire temperature increases over time? or will the temperature remain constant?

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    \$\begingroup\$ The more power you dissipate the hotter it gets. Without a detailed mechanical design I can't estimate how much power you need. But \$ P=\dfrac{V^2}{R} \$, \$ I = \dfrac{V}{R} \$. The power you need depends on how easily the heat can escape. \$\endgroup\$ Mar 14 '18 at 19:16
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    \$\begingroup\$ There isn't any such relation, without taking into account furnace size, heat loss etc. So, leaving all that out as you request ... hard luck. \$\endgroup\$ Mar 14 '18 at 19:34
  • \$\begingroup\$ The furnace has a base diameter of 54cm and top diameter of 34cm with a height of 40cm. Total volume is 61869cm^3 and is made of mild steel with no insulation. Also I need to know: Can I power it using AC or DC supply? If I give a constant supply for some time, will the nichrome wire temperature increases over time? or will the temperature remain constant? \$\endgroup\$
    – MegaMind
    Mar 15 '18 at 10:38
  • \$\begingroup\$ Side note: With no insulation, this thing is probably going to take a crazy amount of power. At 450C surface temp, your thermal radiation alone is going to be like 20-30kW. This added to the convective heat loss will result in a pretty big number. You probably will have a significant temperature gradient within your furnace if you dont have insulation. \$\endgroup\$
    – BeB00
    Mar 27 '19 at 22:10
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I have read about people saying about furnace size, heat loss, etc. Please leave all that.

Nope. That is the stuff you need to figure out before anything else. Start by defining your interior volume, and then specify your insulation. Assuming 450 C inside the box, and knowing the thermal resistance of your insulation, you can figure the power necessary.

Once you know the power, you can make an operating assumption about the wire temperature. Let's say the wire will operate at 900 C, which will allow 50% duty cycle. Using the date sheet for your nichrome alloy you can find the resistivity of the material, and determine the wire length and diameter.

At this point, you have a known wire length and resistance. Then, given the power you need (remember power?) you can calculate the supply voltage as Warren Hill suggested. Dividing power by voltage will give you the current required.

Then you will need to calculate the resistance of the wire at room temperature, and rerun your calculations. The previous numbers gave power and current at operating temperature, and the wire will dissipate a good deal more than that at turn-on when the wire is cold and has less resistance.

But first things first. The very first thing you MUST do when designing a system is to determine your requirements. In this case, the most important requirement is the power needed at operation - all else follows from this, and in order to determine it you must know the insulation values of your oven.

"Please leave all that" doesn't work.

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  • \$\begingroup\$ The furnace has a base diameter of 54cm and top diameter of 34cm with a height of 40cm. Total volume is 61869cm^3 and is made of mild steel with no insulation. Also I need to know: Can I power it using AC or DC supply? If I give a constant supply for some time, will the nichrome wire temperature increases over time? or will the temperature remain constant? \$\endgroup\$
    – MegaMind
    Mar 15 '18 at 10:38
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    \$\begingroup\$ @MegaMind - This is now a completely different question. Please start one. In the meantime, start learning about convection cooling and black-body radiation \$\endgroup\$ Mar 15 '18 at 22:41
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You're going to need to estimate how many watts your furnace needs to get up to 450 degrees. A simple no-math way to do this would be to look up similar devices on the internet and see how many watts of heating they have.

Next you're going to calculate the voltage required on your nichrome wires to get that wattage. It's quite simple, WATTAGE = V^2/R. The voltage can either be DC or AC, doesn't matter.

Lets say for example you need 750 watts. If you hook up your nichrome wires in series, you will need sqrt(750*8.8) = 81V. In parallel you will need sqrt(750*4.4) = 57v.

The amperage your furnace will draw is V/R. Find a power supply that can supply at least 1.2x this many amps, at the voltage you calculated earlier. You may be able to use the mains voltage directly if you adjust the nichrome wire lengths a bit. Make sure to redo all the math and check it. You may also be able to use mains through a transformer to lower the voltage. This will probably be cheaper than using a burly DC supply unless your furnace is very small.

Continuing our example: 57/4.4 = 12 Amps (in the parallel configuration). 81/8.8 = 9.2A in the series config. So we want a supply that's either 57V >15A, or 81V >11A. It looks like you'll probably want to increase the nichrome wire length a bit and get the target voltage up to 110V, so you can run it straight from mains. ..but anyway.

Last you're going to need to buy a PID controller to control the temperature. These are cheap and commonly available. For example: https://smile.amazon.com/Inkbird-Temperature-Thermostat-Controllers-Fahrenheit/dp/B01KNXETWS/

Just make sure:

  1. The temp sensor can handle 450C
  2. The controller (or bundled relay) can handle the voltage and amperage your going to run at. The amperage will be V/R.
  3. Make sure the output is AC if you're using AC, and DC if you're using DC.

If you bought the product that I linked, you would have to buy a new thermocouple, since the one it comes with is only rated up to 400C. This shouldn't be an issue, as you can hook any old thermocouple up to these controllers. Just make sure you change the termocouple type when you set the controller up. Here's one that's rated to 800C: https://smile.amazon.com/Perfect-Prime-TL1815-HeadProbe-Thermocouple-Temperature/dp/B0142S9J4S/

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  • \$\begingroup\$ The furnace has a base diameter of 54cm and top diameter of 34cm with a height of 40cm. Total volume is 61869cm^3 and is made of mild steel with no insulation. Also I need to know: Can I power it using AC or DC supply? If I give a constant supply for some time, will the nichrome wire temperature increases over time? or will the temperature remain constant? \$\endgroup\$
    – MegaMind
    Mar 15 '18 at 10:38
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Also I need to know: Can I power it using AC or DC supply?

A heater wire will work equally well on AC or DC.

If I give a constant supply for some time, will the nichrome wire temperature increases over time? or will the temperature remain constant?

The temperature will rise until it stabilizes at some temperature. It's very difficult to tell what that temperature will be without knowing all the thermodynamics of the system.

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  • \$\begingroup\$ Worst case is that it will try and stabilise above the melting point in which case it will function as an expensive fuse and fail on each attempt. \$\endgroup\$
    – KalleMP
    Mar 27 '19 at 21:08

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