Energy to hold furnace to a specific time-temperature curve

[XFurn]

I have a furnace that is 18"w x18" h x 24" deep. My customer has given me a specific time-temperature curve to hold to, e.g., Heat the furnace from ambient to 1000°F in 10 minutes then to 2000°F over the next 3 hours.

The furnace will most likely be heated with natural gas and I would like to do the same calc for electric.

What I don't know are the formulas to calc the required BTU or KW input to obtain the desired curve. So I'm here asking y'all for assistance.

Thanks

 

[jambaugh]

That will depend greatly on the insulation as well as the loading of the furnace. If it is not a standard model with available specs you will need to determine this empirically.

As far as insulation goes, you can do some trials to determine the insulation efficiency... heat the furnace electrically and sustain at various temperatures seeing how much power it draws over time for that constant temp.

Plotting you should see the power pretty linearly proportional to the temperature difference power = k * (inner temp - outside temp). This you could do at reasonable temperatures say, 200, 300, 400 degrees and extrapolate.

The best thing to do is to supply the furnace with a constant power level and record the temperature it finally settles down to. At the same time you can see how long it takes to get there.

The heating rate for a given load you can also assume is a linear function of the excess power input. After plotting the rate of heat loss (power needed to sustain a given temp, you can determine the rate of temperature rise at a given power level at different temperatures. Subtract the steady state power at each temperature from the input power to get the excess at that temp.