Power required to raise air temperature

[oldtugs]

thread391-260422

Starting with 500lb/min of dry air at 400F moving through a pipe at 84fps (appr. 11,000ACFM) what is the wattage required to raise the temperature 100F?

CP 1.026
Density .046 lb/ft3

It's a real life problem, not homework so any help will be much appreciated.

 

[MintJulep]

Watts = 1.1 x .3 x cfm x ΔT = 363,000

Ballpark at least. The 1.1 factor is likely a bit off for your elevated temperatures.

 

[macmet]

Hello MJ,

Can you tell me where you get 1.1 and 0.3 in your formula?

Is your 1.1 the Cp and then the 0.3 is a conversion of the air to mass?

Thanks,
Rich

 

[racookpe1978]

If this is not a homework problem, it makes no sense:
-What diameter pipe?
-What 'efficiency" are you going to assume for the wall-to-gas heat transfer?
-How long a heater are going to wrap around the pipe? (That question works frmo the above efficiency assumption?
-How are you going to insulate the outside of that heat exchanger so "all" of your heat from electricity is going to go "into" the pipe wall then through the pipe wall then into the air inside the pipe?

By the way, the 1.206 cp is for degrees C = 200 C, NOT for a Fahrenheit unit of measurement (400 F) like your density of lbs/ft^3

 

[oldtugs]

The diameter doesn't matter, the flow rate, temperature, and volume of the mass to be heated have been supplied.

The heat will not be applied externally so the wall to gas transfer is immaterial.

The question is how much power will it take to raise the temperature of 500lb/min of dry air at 400F moving through a pipe at 84fps which equals approximately 11,000ACFM.

Intuitively, I don't buy the 300 kW either, about half that seems more reasonable based on field experience with smaller systems. Not having experience with this volume of flow I thought I would throw it out to the thermo gurus.

 

[IRstuff]

Using strictly mass, 500 lb/min * 1.026 kJ/kg*K * 100F = 215kW

TTFN
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[ione]

I've got 219 kW (slightly different from the value reported by IRstuff just because of slightly different specific heat and/or density used in calculation). Anyway this is a strictly theoretical value since, as pointed out by racookpe1978, it is undeniable the heating process will have a certain efficiency < 1 which must be accounted for.

 

[oldtugs]

Thanks, that is much closer to what I was expecting. I don't need a 100F rise (closer to 70) but was padding it by a fair amount. I really appreciate the feedback, thank you.

 

[sailoday280]

Piping diam does matter if Kinetic Energy is to be accounted for. If change in velocity is small, then KE can be neglected.
Energy input is w*change in stagnation enthalpy.
Regards

 

[oldtugs]

Thanks for the update. In this case the velocity change is virtually nil so I didn't mention it.