Calculating Outside Wall Temperature of Heated Chamber

[jmkobe]

Hello All,

I'm trying to find an equation that will calculate/estimate the outside wall surface temperature of a heated chamber when I know the temperature inside the heated chamber, as well as the thickness and thermal conductivity of the insulation material. To put it another way, I'm trying to calculate/estimate how thick the insulation has to be to have the outside surface temperature be a certain temperature.

The inside of the chamber is held at 300F using recirculated air heated by a natural gas fired burner. The ambient temperature in the building is ~ 70F. The construction of the chamber "wall" is as follows:
Inner wall is 14 gauge mild steel.
Followed by a layer of high temperature insulation board (Thermal Conductivity ~ 0.33 BTU*in/hr*sq.ft*F)
Outer wall is 22 gauge galvanized steel sheet metal.

For the sake of simplicity, I'm okay with ignoring the effect of the inner and outer steel walls and saying the wall is made of only the insulation board.

Please help if you can. Thanks!

 

[IRstuff]

Solve

thermal_conductivity*(300F-T)/thk = (7.5W/m^2-K)(T-70F) for specific T

TTFN (ta ta for now)
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[MortenA]

this online calculator may help your:

https://checalc.com/calc/insFlat.html

Best regards, Morten

 

[jmkobe]

IRstuff & MortenA -

Thank you both for your input.

IRstuff, I don't get the right side of the "=" sign. Where does the (7.5W/m^2-K) come from and is it 7.5 Watts/(square meter * degrees K)? I'm unsure of those units.

Thanks again for your valued input.

 

[som1973]

The Thickness of Insulation is purely dependent on Economics, we need to provide optimum wall thickness so heat loss through wall should be minimum, also cost of insulation is also kept minimum.

Hence you need to work out what should be allowable heat loss through wall & work backwards to calculate minimum thickness required.

Generally heat loss through Heated chamber wall accounts for 10-15% of total heat input.

so calculate the total heat loss through wall ( BTU/HR)or KW = 0.15 (Worst case) x Total Heat Input.

once you found Q (heat loss through wall) then calculate the Insulation thickness required.

Heat Loss through wall

Q = U x A x ΔT

 

[IRstuff]

7.5W/m^2-K is a typical guess at the natural convection coefficient. Once you determine what heat loss you can tolerate, you can use the right-hand side to solve for the surface temperature and then use the surface temperature on the left side to solve for the thickness of insulation.

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[chicopee]

Convection and radiant heat inside the chamber and you have convection from air circulation outside the chamber. Convective heat transfer coefficients will need to be determined inside and outside the chamber walls. Then the emissivity of the surface lining the inside wall of the chamber will be needed to figure out the radiation heat transfer. If the outside wall temperature is to be allowed over 200 dF then you also have radiation heat transfer to the surroundings. Get a heat transfer text book or a ME or Chem E handbook and look up heat transfer equations thru composite wall involving all three modes of heat transfer.