# Heat Transfer Calculations

PWoolfall
I would be grateful for your help with a small project I am involved in at work. I would like to set up an excel spread sheet to calculate either the thickness of insulation required to reduce the temperature of say a furnace wall from the inside to the outside, or calculate the resultant outside wall temperature, knowing the insulation details and inside temperature. I have come across several different formulas on the net, which unfortunately have left me a little confussed.
An application I am currently looking at involves adding a piece of equipment to a furnace roof. This equipment consists of an outer stainless steel cylinder having an outside diameter of 750 mm, a wall thickness of 3 mm, and externally subjected to a temperature of 650 deg C. Inside the cylinder is another cylinder again constructed with stainless steel with a wall thickness of 5 mm. I need to sandwich a sufficient thickness of insulation between the cylinders, to achieve a temperature within the internal cylinder of +/- 60 Deg C.

Any help would be much appreciated.

lalbatros
Hello PWoolfall,

If I understand correctly:

• you want to build a system made of two coaxial cylinders
• the gap in between the cylinders would be filled by some insulation
• the external cylinder would be in contact with hot air at 650°C
• you want to keep the internal cylinder below 60°C
Obviously, if there is no cold air flowing inside the inner cylinder, then you will never be able to keep it below 60°C. Regardless of the amount and quality of the insulation, after some time, the inner cylinder will reach 650°C.

If there is cool air flowing in the inner cylinder, then the design is possible but needs more information:

• composition of the fluid inside the inner pipe
• temperature of the fluid flowing in the inner pipe
• flowrate inside the inner pipe
• similar information regarding the outer pipe:
is it in contact with some hot fluid?
what is the composition of this fluid?
is this fluid moving?
where does the heat come from?
some combustion?
...
• which kind of insulation material are you considering?
• what are you geometrical constraints?

If you chose a insulation material with heat conductivity of 0.04 W/K.m,
if you use an insulation thickness of 0.1 m,
then the cold air inside the inner tube should take out an amount of heat of at least q=236 W/m²:

since q = 0.04/0.1 * (650-60) W/m²

if you pipe is 1 meter long, its surface would be 4.7 m², and this would imply a cooling power of

Q = q*4.7 = 1100 W = 1.1 kW

This would only be possible if the cooling fluid is cold enough and has a sufficient velocity.