Temperature on the outer surface of insulation

[anolan23]

This seems basic, but I'm stuck.

Look at the attached picture. I'm trying to find the temperature on the outer surface of the insulation. Is it not possible because I do not know the rate of heat transfer? How do pipe designers know the required thickness of insulation needed to reduce to a desired surface temp?

Ambient is 32F
http://imgur.com/a/TJmxO

 

[russ_watters]

The outer surface temperature is approximately ambient.

 

[anolan23]

I know it goes hot to cold, but I'm pretty sure the -150F has an influence on the outer temp.

 

[Cbergeron]

The outer surface cannot be ambient. There will be some conduction through the insulation to the outer surface based off the large difference in temperature.

 

[Chestermiller]

You need to know the heat transfer coefficient between the surface and the ambient. This may be the result of natural convection and forced convection.

 

[russ_watters]

The outer surface cannot be ambient.

No, but it can be approximately ambient...and that assumption is reasonable for any significant amount of insulation...just as the inside surface temp is approximately equal to the pipe fluid temp.

 

[russ_watters]

Is it not possible because I do not know the rate of heat transfer? How do pipe designers know the required thickness of insulation needed to reduce to a desired surface temp?

Pipe designers don't design to a particular surface temp, they design to a particular heat flow rate and then decide on an insulation R/U value required to achieve it.

 

[anolan23]

No, but it can be approximately ambient...and that assumption is reasonable for any significant amount of insulation...just as the inside surface temp is approximately equal to the pipe fluid temp.

If the insulation was a few feet thick, then yes id assume it was approximately ambient. What if the insulation is only 2mm thick? I'd expect the temperature to be much less than 32F ambient.

 

[russ_watters]

If the insulation was a few feet thick, then yes id assume it was approximately ambient. What if the insulation is only 2mm thick? I'd expect the temperature to be much less than 32F ambient.

Sure, if it is 2mm that assumption would not hold...but who ever uses 2mm thick insulation? So I guess the real question is: what is the context and rest of your question? Homework? Exam? Your OP appeared to be asking about real-world, but you didn't post the entire problem and it doesn't look to me to be real-world.

FYI, I quickly found an insulation calculator via google and found that for your problem and some real-world assumptions about typical insulation type/thickness, the surface temperature was further off than I expected. I was expecting just a couple of percent, but it was more like 8%. For real-world engineering that is plenty close enough for this problem, but again, I don't know what your needs are.

edit:
Also, before I googled for the calculator I poured myself a cup of coffee and was concerned enough about what I felt that I did a quick calc, which then prompted the search for more info. Point being, this issue is really easy to test.

 

[anolan23]

Thanks for your help. I'm trying to find how much thickness 'till we can approximate 32F.

I know convection on the outer surface matters.

 

[russ_watters]

Thanks for your help. I'm trying to find how much thickness 'till we can approximate 32F.

How "approximate" are you willing to accept? And to what level of rigor do you want to do the problem(is an online calculator ok?)? Is this real-world?

 

[anolan23]

To 1 Degree Fahrenheit. online calculator is fine.

I calculated the Qrate to be 340W, but that is assuming 1.5 inches.
http://imgur.com/a/HyIOF

I want to calculate the thickness needed to reach 32F from purely conduction

 

[Tom.G]

Look at the attached picture. I'm trying to find the temperature on the outer surface of the insulation. Is it not possible because I do not know the rate of heat transfer? How do pipe designers know the required thickness of insulation needed to reduce to a desired surface temp?

Ambient is 32F
http://imgur.com/a/TJmxO

I'm used to doing it in R=BTU/Hr/ SqFt/ °F. Here goes.

• Rule of Thumb: Most surfaces in free air have an 'R' value of 1. Exception: Metal and Glass surfaces are half that.
• You want external surface within 1°F of 32°F
• For 1°F Temp difference at the surface you can have no more than 1BTU/Hr/Ft²
• the Temperature difference is 150+32 = 182°F
• ∴Insulation 'R' value ≥ 182
• 3" of fiberglass batting is around R12, or R4 per inch (If I remember correctly)
• ∴Insulation thickness is 182/4 = 45.5 inches of fiberglass batting for 1°F Temp difference at insulation surface

How do pipe designers know the required thickness of insulation needed to reduce to a desired surface temp?

That's how. Sometimes they need to design for a maximum allowed surface temperature when human contact is likely. For instance if you are on a ladder working next to a steam pipe, you don't want to suddenly jerk away from a hot surface!

Have Fun!

p.s. Actually the original image showed a K of 0.2. (K is thermal conductivity in metric units, and R is thermal resistance in English units.) Since there was no dimension given, that could be interpreted as the total conductivity of the insulation. If you use that interpretation, and the Rule of Thumb above, you have all the information needed to find the surface temperature. Or if this is a homework problem (likely), an analytical solution may be expected.

 

[anolan23]

I'm used to doing it in R=BTU/Hr/ SqFt/ °F. Here goes.

• Rule of Thumb: Most surfaces in free air have an 'R' value of 1. Exception: Metal and Glass surfaces are half that.
• You want external surface within 1°F of 32°F
• For 1°F Temp difference at the surface you can have no more than 1BTU/Hr/Ft²
• the Temperature difference is 150+32 = 182°F
• ∴Insulation 'R' value ≥ 182
• 3" of fiberglass batting is around R12, or R4 per inch (If I remember correctly)
• ∴Insulation thickness is 182/4 = 45.5 inches of fiberglass batting for 1°F Temp difference at insulation surface

The only math is the temperature difference divided by R value per inch (182/4)? How is the 1 degree temp difference included in that?

Is the 1 BTU/Hr/Ft^2 the convection on the outside ?

 

[russ_watters]

• ∴Insulation thickness is 182/4 = 45.5 inches of fiberglass batting for 1°F Temp difference at insulation surface

I am ok in principle with most of the assumptions, but I'm sure you realize that an 8' diameter pipe that is almost entirely insulation is ridiculous. I too would have guessed that the surface temperature off by 1F was reasonable, but it turns out it isn't.

That's how. Sometimes they need to design for a maximum allowed surface temperature when human contact is likely. For instance if you are on a ladder working next to a steam pipe, you don't want to suddenly jerk away from a hot surface!

Well, that's a very very different requirement from being 1F off ambient. I think you'll find that it takes only a tiny amount of insulation - a fraction of an inch - to get hot steam piping down to a surface temperature you can touch. Generally, personnel protection is a secondary consideration; primarily the interest is minimizing heat loss (which wastes energy).

 

[russ_watters]

@anolan23, here is the piping insulation calculator I found:
https://checalc.com/calc/inshoriz.html

It doesn't go as cold as you are looking for, but if you use the same delta-Ts, you should get similar results. It also compares insulated pipe heat loss to bare pipe heat loss. I recently did a project where we specified 3" of insulation on 1" steam and condensate piping 350F and below. Using your delta-T (118F) for a 190F pipe gives a bare pipe loss of 243 BTU/h/ft and insulated pipe loss of 16 BTU/hr/ft. Surface temp 77F in a 72F room.

 

[Tom.G]

The only math is the temperature difference divided by R value per inch (182/4)? How is the 1 degree temp difference included in that?

You are right. That should have been 181/4 = 45.25" of insulation. Good catch anolan23!

Is the 1 BTU/Hr/Ft^2 the convection on the outside ?

Yes. With the assumption you want the outside surface temperature not more than 1°F different from ambient. If you can accept 10°F temperature difference you can reduce the insulation to around 4.3".

Using your delta-T (118F)...

The picture from th OP shows pipe temp. of minus 150.

Ambient is 32F
http://imgur.com/a/TJmxO