Heat Transfer & Combustion: Estimate Pipe Heat Loss/m

[Tiberious]

<< Mentor Note -- poster reminded to use the standard Template >>

Question Three
A pipe of outside diameter 200 mm is lagged with an insulating material of thermal conductivity 0.06 W m-1 K-1 and thickness 75 mm. The pipe carries a process fluid at a temperature of 300 °C and the average temperature of the outer surface of the lagging is 45 °C.
(a) Estimate the rate of heat loss per metre length of pipe.
(b) Explain why the thermal resistance of the pipe wall can be ignored.

SOLUTION

Determine r_1

r_1=(200/2)=100mm or 1∙10^(-3) m^2
Determine r_2

r_2=(200/2+75)=175mm or 1.75∙10^(-3) m^2

r_(2 )/r_1 =(((200/2+75))/((200/2) ))

=1.75

ϕ= (2π∙1∙0.06∙(300-45))/(in (1.75))

=171.78 W per metre of pipe length


SOLUTION

The thermal resistance of the pipe wall can be ignored due to the pipe's relatively low wall thickness. Based on the below worked example we can see accounting for the mean pipe wall thickness the difference between the above and below answer's is 2.60pc.

If the wall thickness was to increase it would be prudent to use the logarithmic expression as this accounts for the change in area which becomes more important the thicker the pipe wall.

However, as no dimensions have been provided for the pipe wall thickness we can assume that the pipe wall is this and thus have a negligible effect impact.

Determining the width of the plate:

W=2πr_(mean )

r_(mean ) being the average of the radii given.

Determine r_(1 )

r_1=(200/2)=100mm

Determine r_(2 )

r_2=(200/2+75)=175mm

Hence

r_mean= (100+175)/2

= 137.5mm

Hence A_(mean ):

A_(mean )=W L

=2πr_mean L

=0.8649..
Applying Fourier's equation

ϕ= -kA(dT/dx)

We Get

ϕ= (kA_mean (T_1-T_2 ))/(r_2-r_1 )

= ((0.06)∙(0.8649)∙(300-45))/((175-100)∙10^(-3) )

=176.24..WThe percentage difference between this and the previous result is..

(176.24..-171.78)/171.78∙100pc

i.e.2.60pc

 

[rude man]

You can't go with some kind of mean radius; you have to integrate all the differentially thin sections to come up with the correct thermal resistance.

 

[Tiberious]

Sorry - I'm not clear on what you mean.

From the example we have been given. The approximation is just to show why the pipe wall thickness can be ignore in question a Is the answer sufficient?

Pardon me for any ignorance, I'm not entirely clear on this one.

 

[rude man]

Sorry - I'm not clear on what you mean.

From the example we have been given. The approximation is just to show why the pipe wall thickness can be ignore in question a Is the answer sufficient?

Pardon me for any ignorance, I'm not entirely clear on this one.

For part (a) i got a significantly higher number than you did; I could well have made a computational mistake, did it quickly.
As for part (b) I thought the answer was either that the pipe wall is thin or the metal has a low thermal resistivity.

 

[Tiberious]

How have you calculated part a ?

Furthermore, as far as I can interpret the question for part b. It's asking for more of an explanation as to why we ignore the thermal resistance for part a.