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Multi-layer flat wall if the number of layers is n:

t t t  t t  t
q  1 n (  )1  1 n n (  )1  1 n n (  )1

 1   2 .....   n   i  R ( 1.4)
    i
1 2 n  i 1 i  i 1

3.2 Thermal conduction at a one-layer pipe

The Fourier equation in cylinder coordinates:

dt dt
I
Q    F    2   r  l  , W
( 1.5)
dr dr

r – radius;

L – length of the pipe;

k – thermal conductivity;

dt/dr – temperature gradient;

The solution of the equation:

2 l    l  t (  t )
I
Q  t (  t )  1 2 , W
r 1 2 1 d ( 1.6)
ln 2  ln 2
r 1 2 d 1
Fig. 7 - Conduction at a
The heat transfer rate per unit area
one-layer pipe
Q I  (t  t )
q   1 2
l 1 d ( 1.7)
ln 2
2 d
1

At the same way, with the thermal conduction resistance:

t 
I
Q  , W (1.8)
R
The thermal conduction resistance:

1  r 2  1  d 2  m K
R  ln   , or R  ln  ,  (1. 9)



2   l  r 2 l   d 1  W
 1  

Thermal conduction at a multi-layer pipe

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