Roxul Industrial Insulation Process - Manual (Page 127)

2.3 Bases for thermal calculations
2.3.2 Heat transfer (European basis and terms)
Heat transfer resistance 1/α
The heat transfer resistance “1/α” is the
reci procal of the surface coefficients of heat
transfer. The unit used to express the heat
transfer resistance is (m²K)/W.
Coefficient of thermal transmittance k
The coefficient of thermal transmittance “k”
indicates the heat flow density “q” circulating
through a body, when there is a temperature
difference of 1 K between the two media, which
are separated by the body. The coefficient of
thermal transmittance includes the thermal
resistance and heat transfer components. The unit
used to express coefficients of thermal transmit-
tance is W/(m² K).
Thermal transmission resistance 1/k
The thermal transmission resistance is the
reciprocal of the coefficients of thermal transmit-
tance. The unit used to express thermal transmis-
sion resistance is (m²K)/W.
1 = Heat transfer
resistance
inside
+ Heat transfer
resistance
inside
+ Heat transfer
resistance
outside
k
1 1 1
k
R
w i
w
a
= + +
α α
m K
W
2 ⋅ ⎡
⎣
⎢
⎤
⎦
⎥
for a wall
1 1 1
k d
R
d
R i i
R
a a
=
⋅ ⋅
+ +
⋅ ⋅ π α π α
m K
W
⋅ ⎡
⎣
⎢
⎤
⎦
⎥
for pipe insulation
Calculation bases
The heat flow density through a flat wall
constructed of multiple layers is calculated
as follows:
q k
M L
= ⋅ − ( ) ϑ ϑ
1 1 1
1
1
2
2
k
s s s
i
n
n a
= + + + + +
α λ λ λ α
...
q
s s s
M L
i
n
n a
=
−
+ + + + +
( )
....
ϑ ϑ
α λ λ λ α
1 1
1
1
2
2
W
m 2
⎡
⎣
⎢
⎤
⎦
⎥
The following symbols are used in this calculation:
q
Heat flow density W/m²
ϑ
M
Temperature of the medium in °C
ϑ
L
Ambient temperature in °C
α
i
Surface coefficient of
heat transfer inside W/(m² K)
α
a
Surface coefficient of
heat transfer outside W/(m² K)
s
1
…s
n
Thickness of the individual layers of insulation m
λ
1
…λ
n
Thermal conductivity of the W/(m K)
individual insulation layers
k Coefficient of thermal transmittance W/(m² K)
With multiple-layer hollow cylinder (pipe insula-
tion), the heat flow density is calculated as follows:
q k
R R M L
= ⋅ −
( )
ϑ ϑ
1 1
2
2
1
1
3
2
k d
d
d
d
d
R i i
=
⋅ ⋅
+
⎛
⎝⎜ ⎞
⎠⎟
⋅ ⋅
+
⎛
⎝⎜ ⎞
⎠
π α π λ
ln ln
⎟⎟
⋅ ⋅
+ +
⎛
⎝⎜ ⎞
⎠⎟
⋅ ⋅
+
⋅ ⋅ 2 2
1
2
π λ π λ π α
....
ln
d
d
d
a
n
n a a
q
d
d
d
d
d R
M L
i i
=
⋅ −
( )
⋅
+
⎛
⎝⎜ ⎞
⎠⎟
⋅
+
⎛
π ϑ ϑ
α λ
1
2
2
1
1
3
2
ln ln
⎝⎝⎜
⎞
⎠⎟
⋅
+ +
⎛
⎝⎜ ⎞
⎠⎟
⋅
+
⋅ 2 2
1
2
λ λ α
....
ln
d
d
d
a
n
n a a
m K
W
⋅ ⎡
⎣
⎢
⎤
⎦
⎥
W
m
⎡
⎣
⎢
⎤
⎦
⎥
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