Lesson 5 Lagging Aim LO1 Understanding Heat Transfer Rates for Composite Systems Critical Thickness of Insulation Lets consider a layer of insulation which might be installed around a circular pipe ID: 478246
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Slide1
Unit 42: Heat Transfer and Combustion
Lesson 5: LaggingSlide2
Aim
LO1: Understanding Heat Transfer Rates for Composite Systems.Slide3
Critical Thickness
of Insulation
Let’s consider a layer of insulation which might be installed around a circular pipe.If the pipe is metal then as has been shown the temperature on the inner surface of the pipe varies little to that of the outer surface and therefore for practical purposes it can be ignored
r
o
r
i
T
i
h, T
∞
T
o
T
∞
Ln(
r
o
/
r
i
)
2π
kL
1
2π
kLSlide4
Critical Thickness
of InsulationThe inner temperature of the insulation is fixed at T
i and the outer surface is exposed to a convection environment at T∞.
From the equivalent resistor network the heat transfer is… q =
2πL(Ti – T
∞
)
Ln(
r
o
/ri) +
1 k rohSlide5
Critical Thickness
of InsulationIn interesting consideration is the amount of insulation (lagging) required (i.e. radius
ro) that will
maximise the heat transfer…i.e.
dq = 2πL(T
i
–
T
∞
)[(1/
kr
o
) – (1/hro2)] = 0
dro Ln(r
o/ri) + 1
2 k roh
Thus at a maximum ro = k/h
ro being referred to as the critical radiusSlide6
Critical Thickness
of Insulation
q
r
r
o
This shows that lagging (insulation) when placed onto the outer surface of a pipe will increase the heat flow if it is less that the critical radius r
o
. Greater that
r
o
, the heat flow will
decrease
.Slide7
Critical Thickness
of InsulationThus if the outer radius is less than the value
given by ro
= k/h, then the heat transfer will be increased by adding further insulation.For radii greater than the critical value an increase insulation thickness will cause a decrease in heat transfer.
The central concept is that for sufficiently small of h the convection heat loss may actually increase with the addition of insulation because of the increased surface area. Slide8
Critical Thickness
of InsulationCalculate the critical radius of insulation for asbestos (k=0.17 W/
m.oC) surrounding a pipe and exposed to room air at 20
oC with h = 3.0 W/m2.
oC. Calculate the heat loss from a 200oC, 5.0 cm diameter pipe when covered with the critical radius of insulation and without insulation.Slide9
Critical Thickness
of Insulation
ro = k/h = 0.17/3.0 = 0.0567 m = 5.67 cm
q =
2π(200 – 20) =
105.7 W/m
L
Ln(5.66/2.5)
+
1
0.17 (0.0567)(3.0)Without insulation the convection from the outer surface of the pipe is…
q = h(2πr)(Ti – To
) = 3 x 2π x 0.025 x (200 -20) = 84.8 W/mLSlide10
Critical Thickness
of InsulationSo the addition of 3.17 cm (5.67 – 2.5) of insulation actually increases the heat transfer by 25%.
As an alternative, fibreglass having a thermal conductivity of 0.04 W/m.
oC might be employed as the insulation material. Then the critical radius would be…
ro = k/h = 0.04/3.0 = 0.0133 = 1.33 cmSlide11
Critical Thickness
of InsulationNow the critical radius is less than the outside radius of the pipe (2.5 cm) so addition of any
fibreglass insulation would cause a decrease in the heat transfer.In a practical pipe insulation problem, the total heat loss will also be influenced by radiation as well as convection from the outer surface of the insulation.