Heat Transfer -- Rate of heat loss from a pipe with superheated steam

[Tiberious]

Question - Four

A pipe carrying superheated steam at 300 °C has an outside diameter of 120 mm and is lagged with two layers of insulating material. The first layer (adjacent to the outer pipe wall) is 25 mm thick and has a thermal conductivity of 0.072 W m-1 K-1. The second layer (covering the first layer) is 20 mm thick, has a thermal conductivity of 0.051 W m-1 K-1 and an outside temperature of 28 °C.
Estimate the rate of heat loss per metre length of pipe (assume the thermal resistance of the pipe wall is negligible).

SOLUTION:

Determining r_1

r_1=(120/2)mm

= 60 mm
Determining r_2

r_2=( 120/2+25)mm

= 85 mm
Determining r_3

r_3=(( 120/2+25)+20)mm

= 105 mm

Rate of heat loss ϕ= (Total temperature difference)/ΣR

Determining R_12

R_12= in(r_2/r_1 )/(2πLk_12 )

= in(85/60)/(2π∙1∙0.072)

= 0.7699..K W^(-1)

Determining R_23

R_23= in(r_3/r_2 )/(2πLk_12 )

= in(105/85)/(2π∙1∙0.051)

= 0.6594..K W^(-1)
Determining ΣR

ΣR= R_12+R_23

=0.7699..+0.6594..

= 1.4293..K W^(-1)

Temperature difference between the two points

T_1-T_2=300-28=272°C
Hence

ϕ= 272/(1.4293..)

= 190.30 W

≈190 W per metre length of pipe

 

[KataKoniK]

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Therefore, the estimated rate of heat loss per metre length of pipe is approximately 190 watts. This calculation takes into account the thermal resistance of both layers of insulation and the temperature difference between the inside and outside of the pipe. It is important to note that this is an estimated value and may vary depending on other factors such as air flow and the type of insulation used. Further analysis and experimentation may be necessary for a more accurate calculation.