Determine the rate of heat loss from a 100 mm diameter steam pipe placed horizontally in ambient air at 30oC. The length of the pipe is 4 m and wall temperature, Tw = 170oC.
Use the following empirical expression:
Nu=0.53 (Gr x Pr)1/4
Properties of air at 100oC are as following
β =1/373 K-1; ν = 23.13 x 10 -6 m2 /sec
k= 0.0325 W/m.K
Pr = 0.7
Gr = gβD3(Tw - T∞)ρ2/μ2
Where β = 1/Tf ; Tf = 0.5 (Tw + T∞) = 0.5 x (170 + 30) = 100oC = 373 K
ν= μ/ρ
Substituting for the values,
Gr = 9.812 x (1/373) x 0.13 x (170 - 30) / (23.13 x 10-6)2 = 6.884 x 106
Nu = 0.53 x (6.884 x 106 x 0.7)1/4 = 24.832
Nu = hD/k = 24.832
h = 24.832 x 0.0325 / 0.1 = 8.07 W/m2.oC
Rate of heat loss
Q = hA(Tw - T∞) = h 2πRL (Tw - T∞)= 8.07 x 2 x 3.142 x 0.05 x 4 x (170 - 30) = 1419.8 W
Last Modified on: 04-Feb-2022
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