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Heat Loss by Convection to Air

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Determine the rate of heat loss from a 100 mm diameter steam pipe placed horizontally in ambient air at 30^{o}C. The length of the pipe is 4 m and wall temperature, T_{w} = 170^{o}C.

Use the following empirical expression:

Nu=0.53 (Gr x Pr)^{1/4}

Properties of air at 100^{o}C are as following

β =1/373 K^{-1}; ν = 23.13 x 10 ^{-6 }m^{2 }/sec

k= 0.0325 W/m.K

Pr = 0.7

Calculations:

Gr = gβD^{3}(T_{w} - T_{∞})ρ^{2}/μ^{2}

Where β = 1/T_{f} ; T_{f} = 0.5 (T_{w} + T_{∞}) = 0.5 x (170 + 30) = 100^{o}C = 373 K

ν= μ/ρ

Substituting for the values,

Gr = 9.812 x (1/373) x 0.1^{3} x (170 - 30) / (23.13 x 10^{-6})^{2} = 6.884 x 10^{6}

Nu = 0.53 x (6.884 x 10^{6 }x 0.7)^{1/4} = 24.832

Nu = hD/k = 24.832

h = 24.832 x 0.0325 / 0.1 = 8.07 W/m^{2}.^{o}C

Rate of heat loss Q = hA(T_{w} - T_{∞}) = h 2πRL (T_{w} - T_{∞) }

= 8.07 x 2 x 3.142 x 0.05 x 4 x (170 - 30) = 1419.8 W

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Last Modified on: 04-Feb-2022

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