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

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

k= 0.0325 W/m.K

Pr = 0.7

Calculations:

Gr = gbD^{3}(T_{w} - T_{µ} )r^{2} / m^{2}

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

g = m/r

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_{µ} ) = h 2pRL (T_{w} - T_{µ} )

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