Heat Loss by Convection to Air

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
b =1/373 K-1; g = 23.13 x 10 -6 m2 /sec
k= 0.0325 W/m.K
Pr = 0.7
Calculations:

Gr = gbD3(Tw - T )r2 / m2

Where b = 1/Tf ; Tf = 0.5 (Tw + T ) = 0.5 x (170 + 30) = 100oC = 373 K

g = m/r

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 2pRL (Tw - T )

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