A5-cm-external-diameter, 10-m-long hot-water pipe at 80°c loses heat to the surrounding air at 16°c by natural convection with a heat transfer coefficient of 25 w/m2·k. determine the rate of heat loss from the pipe by natural convection.

Refer to the diagram shown below.

Neglect the area at the ends of the pipe because 5 cm << 10 m.
The diameter of the pipe is
d = 5 cm = 0.05 m
The difference in temperature between the surface temperature and ambient temperature is
ΔT = 80 - 16 = 64 °C = 64 K
The convective heat transfer coefficient is
h = 25 W/(m²-K)

Calculate the surface area of the pipe.
A = π*(0.25 m)*(10 m) = 2.5π m²

The convective heat loss from the pipe surface is

That is,
Q = 12.566 x 10³ W = 12.566 kW

12.6 kW (nearest tenth)