Estimate the rate of heat loss per unit length from a 5 cm ID, 6 cm OD steel pipe covered with high temperature insulation having a thermal conductivity of 0.11 W/(m K) and a thickness of 1.2 cm. Steam flows in the pipe. It has a quality of 99% and is at 150°C. The unit thermal resistance at the inner wall is 0.0026 (m2 K)/W, the heat transfer coefficient at the outer surface is 17 W/(m2 K), and the ambient temperature is 16°C.

Question

GIVEN

Insulated, steam filled steel pipe Diameters

? ID of pipe (Di) = 5 cm=0.05 m

? OD of pipe (Do) = 6 cm=0.06 m Thickness of insulation (Li) = 1.2 cm=0.012 m Steam quality = 99% Steam temperature (Ts) = 150°C Unit thermal resistance at inner wall (A Ri) = 0.026 (m2 K)/W Heat transfer coefficient at outer wall (ho) = 17 W /(m2 K) Ambient temperature (T ) = 16°C Thermal conductivity of the insulation (kI) = 0.11 W /(m K)

FIND

Rate of heat loss per unit length (q/L)

ASSUMPTIONS

1% carbon steel Constant thermal conductivities Steady state conditions

SKETCH

Answer 1

The outer diameter of the insulation (DI) = 6 cm + 2(1.2 cm) = 8.4 cm

The thermal circuit of the insulated pipe is shown below



The values of the individual resistances are





The rate of heat transfer is