Solve the below problem:
Q: Estimate the rate of heat loss per unit length from a 2 in. ID, 23/8 in. OD steel pipe covered with high temperature insulation having a thermal conductivity of 0.065 Btu/(h ft) and a thickness of 0.5 in. Steam flows in the pipe. It has a quality of 99% and is at 300°F. The unit thermal resistance at the inner wall is 0.015 (h ft2 °F)/Btu, the heat transfer coefficient at the outer surface is 3.0 Btu/(h ft2 °F), and the ambient temperature is 60°F.
GIVEN
Insulated, steam filled steel pipe
Diameters
ID of pipe (Di) = 2 in.
OD of pipe (Do) = 2.375 in.
Thickness of insulation (Li) = 0.5 in.
Steam quality = 99%
Steam temperature (Ts) = 330°F
Unit thermal resistance at inner wall (A Ri) = 0.015 (h ft2 °F)/Btu
Heat transfer coefficient at outer wall (ho) = 3.0 Btu /(h ft2 °F)
Ambient temperature (TA) = 60°F
Thermal conductivity of the insulation (kI) = 0.065 Btu /(h ft °F)
ASSUMPTIONS
1% carbon steel
Constant thermal conductivities
Steady stateconditions
