A 30-cm-OD pipe with a surface temperature of 90°C carries steam over a distance of 100 m. The pipe is buried with its center line at a depth of 1 m, the ground surface is –6°C, and the mean thermal conductivity of the soil is 0.7 W/(m K). Calculate the heat loss per day, and the cost of this loss if steam heat is worth $3.00 per 106 kJ. Also, estimate the thickness of 85% magnesia insulation necessary to achieve the same insulation as provided by the soil with a total heat transfer coefficient of 23 W/(m2 K) on the outside of the pipe.

Question

GIVEN



FIND

(a) The heat loss per 24 hour day

(b) The value of the lost heat

(c) The thickness of 85% magnesia insulation necessary to achieve the same insulation

ASSUMPTIONS

Steady state conditions

Uniform thermal conductivity

Two dimensional heat transfer from the pipe

SKETCH

Answer 1

(a) The shape factor for this problem, is



Note that the condition Z/L << 1 is satisfied in this problem.



the rate of heat transfer is



(b) The cost of this heat loss is



(c) The thermal circuit for the pipe covered with insulation is



The rate of heat loss from the pipe is



COMMENTS

The value of the heat loss per year is 365 x $4.23 = $1544. Hence insulation will pay for itself quite rapidly.