Problem 5.5.6

A 12.85-inch pipe carrying steam at 320 degrees Fahrenheit is buried 9 feet below the soil. Calculate the heat loss from 100 feet of pipe length if soil surface is at 50 degrees Fahrenheit. Thermal conductivity of soil could be taken as 0.3 BTU per hour per foot per degree Fahrenheit.

Solution:

Heat loss, Q, from a buried-pipe is given as S time k times (T_s minus T_a), where S is a shape factor. This shape factor is given as 2 time pi time L over cosine hyperbolic inverse of (2 z over D). In this relationship z is the distance from ground surface to the center of the pipe, and D is the outside diameter of the pipe.

Plugging in the values of z (9 feet), D (12.85 inch or 1.07 feet), the argument 2 z over D is 16.809. Cosine hyperbolic inverse of 16.809 can be found as 3.515.

The shape actor, S, is 2 time pi time L (100 feet) over 3.515 is 178.794 feet.

Now using the values of pipe surface temperature, T_s, and soil surface temperature, T_a, heat loss, Q, is found to be 1.448 x 10⁴ BTU per hour.