Question

A horizontal pipe 15 cm in diameter and 4 m long is buried in the earth at a depth of 20 cm. The pipe-wall temperature is 75 degree C and the earth surface temperature is 5 degree C. Assuming that the thermal conductivity of the earth is 0.8W/m. degree C. Calculate the heat lost by the pipe. What is the heat lost if the pipe was buried at a depth of 180 cm?

Answer 1

Explanation:

The given data for case (1) is as follows.

  h = 20 cm = 0.2 m

Assuming that a rectangular slab is placed above the pipe and we will calculate the heat transfer as follows.

              Q = $kA \frac{\Delta T}{L}$

  where,    A = area

                  L = length

                  k = thermal conductivity = 0.8 W/m

             $\Delta T$ = change in temperature.

Therefore, putting the given values into the above formula as follows.

            Q = $kA \frac{\Delta T}{L}$

                = $0.8 W/m \times (4 m \times 0.15 m) \frac{75 - 5}{0.2}$

                = 168 W

For case (2), h = 180 cm = 1.8 m

Therefore, heat lost will be calculated as follows.

                       Q = $kA \frac{\Delta T}{L}$

                           = $0.8 W/m \times (4 m \times 0.15 m) \frac{75 - 5}{1.8}$

                           = 18.67 W

Thus, we can conclude that 18.67 W heat lost if the pipe was buried at a depth of 180 cm.