Question

A 100 ft length of buried, uninsulated steel pipe carries chilled water at a mean temperature of 42 F. The pipe is 30 in. deep and has a 4 in. diameter. The thermal conductivity of the earth is about 8 Btu-in./(hr-ft2-F). Assume the temperature of the ground near the surface is 70 F and estimate the heat transfer rate from the water

Answer 1

Step-by-step explanation:

Conduction of heat through a thick layer is governed by the following relation

Q = KA( T₂ -T₁ ) / d

K is thermal conductivity of medium ( it is earth here ) , A is surface area though which heat conducts and T₂ -T₁ is temperature difference and d is thickness of medium through which heat conducts.

k = 8 units

A = surface area= 2πrL

= 2x 3.14 x 2/12 x 100

= 104.67 ft²

T₂ -T₁ = 70 - 42

= 28 F

d = thickness

= 30 /12 ft

= 2.5 ft

Putting the given values here

Q =
`(8*104.67*28)/(2.5)`

= 9378.4 Btu per hour.