Chapter 5, Problem 5.100P

Ground source heat pumps operate by using the soil, rather than ambient air, as the heat source (or sink) for heating (or cooling) a building. A liquid transfers energy from (to) the soil by way of buried plastic tubing. The tubing is at a depth for which annual variations in the temperature of the soil are much less than those of the ambient air. For example, at a location such as South Bend, Indiana, deep-ground temperatures may remain at approximately $11°\text{C,}$ while annual excursions in the ambient air temperature may range from $-25°\text{C}$ to $+37°\text{C}\text{.}$ Consider the tubing to be laid out in a closely spaced serpentine arrangement.

To what depth should the tubing be buried so that the soil can be viewed as an infinite medium at constant temperature over a 12-month period? Account for the periodic cooling (heating) of the soil due to both annual changes in ambient conditions and variations in heat pump operation from the winter heating to the summer cooling mode.