Heat Transfer Models for a Subsurface, Water Pipe, Soil‐Warming System

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Abstract
Mathematical models are developed for the prediction of heat losses from subsurface pipes carrying hot water. The method of images is used to calculate the heat loss from a hot water pipe buried at a given depth below the surface of a homogeneous soil with a constant soil surface temperature. The heat loss is described as a function of the difference between the temperature of the water and the temperature of the soil surface. The energy balance is used to determine the longitudinal temperature distribution of the water. The method is extended to describe the heat loss and the longitudinal temperature distribution for a system of equally spaced, parallel, subsurface pipes with water flowing in the same direction in neighboring pipes. Finally, the method is extended to calculate the heat loss and the longitudinal temperature distribution for a system of equally spaced, parallel, subsurface pipes with water flowing in opposite directions in neighboring pipes. Soil temperature profiles around the buried pipes are presented. The models are used to calculate the land area which can be heated with an underground piping system carrying the cooling water from the condensers of a 1000‐megawatt nuclear‐powered steam generation electric power plant.

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