Models for Heat Transfer from a Buried Pipe

Analytical solutions are presented for the temperature distribution along a buried pipe. Two different geometries are used to model the surrounding material, and isothermal and convective boundary conditions at the pipe wall are considered. Firstly an 'effective cylinder' model in which the burial medium is modelled as a homogeneous annular layer around the pipe is considered and secondly a 'half-space' model in which the pipe is modelled as a cylinder in an infinite half-space is used. The effective cylinder configuration is of importance because it is often used in more complex computational heat transfer models. In both models coupled differential equations representing conservation of energy in the pipe and its surroundings are solved. By comparing the solution for the effective cylinder model to that for the physically more realistic half-space model, the most suitable radius of the annular layer of material in the effective cylinder model can be calculated. For a deeply buried pipe the effective cylinder radius tends to twice the burial depth of the pipe. This work also gives a calculation of the effective conductivity of the burial medium when two different materials are used, such as is the case when a pipe is placed in a trench and covered in backfill material.