Approximate analytical solutions are presented for the steady-state heat transfer from fully buried and partially buried pipelines. Although other analytical solutions exist, they suffer from limitations in the coverage of the range of burial depths and use of unphysical boundary conditions. Naturally this leads to inaccurate results, particularly, for shallow burial depths. Furthermore, heat transfer from partially buried pipes has received surprisingly little attention. Although accurate numerical solutions exist, they can be difficult to implement and time-consuming to execute.

All the limitations described above have been eliminated by the approach taken in the current study. The governing diffusion equation in this complicated geometry was solved elegantly by transformation to the bipolar cylindrical coordinate system. Convective boundary conditions connecting the pipe and ground to the fluid and ambient temperatures, respectively, were considered. Results include temperature fields and shape factors for the fully and partially buried configurations. The shape factors obtained were found to be continuous across the entire range of burial depths. Furthermore, asymptotic limits of these equations were examined to obtain expressions for when the pipe is touching the ground surface and the expressions were found to coincide.

Good success is indicated as the fully buried shape factor was found to agree with numerical results to within 2.5%. Scarcity of numerical data for partially buried pipes did not allow an analogous comparison to be done. However, it has been argued that the error in the two shape factors is the same. Consequently, the formulae given are the most accurate analytical solutions currently available. Moreover, they are computationally easier to implement and far less intensive to execute than rigorous numerical solutions, losing little accuracy.

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