An Approximate Three-Dimensional Solution for Melting or Freezing Around a Buried Pipe Beneath a Free Surface

This paper presents a quasi-steady-state approximate solution for small Stefan number for the three-dimensional melting or freezing around a fluid-carrying pipe buried in a semi-infinite phase change medium (PCM). The two-dimensional quasi-steady approximate solution method, the virtual free surface technique [18], has been extended to three dimensions where axial thermal interaction between the moving fluid and the PCM is considered. Of particular interest in the motion of the phase change interface and the time variation of the axial temperature distribution in the fluid. Due to the singularities of the differential equations along the pipe surface, an axisymmetric analytic solution is provided for the region near the pipe wall. Solutions are presented for several representative dimensionless pipe burial depths and initial conditions. The computational time to predict the three-dimensional interface location up to 10 years is several minutes on an IBM 4341 computer.